ClusteringTextAnalysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Why to Read this Tutorial?\n",
    "* In this tutorial, you will learn about _clustering_ (or cluster analysis). Clustering means to group a set of elements that have similar properties. In other words, clustering forms groups of elements that are more similar to each other than to all elements in the other groups. These groups are typically called _clusters_. This tutorial will introduce and illustrate the very basics of clustering.\n",
    "* The clustering algorithm used is called $k$-means and is used to discover $k$ clusters in your data while you are free to choose $k$.\n",
    "* Furthermore, an algorithm for topic detection within a text corpus will be presented.\n",
    "* You might want to read [NaiveBayes.ipynb](NaiveBayes.ipynb) first as it introduces some vector space model-related concepts that will be used in this tutorial.\n",
    "* At the end of this tutorial, you will be able to cluster arbitrary input data (although the tutorial will use text). Additionally, you will be able to detect topics within a text corpus.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Preparation\n",
    "\n",
    "The following code snippet initializes your Python run-time enviroment in order to run all of the subsequent actions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# The %... is an iPython thing, and is not part of the Python language.\n",
    "# In this case we're just telling the plotting library to draw things on\n",
    "# the notebook, instead of on a separate window.\n",
    "%matplotlib inline\n",
    "# See all the \"as ...\" contructs? They're just aliasing the package names.\n",
    "# That way we can call methods like plt.plot() instead of matplotlib.pyplot.plot().\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "pd.set_option('display.width', 500)\n",
    "pd.set_option('display.max_columns', 100)\n",
    "pd.set_option('display.notebook_repr_html', True)\n",
    "\n",
    "import seaborn as sns\n",
    "import sklearn\n",
    "from time import time\n",
    "#import nltk\n",
    "import seaborn as sns\n",
    "sns.set_style(\"whitegrid\")\n",
    "sns.set_context(\"poster\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, we start with reading our data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>critic</th>\n",
       "      <th>fresh</th>\n",
       "      <th>imdb</th>\n",
       "      <th>publication</th>\n",
       "      <th>quote</th>\n",
       "      <th>review_date</th>\n",
       "      <th>rtid</th>\n",
       "      <th>title</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Owen Gleiberman</td>\n",
       "      <td>fresh</td>\n",
       "      <td>114709</td>\n",
       "      <td>Entertainment Weekly</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2011-09-07</td>\n",
       "      <td>9559</td>\n",
       "      <td>Toy story</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Derek Adams</td>\n",
       "      <td>fresh</td>\n",
       "      <td>114709</td>\n",
       "      <td>Time Out</td>\n",
       "      <td>So ingenious in concept, design and execution ...</td>\n",
       "      <td>2009-10-04</td>\n",
       "      <td>9559</td>\n",
       "      <td>Toy story</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Richard Corliss</td>\n",
       "      <td>fresh</td>\n",
       "      <td>114709</td>\n",
       "      <td>TIME Magazine</td>\n",
       "      <td>The year's most inventive comedy.</td>\n",
       "      <td>2008-08-31</td>\n",
       "      <td>9559</td>\n",
       "      <td>Toy story</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>David Ansen</td>\n",
       "      <td>fresh</td>\n",
       "      <td>114709</td>\n",
       "      <td>Newsweek</td>\n",
       "      <td>A winning animated feature that has something ...</td>\n",
       "      <td>2008-08-18</td>\n",
       "      <td>9559</td>\n",
       "      <td>Toy story</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Leonard Klady</td>\n",
       "      <td>fresh</td>\n",
       "      <td>114709</td>\n",
       "      <td>Variety</td>\n",
       "      <td>The film sports a provocative and appealing st...</td>\n",
       "      <td>2008-06-09</td>\n",
       "      <td>9559</td>\n",
       "      <td>Toy story</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            critic  fresh    imdb           publication                                              quote review_date  rtid      title\n",
       "0  Owen Gleiberman  fresh  114709  Entertainment Weekly                                                NaN  2011-09-07  9559  Toy story\n",
       "1      Derek Adams  fresh  114709              Time Out  So ingenious in concept, design and execution ...  2009-10-04  9559  Toy story\n",
       "2  Richard Corliss  fresh  114709         TIME Magazine                  The year's most inventive comedy.  2008-08-31  9559  Toy story\n",
       "3      David Ansen  fresh  114709              Newsweek  A winning animated feature that has something ...  2008-08-18  9559  Toy story\n",
       "4    Leonard Klady  fresh  114709               Variety  The film sports a provocative and appealing st...  2008-06-09  9559  Toy story"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# reads the CSV using the pandas Python package, this creates a variable called \"df\" that will store the\n",
    "# CSV contents in form of a table, the so-called data frame\n",
    "df=pd.read_csv(\"./critics.csv\")\n",
    "# let's drop rows with missing publication, store the results in a variable called \"df2\"\n",
    "df2=df[df.publication.notnull()]\n",
    "# ... and display the first 5 rows of the table, the argument within the paratheses tells you how many rows will be read\n",
    "df2.head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The [_data frame_](http://pandas.pydata.org/pandas-docs/stable/generated/pandas.DataFrame.html) is one of the central objects you will be working with. For instance, it features the _head()_ method for inspecting the first rows of the data frame or the _shape_ attribute which shows you its actual dimensions.\n",
    "\n",
    "Amongst others, data frames can also be sorted using the _sort()_ method. However, sorting should only be carried out when it is really needed as it may take a long time. A general rule of thumb is that you should sort your data frame in the last possible moment, e.g., directly before you display its contents."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rows: 27631\n",
      "Columns: 8\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>critic</th>\n",
       "      <th>fresh</th>\n",
       "      <th>imdb</th>\n",
       "      <th>publication</th>\n",
       "      <th>quote</th>\n",
       "      <th>review_date</th>\n",
       "      <th>rtid</th>\n",
       "      <th>title</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>26745</th>\n",
       "      <td>Derek Adams</td>\n",
       "      <td>none</td>\n",
       "      <td>11652</td>\n",
       "      <td>Time Out</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2006-06-24</td>\n",
       "      <td>575684525</td>\n",
       "      <td>The Saphead</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26746</th>\n",
       "      <td>NaN</td>\n",
       "      <td>none</td>\n",
       "      <td>11652</td>\n",
       "      <td>New York Times</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2006-03-25</td>\n",
       "      <td>575684525</td>\n",
       "      <td>The Saphead</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21470</th>\n",
       "      <td>NaN</td>\n",
       "      <td>none</td>\n",
       "      <td>13140</td>\n",
       "      <td>Variety</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2008-10-16</td>\n",
       "      <td>22731</td>\n",
       "      <td>Foolish Wives</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21471</th>\n",
       "      <td>NaN</td>\n",
       "      <td>none</td>\n",
       "      <td>13140</td>\n",
       "      <td>New York Times</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2006-03-25</td>\n",
       "      <td>22731</td>\n",
       "      <td>Foolish Wives</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21472</th>\n",
       "      <td>NaN</td>\n",
       "      <td>none</td>\n",
       "      <td>13140</td>\n",
       "      <td>Time Out</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2006-01-26</td>\n",
       "      <td>22731</td>\n",
       "      <td>Foolish Wives</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            critic fresh   imdb     publication quote review_date       rtid          title\n",
       "26745  Derek Adams  none  11652        Time Out   NaN  2006-06-24  575684525    The Saphead\n",
       "26746          NaN  none  11652  New York Times   NaN  2006-03-25  575684525    The Saphead\n",
       "21470          NaN  none  13140         Variety   NaN  2008-10-16      22731  Foolish Wives\n",
       "21471          NaN  none  13140  New York Times   NaN  2006-03-25      22731  Foolish Wives\n",
       "21472          NaN  none  13140        Time Out   NaN  2006-01-26      22731  Foolish Wives"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# display the data frame's dimensions: 27631 rows and 8 columns\n",
    "dimensions=df2.shape\n",
    "print \"Rows: \"+str(dimensions[0]) \n",
    "# Python does not allow you to concatenate strings and integers directly hence the str() that casts any object into a string\n",
    "print \"Columns: \"+str(dimensions[1]) \n",
    "\n",
    "df2=df2.sort(['imdb'])\n",
    "df2.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Analysing Texts and Representing them in the Vector Space Model\n",
    "\n",
    "Typically, text is represented in the vector space model (VSM) that has been introduced [in another tutorial](NaiveBayes.ipynb). In this tutorial, we will use the [_TfidfVectorizer_](http://scikit-learn.org/stable/modules/generated/sklearn.feature_extraction.text.TfidfVectorizer.html) instead of the [_CountVectorizer_](http://scikit-learn.org/stable/modules/generated/sklearn.feature_extraction.text.CountVectorizer.html) used before to represent our documents in the VSM.\n",
    "\n",
    "Furthermore, we make use of a technique called [_stop word elimination_](https://en.wikipedia.org/wiki/Stop_words).\n",
    "Roughly speaking, stop words are filtered out from texts in a natural language before further processing because they do not contribute much to the semantics of a certain text.\n",
    "Typically, stop words are the most commonly used terms in the natural language, i.e., they differ per language.\n",
    "As stop word elimination limits the number of index terms, it can increase performance of retrieval but at the same time it may also have specific downsides depending on the retrieval scenario. For instance, imagine a music retrieval system. If you remove the term \"the\" from the index terms, you will no longer be able to search for compound terms such as \"The Cure\" or the like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#http://scikit-learn.org/dev/modules/feature_extraction.html#text-feature-extraction\n",
    "#http://scikit-learn.org/dev/modules/classes.html#text-feature-extraction-ref\n",
    "from sklearn.feature_extraction.text import TfidfVectorizer\n",
    "tfidfvectorizer = TfidfVectorizer(min_df=1, stop_words='english')\n",
    "# we will now drop all lines without a quote (if there are any)\n",
    "df2=df2[df2.quote.notnull()]\n",
    "#df2.head()\n",
    "corpus=df2.quote\n",
    "Xtfidf=tfidfvectorizer.fit_transform(corpus)\n",
    "wordstfidf=tfidfvectorizer.get_feature_names()\n",
    "tfidfvectorizer = TfidfVectorizer(min_df=2, max_df=0.5, max_features=50000, stop_words='english')\n",
    "Xtfidf=tfidfvectorizer.fit_transform(corpus)\n",
    "#wordstfidf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cluster Analysis\n",
    "\n",
    "Representing documents in the VSM is the first towards the utilization of methods from machine learning (ML). As a result from running the cells above, we yield VSM representations from the input documents. In other words, we obtain a lot of different vectors embedded into a vector space.\n",
    "The representation of data as vectors is especially handy if you want to apply methods from ML because ML assumes quite often that you work within a vector space. For instance, you can easily compute how distant two vectors are using the Euclidean distance (or other [distance measures](https://en.wikipedia.org/wiki/Distance)) within a vector space:\n",
    "\n",
    "$$ \\delta_{Euclid}(q,p)=\\sqrt{\\sum_{i=1}^n (q_i-p_i)^2},$$\n",
    "\n",
    "where $q$ and $p$ are the vectors whose distance you are interested in. The index $i$ indicates each component of the vectors. Calculating the distance between two vectors can be helpful to determine how similar two documents are.\n",
    "\n",
    "The utility of the vector space representation becomes most obvious with the help of an example and some test data that we will create next. To facilitate understanding, we will work in a two-dimensional vector space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>obs01</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>obs02</th>\n",
       "      <td>10</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>obs03</th>\n",
       "      <td>60</td>\n",
       "      <td>40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>obs04</th>\n",
       "      <td>100</td>\n",
       "      <td>80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>obs05</th>\n",
       "      <td>99</td>\n",
       "      <td>81</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>obs06</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>obs07</th>\n",
       "      <td>45</td>\n",
       "      <td>55</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>obs08</th>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>obs09</th>\n",
       "      <td>11</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>obs10</th>\n",
       "      <td>1</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         0   1\n",
       "obs01    1   2\n",
       "obs02   10  10\n",
       "obs03   60  40\n",
       "obs04  100  80\n",
       "obs05   99  81\n",
       "obs06    1   1\n",
       "obs07   45  55\n",
       "obs08    9  10\n",
       "obs09   11  11\n",
       "obs10    1  11"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create sample data\n",
    "d = {'obs01': (1,2), 'obs02': (10,10),'obs03':(60,40),'obs04':(100,80),'obs05':(99,81),'obs06':(1,1),'obs07':(45,55),'obs08':(9,10),'obs09':(11,11),'obs10':(1,11)}\n",
    "# create a data frame from our sample data\n",
    "sampleDF=pd.DataFrame(data=d)\n",
    "# transpose the data frame for later use\n",
    "sampleDF=sampleDF.transpose()\n",
    "sampleDF.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The sample data contains 10 observations, one per row, and an $x$ and $y$ coordinate found in columns $0$ and $1$. This data can be easily plotted to visualize its distribution. In this example, we use a scatter plot that is also offered by the _DataFrame_ object of _pandas_, the Python data analysis library. Other kinds of plots can be found in the [documentation](http://pandas.pydata.org/pandas-docs/stable/generated/pandas.DataFrame.plot.html) of the _plot()_ method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x10e66db90>"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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AEeICAAAoQlwAAABFiAsAAKAIcQEAABQhLgAAgCLEBQAAUIS4AAAAitin4+JX\nv/pVPvnJT2bYsGE58cQTM23atDzzzDPtHvPLX/4yZ555ZgYPHpyxY8fm9ttvr9O0+5dvf/vbGTNm\nTAYNGpSPf/zjWbFiRb1H2u9s3749N998c04++eQMGTIkp556ar71rW+1e0xzc3NGjhyZwYMHZ9Kk\nSXn88cfrNO3+afPmzTn55JPz+c9/vt1xe6mPpUuX5swzz8ygQYMyevTozJ07N9u3b287by8dr6qq\n3HLLLRk7dmyGDBmSj33sY1m2bFm7x9hLx/nxj3+coUOH7nT8H+1g8+bNueqqq/KBD3wgQ4cOzWc/\n+9k8/fTTHTX2Pm9Xe/nb3/6Wr33ta/mnf/qnDBkyJOPGjcvdd9/d7jGveS/VPuqxxx6rjjnmmOpf\n//Vfq5/97GfV97///epDH/pQ9ZGPfKTasmVL22MGDRpUTZkypVqyZEl11VVXVUcccUR177331nn6\nfdt3v/vdauDAgdX1119fPfDAA9XkyZOroUOHVqtXr673aPuV6667rjrmmGOqefPmVUuXLq3mzp1b\nvec976nmz59fVVVVzZ07tzr22GOr2267rfrxj39cjR8/vjrxxBOr9evX13ny/ce1115bHXHEEdVl\nl13Wdsxe6uOXv/xlddRRR1WXXXZZtWzZsuqmm26qjjnmmGru3LlVVdlLvdx8883Ve97znuqGG26o\nHnzwwWrKlCnVUUcdVf3ud7+rqspeOtJDDz1UDRkypBoyZEi7469kB5dddll13HHHVXfccUd17733\nVmPGjKk+8pGPVNu2bevoT2Ofs7u9TJs2rXrf+95XffOb36wefPDBaubMmdURRxxR3X333W2Pea17\n2WfjYsaMGdWHPvShauvWrW3Hfv3rX1dHHHFE9cADD1RVVVWXXnpp9eEPf7jd+11yySXVaaed1qGz\n7k+2b99ejRo1qpoxY0bbsS1btlQf/OAHq5kzZ9Zxsv3L1q1bq6FDh1Zz5sxpd/yKK66oRowYUW3Y\nsKEaPHhwW2hUVVWtW7euGjp0aHXzzTd38LT7p9/+9rfV4MGDq+HDh7fFxfr16+2lTj7xiU9Un/nM\nZ9odmzVrVvXJT37S90sdffjDH66mTZvW9va2bduqkSNHVldeeaXvlw7ywgsvVDfeeGN19NFHV8cd\nd1y7f8S+kh08+eST1cCBA9v9o3bVqlXVkUceWf3whz/ssM9jX/Nye/nrX/9aHXHEEdXixYvbvc/5\n559fjR9apvt2AAALSUlEQVQ/vqqqPdvLPvuyqHe/+90599xz07lz57Zjhx56aJJkzZo1SZIHH3ww\nI0eObPd+H/zgB/P73/8+f/nLXzps1v3Jk08+mT/96U8ZPXp027EuXbpk5MiRWbJkSR0n27+0trZm\n3LhxGTNmTLvjAwYMyLPPPptly5Zl06ZN7fZUq9UybNgwe+oAW7duzRe+8IVMnjw5vXv3bjv+yCOP\n2EsdPPvss3n44Ydz1llntTs+derU3HrrrVmxYoW91MmGDRvSo0ePtrc7deqUnj17Zt26db5fOsjP\nfvazzJ8/P9OmTcuECRNSVVXbuVeygx0vYxs1alTbY/r37593vetd9rQHXm4vGzduzCc+8Yl84AMf\naPc+AwYMaPs38p7sZZ+Ni7PPPjtnn312u2P3339/kuSwww7Lxo0b85e//CX9+vVr95i+ffsmSVat\nWtUhc+5vdnxd+/fv3+54nz59snr16nb/52fvqdVq+dKXvpQjjzyy3fGf/OQnOfjgg7N27dok2en7\no0+fPnniiSc6bM791fz587Nt27acf/757b4ndnz/2EvHevTRR1NVVd7whjfkggsuyLHHHpvjjz8+\n119/faqqspc6Ov300/O9730vS5cuzfr167No0aI89thjOfXUU+2lgxxzzDG5//77M2HChJ3OvZId\nPPHEEznooIPyhje8od1j+vbta0974OX20rdv31x++eXtnrzatm1bfvazn+Wd73xnkj3bS5cC83e4\nrVu35sknn9zt+YMOOii1Wq3dsT//+c+55pprcswxx2T48OFtN6S89BmPl769YcOGwlOT/N/XdVdf\n9+3bt2fjxo07naNjfOc738nSpUszffr0bNiwIV27dk2XLu3/iujRo0daW1vrNOH+4Y9//GNuuOGG\nLFq0KAcccEC7c/ZSH88991ySZNq0aTnttNMyadKkLF++PM3NzenWrVu2b99uL3Xy2c9+No8++mjO\nPffctmMXXXRRRo0alRtuuMFeOsBL/4H6917J31mtra3p3r37Tu/bvXv3tie6ePVebi+7ct111+WJ\nJ57ItGnTkuzZXl6XcbF27dqceuqpuz3/hS98IZ/61Kfa3v7zn/+ciRMnJklmz56dJG3PBjY1Ne3y\nY3TqtM9e1KkrX/fGdNddd+Xyyy/PSSedlHPOOSfz5s3b7Y52d5w9t3379nzxi1/M+PHjM2jQoCTt\nv95VVdlLHWzZsiVJcuKJJ+aSSy5Jkhx33HF57rnn0tzcnPPPP99e6uSSSy7Jww8/nBkzZuSd73xn\nfvGLX2Tu3Lnp2bOn75cG8HI72PHf+1fyGPauG2+8MTfccEMmTZrUdrvAnuzldRkXffr0yf/8z/+8\nosf+/ve/z3nnnZdt27Zl4cKFbS976tmzZ5Ls9OzFjrd3nKesXr16JXnx6/yWt7yl7Xhra2s6d+6c\nAw88sF6j7bduvvnmXHPNNfngBz+YWbNmJXlxT5s3b862bdva3bfU2tq601VByrntttuydu3azJ8/\nP1u3bk3y4l/wVVVl69at9lInO66mnnjiie2OjxgxIt/61rfspU5+85vf5O67786cOXMyduzYJMmw\nYcOybdu2zJo1KxdddJG91NnLfW/s+PdAz549d3kl6aWPYe+oqipf+cpXsmjRopxzzjm59NJL287t\nyV726SR85JFHcs4556RLly75r//6rxx++OFt53r06JGDDjooq1evbvc+O97ecfM3Ze2412JXX3df\n8443e/bs/Od//mfOOOOMXHfddW2Xrvv375+qqtpu7NphzZo19rQX/ehHP8ratWszbNiwHH300Tn6\n6KPz6KOP5s4778zRRx+dAw44wF7qYMfrxXdcwdhhRwDaS33seHn04MGD2x0fOnRoNm3alKamJnup\ns1fy35IBAwbkr3/9azZv3rzbx1De9u3bc+mll2bRokW54IILMn369Hbn92Qv+2xcrF69Ouedd17e\n9ra35b//+793upkoefFZp/vvv7/dL0H60Y9+lMMPP7zds+qUM2DAgBx88MG577772o5t2bIlP/3p\nTzN8+PA6Trb/WbRoUW688cZ8+tOfztVXX93uMueQIUPSrVu3dntat25dli9fnhEjRtRj3P3ClVde\nmdtvv73tf4sXL86AAQMyatSo3H777TnllFPspQ7e/e53p3fv3rnnnnvaHX/ggQfSu3dve6mTHa9E\neOihh9odf+SRR9KlS5eMGTPGXurslfy3ZMSIEdm2bVt+/OMftz1m1apVeeyxx+xpL/rKV76S73//\n+7nsssvyuc99bqfze7KX1+XLol6Jq666Kq2trbn88svz1FNP5amnnmo7d8ghh+Sggw7KpEmTMn78\n+Pz7v/97xo8fnwcffDDf//73c91119Vx8n1bU1NTzjvvvMycOTO1Wi1Dhw7NN7/5zaxbt67tvhj2\nvqeffjqzZs3K4YcfnlNOOWWn35B+zDHHZMKECZkzZ046deqU/v37Z968eanVahk/fnydpt737erZ\noG7duuVNb3pTjjrqqCSxlzpoamrKRRddlMsuuywzZszI2LFj8+CDD+bOO+/MFVdckZ49e9pLHQwa\nNCjHH398rrjiijz//PM57LDDsnz58tx000351Kc+ld69e9tLnfXo0eMf7qBfv3456aST2n6YSK9e\nvTJ79uwceeSR+dCHPlTnz2Df9Nvf/ja33nprTjjhhAwZMqTdvwE6deqUY489do/2sk/GxZYtW7Jk\nyZJs3749U6dO3en8tGnTcu655+bII4/MvHnzMmvWrFx44YV5xzveka985Ss7/ex/yjr77LPzwgsv\n5NZbb82iRYsycODALFiwIH369Kn3aPuNn//859myZUv+8Ic/7PSz+5uamrJ06dJMmTIlnTp1ysKF\nC9Pa2pqhQ4fmmmuucT9SB/v7G+rspT7OOOOMHHDAAZk3b16++93v5uCDD86VV16ZM888M4m91Etz\nc3Oam5uzaNGiPP300+nXr1+mT5/e9veavXSspqam1/R31tVXX52rr746s2bNyvbt23P88cfnS1/6\nkhvvC/n7vfzkJz9J8uLve/vFL37R7rHdu3fPr371qySvfS9NlV8sAAAAFLDP3nMBAAB0LHEBAAAU\nIS4AAIAixAUAAFCEuAAAAIoQFwAAQBHiAgAAKEJcANBhVq1alQsuuCDDhg3L8ccfn5kzZ2bjxo31\nHguAQvwSPQA6xDPPPJNx48ala9euOeecc7Ju3bosXLgw73//+zN//vx6jwdAAV3qPQAA+4eFCxdm\n3bp1ueeee/KOd7wjSXLIIYdk+vTpWbp0aUaMGFHnCQHYU14WBUCHuOeee3LCCSe0hUWSfPSjH033\n7t1zzz331HEyAEoRFwDsdc8//3z+9Kc/5T3veU+74507d87hhx+e3/3ud3WaDICSxAUAe93TTz+d\nJOndu/dO5w466KCsXbu2o0cCYC8QFwDsda2trUmSAw88cKdz3bp18xOjAPYR4gKAve4f/WDCzp07\nd9AkAOxN4gKAva579+5Jkr/97W87nXvhhRfSs2fPjh4JgL1AXACw1x188MFJkr/85S87nXv66afz\ntre9raNHAmAvEBcA7HVvfOMb8453vCMrV65sd3zr1q35/e9/v9NPkQLg9UlcANAhxo4dmwceeCBP\nPfVU27E77rgjmzZtyimnnFLHyQAopan6R3fZAUABzzzzTD784Q+ne/fumThxYp555pksXLgwJ5xw\nQpqbm+s9HgAFiAsAOsxjjz2Wq666Kr/61a9Sq9UyduzYTJkyZZc/ohaA1x9xAQAAFOGeCwAAoAhx\nAQAAFCEuAACAIsQFAABQhLgAAACKEBcAAEAR4gIAAChCXAAAAEWICwAAoAhxAQAAFPH/AaKmSgPS\nA9saAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c555fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the sample data\n",
    "sampleDF.plot(x=0,y=1,kind='scatter',alpha=0.75) # we have to define explicitly which data is used for the x and y axes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data is obviously separated into 3 distant clusters. But imagine a more complex data set with more dimensions than 2 as it is the case with textual data. In this case, it will not be easy to determine the clusters. This motivates the usage of cluster analysis algorithms which you will feed with your data and they will return the clusters present in your data.\n",
    "\n",
    "### The $k$-means Algorithm\n",
    "\n",
    "The [$k$-means algorithm](https://en.wikipedia.org/wiki/K-means_clustering) is a widely used algorithm for cluster analysis. The algorithm tries to partition the observation you have into $k$ different clusters. Please note that you have to define $k$ before running the algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>cluster</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>obs03</th>\n",
       "      <td>60</td>\n",
       "      <td>40</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>obs07</th>\n",
       "      <td>45</td>\n",
       "      <td>55</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>obs01</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>obs02</th>\n",
       "      <td>10</td>\n",
       "      <td>10</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>obs06</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>obs08</th>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>obs09</th>\n",
       "      <td>11</td>\n",
       "      <td>11</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>obs10</th>\n",
       "      <td>1</td>\n",
       "      <td>11</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>obs04</th>\n",
       "      <td>100</td>\n",
       "      <td>80</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>obs05</th>\n",
       "      <td>99</td>\n",
       "      <td>81</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         0   1  cluster\n",
       "obs03   60  40        0\n",
       "obs07   45  55        0\n",
       "obs01    1   2        1\n",
       "obs02   10  10        1\n",
       "obs06    1   1        1\n",
       "obs08    9  10        1\n",
       "obs09   11  11        1\n",
       "obs10    1  11        1\n",
       "obs04  100  80        2\n",
       "obs05   99  81        2"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# import the k-means algorithm\n",
    "from sklearn.cluster import KMeans\n",
    "# define the number of clusters to be found\n",
    "true_k=3\n",
    "# initialize the k-means algorithm\n",
    "km = KMeans(n_clusters=true_k, init='k-means++', max_iter=100, n_init=1)\n",
    "# apply the algorithm on the data\n",
    "km.fit(sampleDF)\n",
    "# add the detected clusters as a new column to the original data frame\n",
    "sampleDF['cluster']=km.labels_\n",
    "sampleDF=sampleDF.sort('cluster')\n",
    "sampleDF.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From inspecting the table, we already see that 3 clusters have been found and how the data is associated with them. Everything worked as expected.\n",
    "We can further inspect the clusters' centroid, i.e., the hypothetical object that lie in the center of the discovered clusters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>52.5</td>\n",
       "      <td>47.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.5</td>\n",
       "      <td>7.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>99.5</td>\n",
       "      <td>80.5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      0     1\n",
       "0  52.5  47.5\n",
       "1   5.5   7.5\n",
       "2  99.5  80.5"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clusterCenters=pd.DataFrame(data=km.cluster_centers_)\n",
    "clusterCenters.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also visualize the centroids (drawn in red) in combination with the scatter plot of the sample data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.patches.Circle at 0x10dc2cd10>"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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AgbaTHBPKBQAAwOE0bmwWz06ebDsJItFvv5ndy+6/33aSY0a5AAAAOJLOnc22n++9ZzsJ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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d2c9fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the sample data and save the plot in the variable \"ax\"\n",
    "ax=sampleDF.plot(x=0,y=1,kind='scatter',alpha=0.75)\n",
    "# plot the centroids in red\n",
    "plt.scatter(x=clusterCenters[0],y=clusterCenters[1],color='red')\n",
    "# next, define the circles' centers surrounding the clusters for a better visualization result\n",
    "cirlePos1=(clusterCenters[0][0],clusterCenters[1][0])\n",
    "cirlePos2=(clusterCenters[0][1],clusterCenters[1][1])\n",
    "cirlePos3=(clusterCenters[0][2],clusterCenters[1][2])\n",
    "# create the unfilled circles with a radius of 20 (this value is arbitrary)\n",
    "circ1=plt.Circle(cirlePos1,20,color='r',fill=False)\n",
    "circ2=plt.Circle(cirlePos2,20,color='r',fill=False)\n",
    "circ3=plt.Circle(cirlePos3,20,color='r',fill=False)\n",
    "# add the circles to your plot\n",
    "ax.add_patch(circ1)\n",
    "ax.add_patch(circ2)\n",
    "ax.add_patch(circ3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Working with Real Data\n",
    "\n",
    "Next, we are using $k$-means with our real data, i.e., the contents of the quotes. What we are trying to find out are the most similar quotes (whatever this means) to each other. A sample use case could be a quote recommendation service that takes a quote and returns all quotes from the same cluster. For educational reasons, we are trying to cluster our data in 10 different clusters.\n",
    "\n",
    "To inspect the results, we will use the [_describe()_](http://pandas.pydata.org/pandas-docs/stable/generated/pandas.DataFrame.describe.html) method of the DataFrame object as it will print some commonly used descriptive statistics of the analysed data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>imdb</th>\n",
       "      <th>rtid</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cluster</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"8\" valign=\"top\">0</th>\n",
       "      <th>count</th>\n",
       "      <td>1678.000000</td>\n",
       "      <td>1.678000e+03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>162540.507151</td>\n",
       "      <td>7.193157e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>173292.544698</td>\n",
       "      <td>2.039235e+08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>13442.000000</td>\n",
       "      <td>1.100000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>97670.750000</td>\n",
       "      <td>1.142500e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>116232.500000</td>\n",
       "      <td>1.351900e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>134789.750000</td>\n",
       "      <td>1.687625e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1186367.000000</td>\n",
       "      <td>7.709273e+08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"8\" valign=\"top\">1</th>\n",
       "      <th>count</th>\n",
       "      <td>305.000000</td>\n",
       "      <td>3.050000e+02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>165855.019672</td>\n",
       "      <td>7.380015e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>170748.051634</td>\n",
       "      <td>1.986861e+08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>13442.000000</td>\n",
       "      <td>2.100000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>79714.000000</td>\n",
       "      <td>1.205200e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>110475.000000</td>\n",
       "      <td>1.369200e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>162661.000000</td>\n",
       "      <td>1.721700e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1190539.000000</td>\n",
       "      <td>7.708023e+08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"8\" valign=\"top\">2</th>\n",
       "      <th>count</th>\n",
       "      <td>7478.000000</td>\n",
       "      <td>7.478000e+03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>155174.212757</td>\n",
       "      <td>5.396261e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>151764.599913</td>\n",
       "      <td>1.789374e+08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>13442.000000</td>\n",
       "      <td>1.100000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>101556.250000</td>\n",
       "      <td>1.129200e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>116999.000000</td>\n",
       "      <td>1.333000e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>139134.000000</td>\n",
       "      <td>1.624800e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1190539.000000</td>\n",
       "      <td>7.708206e+08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"6\" valign=\"top\">3</th>\n",
       "      <th>count</th>\n",
       "      <td>1676.000000</td>\n",
       "      <td>1.676000e+03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>142084.009547</td>\n",
       "      <td>5.539673e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>146807.608842</td>\n",
       "      <td>1.815422e+08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>13442.000000</td>\n",
       "      <td>1.100000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>88157.250000</td>\n",
       "      <td>1.149175e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>112495.000000</td>\n",
       "      <td>1.346650e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"6\" valign=\"top\">6</th>\n",
       "      <th>std</th>\n",
       "      <td>191791.612975</td>\n",
       "      <td>2.016933e+08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>17925.000000</td>\n",
       "      <td>1.100000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>92991.000000</td>\n",
       "      <td>1.124025e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>115681.500000</td>\n",
       "      <td>1.321550e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>144715.000000</td>\n",
       "      <td>1.669925e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1186367.000000</td>\n",
       "      <td>7.707976e+08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"8\" valign=\"top\">7</th>\n",
       "      <th>count</th>\n",
       "      <td>517.000000</td>\n",
       "      <td>5.170000e+02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>156789.764023</td>\n",
       "      <td>5.540864e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>165072.240125</td>\n",
       "      <td>1.797437e+08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>21749.000000</td>\n",
       "      <td>1.200000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>94336.000000</td>\n",
       "      <td>1.151900e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>113305.000000</td>\n",
       "      <td>1.340800e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>126250.000000</td>\n",
       "      <td>1.639400e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1099212.000000</td>\n",
       "      <td>7.708035e+08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"8\" valign=\"top\">8</th>\n",
       "      <th>count</th>\n",
       "      <td>331.000000</td>\n",
       "      <td>3.310000e+02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>152889.643505</td>\n",
       "      <td>7.135588e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>154623.305994</td>\n",
       "      <td>2.058566e+08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>13442.000000</td>\n",
       "      <td>1.100000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>89269.500000</td>\n",
       "      <td>1.117000e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>113189.000000</td>\n",
       "      <td>1.341700e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>133588.500000</td>\n",
       "      <td>1.700250e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1045655.000000</td>\n",
       "      <td>7.710318e+08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"8\" valign=\"top\">9</th>\n",
       "      <th>count</th>\n",
       "      <td>1621.000000</td>\n",
       "      <td>1.621000e+03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>169384.834053</td>\n",
       "      <td>5.565154e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>177994.246487</td>\n",
       "      <td>1.807566e+08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>17136.000000</td>\n",
       "      <td>1.100000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>105156.000000</td>\n",
       "      <td>1.130600e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>116985.000000</td>\n",
       "      <td>1.332200e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>144168.000000</td>\n",
       "      <td>1.630300e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1186367.000000</td>\n",
       "      <td>7.708206e+08</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>80 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                         imdb          rtid\n",
       "cluster                                    \n",
       "0       count     1678.000000  1.678000e+03\n",
       "        mean    162540.507151  7.193157e+07\n",
       "        std     173292.544698  2.039235e+08\n",
       "        min      13442.000000  1.100000e+01\n",
       "        25%      97670.750000  1.142500e+04\n",
       "        50%     116232.500000  1.351900e+04\n",
       "        75%     134789.750000  1.687625e+04\n",
       "        max    1186367.000000  7.709273e+08\n",
       "1       count      305.000000  3.050000e+02\n",
       "        mean    165855.019672  7.380015e+07\n",
       "        std     170748.051634  1.986861e+08\n",
       "        min      13442.000000  2.100000e+01\n",
       "        25%      79714.000000  1.205200e+04\n",
       "        50%     110475.000000  1.369200e+04\n",
       "        75%     162661.000000  1.721700e+04\n",
       "        max    1190539.000000  7.708023e+08\n",
       "2       count     7478.000000  7.478000e+03\n",
       "        mean    155174.212757  5.396261e+07\n",
       "        std     151764.599913  1.789374e+08\n",
       "        min      13442.000000  1.100000e+01\n",
       "        25%     101556.250000  1.129200e+04\n",
       "        50%     116999.000000  1.333000e+04\n",
       "        75%     139134.000000  1.624800e+04\n",
       "        max    1190539.000000  7.708206e+08\n",
       "3       count     1676.000000  1.676000e+03\n",
       "        mean    142084.009547  5.539673e+07\n",
       "        std     146807.608842  1.815422e+08\n",
       "        min      13442.000000  1.100000e+01\n",
       "        25%      88157.250000  1.149175e+04\n",
       "        50%     112495.000000  1.346650e+04\n",
       "...                       ...           ...\n",
       "6       std     191791.612975  2.016933e+08\n",
       "        min      17925.000000  1.100000e+01\n",
       "        25%      92991.000000  1.124025e+04\n",
       "        50%     115681.500000  1.321550e+04\n",
       "        75%     144715.000000  1.669925e+04\n",
       "        max    1186367.000000  7.707976e+08\n",
       "7       count      517.000000  5.170000e+02\n",
       "        mean    156789.764023  5.540864e+07\n",
       "        std     165072.240125  1.797437e+08\n",
       "        min      21749.000000  1.200000e+01\n",
       "        25%      94336.000000  1.151900e+04\n",
       "        50%     113305.000000  1.340800e+04\n",
       "        75%     126250.000000  1.639400e+04\n",
       "        max    1099212.000000  7.708035e+08\n",
       "8       count      331.000000  3.310000e+02\n",
       "        mean    152889.643505  7.135588e+07\n",
       "        std     154623.305994  2.058566e+08\n",
       "        min      13442.000000  1.100000e+01\n",
       "        25%      89269.500000  1.117000e+04\n",
       "        50%     113189.000000  1.341700e+04\n",
       "        75%     133588.500000  1.700250e+04\n",
       "        max    1045655.000000  7.710318e+08\n",
       "9       count     1621.000000  1.621000e+03\n",
       "        mean    169384.834053  5.565154e+07\n",
       "        std     177994.246487  1.807566e+08\n",
       "        min      17136.000000  1.100000e+01\n",
       "        25%     105156.000000  1.130600e+04\n",
       "        50%     116985.000000  1.332200e+04\n",
       "        75%     144168.000000  1.630300e+04\n",
       "        max    1186367.000000  7.708206e+08\n",
       "\n",
       "[80 rows x 2 columns]"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "true_k=10\n",
    "km = KMeans(n_clusters=true_k, init='k-means++', max_iter=100, n_init=1)\n",
    "# fit the k-means algorithm on the data created above\n",
    "km.fit(Xtfidf)\n",
    "# add the detected clusters as a new column to the original data frame\n",
    "df2['cluster']=km.labels_\n",
    "# group the data by the cluster and describe it\n",
    "df2.groupby('cluster').describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can conclude from the _count_ rows above, our clusters are getting fairly large and probably not very meaningful regarding their contents. This is due to the fact that our data frame is large and we want to \"squeeze\" it into 10 clusters or categories. \n",
    "\n",
    "Consider the following example. You have summaries of all books you have read in your life and your task is to summarize all these summaries using only 3 words. Will this yield meaningful results?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(15561, 9)"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# inspect the dimensions of the data frame\n",
    "df2.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hence, we run the $k$-means algorithm again using a cluster amountof 10% regarding the total amount of reviews. Then, we will inspect the outcome as done above. The choice of 10% is rather arbitrary but you can read a lot about choosing $k$ right [here](https://datasciencelab.wordpress.com/2014/01/21/selection-of-k-in-k-means-clustering-reloaded/).\n",
    "\n",
    "Please note that this step might take __several minutes__ depending on your computer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>imdb</th>\n",
       "      <th>rtid</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cluster</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"8\" valign=\"top\">0</th>\n",
       "      <th>count</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>109813.000000</td>\n",
       "      <td>12326.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>109813.000000</td>\n",
       "      <td>12326.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>109813.000000</td>\n",
       "      <td>12326.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>109813.000000</td>\n",
       "      <td>12326.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>109813.000000</td>\n",
       "      <td>12326.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>109813.000000</td>\n",
       "      <td>12326.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"8\" valign=\"top\">1</th>\n",
       "      <th>count</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>65063.000000</td>\n",
       "      <td>16258.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>65063.000000</td>\n",
       "      <td>16258.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>65063.000000</td>\n",
       "      <td>16258.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>65063.000000</td>\n",
       "      <td>16258.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>65063.000000</td>\n",
       "      <td>16258.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>65063.000000</td>\n",
       "      <td>16258.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"8\" valign=\"top\">2</th>\n",
       "      <th>count</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>137338.000000</td>\n",
       "      <td>14561.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>137338.000000</td>\n",
       "      <td>14561.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>137338.000000</td>\n",
       "      <td>14561.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>137338.000000</td>\n",
       "      <td>14561.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>137338.000000</td>\n",
       "      <td>14561.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>137338.000000</td>\n",
       "      <td>14561.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"6\" valign=\"top\">3</th>\n",
       "      <th>count</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>111503.000000</td>\n",
       "      <td>16394.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>111503.000000</td>\n",
       "      <td>16394.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>111503.000000</td>\n",
       "      <td>16394.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>111503.000000</td>\n",
       "      <td>16394.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"6\" valign=\"top\">1496</th>\n",
       "      <th>std</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>93779.000000</td>\n",
       "      <td>12686.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>93779.000000</td>\n",
       "      <td>12686.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>93779.000000</td>\n",
       "      <td>12686.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>93779.000000</td>\n",
       "      <td>12686.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>93779.000000</td>\n",
       "      <td>12686.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"8\" valign=\"top\">1497</th>\n",
       "      <th>count</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>115744.000000</td>\n",
       "      <td>13333.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>115744.000000</td>\n",
       "      <td>13333.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>115744.000000</td>\n",
       "      <td>13333.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>115744.000000</td>\n",
       "      <td>13333.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>115744.000000</td>\n",
       "      <td>13333.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>115744.000000</td>\n",
       "      <td>13333.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"8\" valign=\"top\">1498</th>\n",
       "      <th>count</th>\n",
       "      <td>2.000000</td>\n",
       "      <td>2.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>112663.000000</td>\n",
       "      <td>13480.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>284.256926</td>\n",
       "      <td>3261.176475</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>112462.000000</td>\n",
       "      <td>11174.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>112562.500000</td>\n",
       "      <td>12327.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>112663.000000</td>\n",
       "      <td>13480.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>112763.500000</td>\n",
       "      <td>14633.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>112864.000000</td>\n",
       "      <td>15786.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"8\" valign=\"top\">1499</th>\n",
       "      <th>count</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>117364.000000</td>\n",
       "      <td>12501.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>117364.000000</td>\n",
       "      <td>12501.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>117364.000000</td>\n",
       "      <td>12501.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>117364.000000</td>\n",
       "      <td>12501.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>117364.000000</td>\n",
       "      <td>12501.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>117364.000000</td>\n",
       "      <td>12501.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>12000 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                        imdb          rtid\n",
       "cluster                                   \n",
       "0       count       1.000000      1.000000\n",
       "        mean   109813.000000  12326.000000\n",
       "        std              NaN           NaN\n",
       "        min    109813.000000  12326.000000\n",
       "        25%    109813.000000  12326.000000\n",
       "        50%    109813.000000  12326.000000\n",
       "        75%    109813.000000  12326.000000\n",
       "        max    109813.000000  12326.000000\n",
       "1       count       1.000000      1.000000\n",
       "        mean    65063.000000  16258.000000\n",
       "        std              NaN           NaN\n",
       "        min     65063.000000  16258.000000\n",
       "        25%     65063.000000  16258.000000\n",
       "        50%     65063.000000  16258.000000\n",
       "        75%     65063.000000  16258.000000\n",
       "        max     65063.000000  16258.000000\n",
       "2       count       1.000000      1.000000\n",
       "        mean   137338.000000  14561.000000\n",
       "        std              NaN           NaN\n",
       "        min    137338.000000  14561.000000\n",
       "        25%    137338.000000  14561.000000\n",
       "        50%    137338.000000  14561.000000\n",
       "        75%    137338.000000  14561.000000\n",
       "        max    137338.000000  14561.000000\n",
       "3       count       1.000000      1.000000\n",
       "        mean   111503.000000  16394.000000\n",
       "        std              NaN           NaN\n",
       "        min    111503.000000  16394.000000\n",
       "        25%    111503.000000  16394.000000\n",
       "        50%    111503.000000  16394.000000\n",
       "...                      ...           ...\n",
       "1496    std              NaN           NaN\n",
       "        min     93779.000000  12686.000000\n",
       "        25%     93779.000000  12686.000000\n",
       "        50%     93779.000000  12686.000000\n",
       "        75%     93779.000000  12686.000000\n",
       "        max     93779.000000  12686.000000\n",
       "1497    count       1.000000      1.000000\n",
       "        mean   115744.000000  13333.000000\n",
       "        std              NaN           NaN\n",
       "        min    115744.000000  13333.000000\n",
       "        25%    115744.000000  13333.000000\n",
       "        50%    115744.000000  13333.000000\n",
       "        75%    115744.000000  13333.000000\n",
       "        max    115744.000000  13333.000000\n",
       "1498    count       2.000000      2.000000\n",
       "        mean   112663.000000  13480.000000\n",
       "        std       284.256926   3261.176475\n",
       "        min    112462.000000  11174.000000\n",
       "        25%    112562.500000  12327.000000\n",
       "        50%    112663.000000  13480.000000\n",
       "        75%    112763.500000  14633.000000\n",
       "        max    112864.000000  15786.000000\n",
       "1499    count       1.000000      1.000000\n",
       "        mean   117364.000000  12501.000000\n",
       "        std              NaN           NaN\n",
       "        min    117364.000000  12501.000000\n",
       "        25%    117364.000000  12501.000000\n",
       "        50%    117364.000000  12501.000000\n",
       "        75%    117364.000000  12501.000000\n",
       "        max    117364.000000  12501.000000\n",
       "\n",
       "[12000 rows x 2 columns]"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t0 = time()\n",
    "true_k=1500\n",
    "km = KMeans(n_clusters=true_k, init='k-means++', max_iter=100, n_init=1)\n",
    "km.fit(Xtfidf)\n",
    "learningTime=(time() - t0)\n",
    "df2['cluster']=km.labels_\n",
    "df2.groupby('cluster').describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Learning was done in 129.339s.\n"
     ]
    }
   ],
   "source": [
    "print(\"Learning was done in %0.3fs.\" % learningTime)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we will sort our data frame with respect to the cluster ID and display the first 100 rows. You will see that the quotes in the same cluster are similar to each other with respect to their choice of words. The results are not perfect as $tf*idf$ does not deal with the semantics of terms. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>critic</th>\n",
       "      <th>fresh</th>\n",
       "      <th>imdb</th>\n",
       "      <th>publication</th>\n",
       "      <th>quote</th>\n",
       "      <th>review_date</th>\n",
       "      <th>rtid</th>\n",
       "      <th>title</th>\n",
       "      <th>cluster</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>3732</th>\n",
       "      <td>Lucy Mohl</td>\n",
       "      <td>rotten</td>\n",
       "      <td>109813</td>\n",
       "      <td>Film.com</td>\n",
       "      <td>It's a dull day in Bedrock.</td>\n",
       "      <td>2000-01-01</td>\n",
       "      <td>12326</td>\n",
       "      <td>The Flintstones</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16615</th>\n",
       "      <td>Roger Ebert</td>\n",
       "      <td>rotten</td>\n",
       "      <td>65063</td>\n",
       "      <td>Chicago Sun-Times</td>\n",
       "      <td>Woody Allen's Take the Money and Run has some ...</td>\n",
       "      <td>2004-10-23</td>\n",
       "      <td>16258</td>\n",
       "      <td>Take the Money and Run</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20753</th>\n",
       "      <td>Mary Elizabeth Williams</td>\n",
       "      <td>rotten</td>\n",
       "      <td>137338</td>\n",
       "      <td>Salon.com</td>\n",
       "      <td>Though it has its moments, 200 Cigarettes fail...</td>\n",
       "      <td>2000-01-01</td>\n",
       "      <td>14561</td>\n",
       "      <td>200 Cigarettes</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3990</th>\n",
       "      <td>James Berardinelli</td>\n",
       "      <td>fresh</td>\n",
       "      <td>111503</td>\n",
       "      <td>ReelViews</td>\n",
       "      <td>An old-fashioned, high-tech, fun time at the m...</td>\n",
       "      <td>2000-01-01</td>\n",
       "      <td>16394</td>\n",
       "      <td>True Lies</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18994</th>\n",
       "      <td>Moira MacDonald</td>\n",
       "      <td>rotten</td>\n",
       "      <td>985699</td>\n",
       "      <td>Seattle Times</td>\n",
       "      <td>You just can't quite enter the world of this f...</td>\n",
       "      <td>2008-12-29</td>\n",
       "      <td>770671940</td>\n",
       "      <td>Valkyrie</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1128</th>\n",
       "      <td>Mike Clark</td>\n",
       "      <td>fresh</td>\n",
       "      <td>113247</td>\n",
       "      <td>USA Today</td>\n",
       "      <td>Writer-director Mathieu Kassovitz mines so muc...</td>\n",
       "      <td>2000-01-01</td>\n",
       "      <td>98832611</td>\n",
       "      <td>La haine</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12349</th>\n",
       "      <td>Joe Leydon</td>\n",
       "      <td>rotten</td>\n",
       "      <td>120389</td>\n",
       "      <td>Variety</td>\n",
       "      <td>Like the TV series, the pic features makeup an...</td>\n",
       "      <td>2008-05-14</td>\n",
       "      <td>12077</td>\n",
       "      <td>Turbo: A Power Rangers Movie</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24608</th>\n",
       "      <td>Eric Harrison</td>\n",
       "      <td>fresh</td>\n",
       "      <td>332047</td>\n",
       "      <td>Houston Chronicle</td>\n",
       "      <td>At the movie's core is a question that all cou...</td>\n",
       "      <td>2005-04-08</td>\n",
       "      <td>23</td>\n",
       "      <td>Fever Pitch</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>395</th>\n",
       "      <td>Jeff Millar</td>\n",
       "      <td>fresh</td>\n",
       "      <td>112682</td>\n",
       "      <td>Houston Chronicle</td>\n",
       "      <td>The City of Lost Children is a series of assoc...</td>\n",
       "      <td>2000-01-01</td>\n",
       "      <td>13050</td>\n",
       "      <td>La cité des enfants perdus</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5035</th>\n",
       "      <td>Brian Lowry</td>\n",
       "      <td>fresh</td>\n",
       "      <td>107614</td>\n",
       "      <td>Variety</td>\n",
       "      <td>Although overly sappy in places and probably 2...</td>\n",
       "      <td>2008-07-22</td>\n",
       "      <td>10997</td>\n",
       "      <td>Mrs. Doubtfire</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24522</th>\n",
       "      <td>Ruthe Stein</td>\n",
       "      <td>rotten</td>\n",
       "      <td>119256</td>\n",
       "      <td>San Francisco Chronicle</td>\n",
       "      <td>Noirish thrillers live or die by their plot tw...</td>\n",
       "      <td>2000-01-01</td>\n",
       "      <td>14170</td>\n",
       "      <td>Sydney</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26783</th>\n",
       "      <td>Lou Lumenick</td>\n",
       "      <td>fresh</td>\n",
       "      <td>141399</td>\n",
       "      <td>New York Post</td>\n",
       "      <td>Amusing, light entertainment.</td>\n",
       "      <td>2000-01-01</td>\n",
       "      <td>15866</td>\n",
       "      <td>Isn't She Great</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10252</th>\n",
       "      <td>Keith Uhlich</td>\n",
       "      <td>fresh</td>\n",
       "      <td>81398</td>\n",
       "      <td>Time Out New York</td>\n",
       "      <td>When has a performer as fully and uniquely sac...</td>\n",
       "      <td>2010-11-03</td>\n",
       "      <td>15121</td>\n",
       "      <td>Raging Bull</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17931</th>\n",
       "      <td>Geoff Andrew</td>\n",
       "      <td>fresh</td>\n",
       "      <td>58329</td>\n",
       "      <td>Time Out</td>\n",
       "      <td>It's still thrilling to watch, lush, cool and ...</td>\n",
       "      <td>2006-02-09</td>\n",
       "      <td>10595</td>\n",
       "      <td>Marnie</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17986</th>\n",
       "      <td>NaN</td>\n",
       "      <td>fresh</td>\n",
       "      <td>123324</td>\n",
       "      <td>USA Today</td>\n",
       "      <td>Entertaining and nostalgically moving!</td>\n",
       "      <td>2000-01-01</td>\n",
       "      <td>14374</td>\n",
       "      <td>Why Do Fools Fall in Love</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19415</th>\n",
       "      <td>Owen Gleiberman</td>\n",
       "      <td>fresh</td>\n",
       "      <td>140888</td>\n",
       "      <td>Entertainment Weekly</td>\n",
       "      <td>A richly tender and moving experience.</td>\n",
       "      <td>2000-01-01</td>\n",
       "      <td>14037</td>\n",
       "      <td>Central do Brasil</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11954</th>\n",
       "      <td>Roger Ebert</td>\n",
       "      <td>fresh</td>\n",
       "      <td>116754</td>\n",
       "      <td>Chicago Sun-Times</td>\n",
       "      <td>A thoughtful and moving film about war.</td>\n",
       "      <td>2000-01-01</td>\n",
       "      <td>14448</td>\n",
       "      <td>Kavkazskiy plennik</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4230</th>\n",
       "      <td>Geoff Andrew</td>\n",
       "      <td>fresh</td>\n",
       "      <td>106226</td>\n",
       "      <td>Time Out</td>\n",
       "      <td>Scorsese's most poignantly moving film.</td>\n",
       "      <td>2006-02-09</td>\n",
       "      <td>10537</td>\n",
       "      <td>The Age of Innocence</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16383</th>\n",
       "      <td>Mick LaSalle</td>\n",
       "      <td>rotten</td>\n",
       "      <td>166813</td>\n",
       "      <td>San Francisco Chronicle</td>\n",
       "      <td>A mishmash that is sometimes moving, sometimes...</td>\n",
       "      <td>2002-05-24</td>\n",
       "      <td>9502</td>\n",
       "      <td>Spirit: Stallion of the Cimarron</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>356</th>\n",
       "      <td>Kevin Thomas</td>\n",
       "      <td>fresh</td>\n",
       "      <td>114057</td>\n",
       "      <td>Los Angeles Times</td>\n",
       "      <td>Parker has shown how involving and moving Shak...</td>\n",
       "      <td>2001-02-13</td>\n",
       "      <td>13094</td>\n",
       "      <td>Othello</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11318</th>\n",
       "      <td>A.D. Murphy</td>\n",
       "      <td>fresh</td>\n",
       "      <td>73195</td>\n",
       "      <td>Variety</td>\n",
       "      <td>The fast-moving 124-minute film engenders enor...</td>\n",
       "      <td>2007-06-27</td>\n",
       "      <td>10288</td>\n",
       "      <td>Jaws</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9201</th>\n",
       "      <td>Jonathan Rosenbaum</td>\n",
       "      <td>fresh</td>\n",
       "      <td>56218</td>\n",
       "      <td>Chicago Reader</td>\n",
       "      <td>powerful experience, alternately corrosive wit...</td>\n",
       "      <td>2008-05-07</td>\n",
       "      <td>12484</td>\n",
       "      <td>The Manchurian Candidate</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10360</th>\n",
       "      <td>Vincent Canby</td>\n",
       "      <td>fresh</td>\n",
       "      <td>97441</td>\n",
       "      <td>New York Times</td>\n",
       "      <td>This is a good, moving, complicated film.</td>\n",
       "      <td>2003-05-20</td>\n",
       "      <td>16760</td>\n",
       "      <td>Glory</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16558</th>\n",
       "      <td>Vincent Canby</td>\n",
       "      <td>fresh</td>\n",
       "      <td>81283</td>\n",
       "      <td>New York Times</td>\n",
       "      <td>A moving, intelligent and funny film about dis...</td>\n",
       "      <td>2003-05-20</td>\n",
       "      <td>13029</td>\n",
       "      <td>Ordinary People</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16978</th>\n",
       "      <td>Bosley Crowther</td>\n",
       "      <td>fresh</td>\n",
       "      <td>56193</td>\n",
       "      <td>New York Times</td>\n",
       "      <td>The picture has a rare power, a garbled but of...</td>\n",
       "      <td>2000-01-01</td>\n",
       "      <td>20226</td>\n",
       "      <td>Lolita</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17633</th>\n",
       "      <td>Vincent Canby</td>\n",
       "      <td>rotten</td>\n",
       "      <td>84649</td>\n",
       "      <td>New York Times</td>\n",
       "      <td>The story manages to be sentimental without be...</td>\n",
       "      <td>2004-08-30</td>\n",
       "      <td>9485</td>\n",
       "      <td>The Secret of NIMH</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24916</th>\n",
       "      <td>Jonathan Foreman</td>\n",
       "      <td>fresh</td>\n",
       "      <td>144178</td>\n",
       "      <td>New York Post</td>\n",
       "      <td>Beautifully shot and often moving.</td>\n",
       "      <td>2000-01-01</td>\n",
       "      <td>770684867</td>\n",
       "      <td>Dreaming of Joseph Lees</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3826</th>\n",
       "      <td>Joe Brown</td>\n",
       "      <td>fresh</td>\n",
       "      <td>107426</td>\n",
       "      <td>Washington Post</td>\n",
       "      <td>Though uneven, the film is engagingly moving a...</td>\n",
       "      <td>2000-01-01</td>\n",
       "      <td>10580</td>\n",
       "      <td>Little Buddha</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11524</th>\n",
       "      <td>Kevin Thomas</td>\n",
       "      <td>fresh</td>\n",
       "      <td>117571</td>\n",
       "      <td>Los Angeles Times</td>\n",
       "      <td>A bravura, provocative sendup of horror pictur...</td>\n",
       "      <td>2001-02-14</td>\n",
       "      <td>17135</td>\n",
       "      <td>Scream</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9102</th>\n",
       "      <td>Joseph McBride</td>\n",
       "      <td>fresh</td>\n",
       "      <td>97576</td>\n",
       "      <td>Variety</td>\n",
       "      <td>What was conceived as a child's dream of a Sat...</td>\n",
       "      <td>2008-05-05</td>\n",
       "      <td>23531</td>\n",
       "      <td>Indiana Jones and the Last Crusade</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2237</th>\n",
       "      <td>Mike Clark</td>\n",
       "      <td>rotten</td>\n",
       "      <td>114666</td>\n",
       "      <td>USA Today</td>\n",
       "      <td>One of the sleaziest movies of the year and ce...</td>\n",
       "      <td>2000-01-01</td>\n",
       "      <td>16726</td>\n",
       "      <td>The Tie That Binds</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27398</th>\n",
       "      <td>Kevin Maynard</td>\n",
       "      <td>fresh</td>\n",
       "      <td>185014</td>\n",
       "      <td>Mr. Showbiz</td>\n",
       "      <td>This is certainly the best studio movie of the...</td>\n",
       "      <td>2000-01-01</td>\n",
       "      <td>13257</td>\n",
       "      <td>Wonder Boys</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26300</th>\n",
       "      <td>Roger Ebert</td>\n",
       "      <td>fresh</td>\n",
       "      <td>151568</td>\n",
       "      <td>At the Movies</td>\n",
       "      <td>One of the year's best films.</td>\n",
       "      <td>2000-01-01</td>\n",
       "      <td>13407</td>\n",
       "      <td>Topsy-Turvy</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24235</th>\n",
       "      <td>Roger Ebert</td>\n",
       "      <td>fresh</td>\n",
       "      <td>171804</td>\n",
       "      <td>At the Movies</td>\n",
       "      <td>One of the best films of the year!</td>\n",
       "      <td>2000-01-01</td>\n",
       "      <td>13339</td>\n",
       "      <td>Boys Don't Cry</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1527</th>\n",
       "      <td>Amy Biancolli</td>\n",
       "      <td>fresh</td>\n",
       "      <td>483726</td>\n",
       "      <td>Houston Chronicle</td>\n",
       "      <td>Man of the Year isn't Movie of the Year. It mi...</td>\n",
       "      <td>2006-10-13</td>\n",
       "      <td>314387293</td>\n",
       "      <td>Man of the Year</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1530</th>\n",
       "      <td>Terry Lawson</td>\n",
       "      <td>fresh</td>\n",
       "      <td>483726</td>\n",
       "      <td>Detroit Free Press</td>\n",
       "      <td>No one will mistake Man of the Year for movie ...</td>\n",
       "      <td>2006-10-13</td>\n",
       "      <td>314387293</td>\n",
       "      <td>Man of the Year</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18952</th>\n",
       "      <td>Roger Ebert</td>\n",
       "      <td>fresh</td>\n",
       "      <td>120789</td>\n",
       "      <td>Chicago Sun-Times</td>\n",
       "      <td>One of the year's best and most original films!</td>\n",
       "      <td>2000-01-01</td>\n",
       "      <td>10341</td>\n",
       "      <td>Pleasantville</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22764</th>\n",
       "      <td>Rod Dreher</td>\n",
       "      <td>rotten</td>\n",
       "      <td>132347</td>\n",
       "      <td>New York Post</td>\n",
       "      <td>This year's The Avengers.</td>\n",
       "      <td>2000-01-01</td>\n",
       "      <td>10623</td>\n",
       "      <td>Mystery Men</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8139</th>\n",
       "      <td>Variety Staff</td>\n",
       "      <td>fresh</td>\n",
       "      <td>32976</td>\n",
       "      <td>Variety</td>\n",
       "      <td>One of the finest productional efforts of the ...</td>\n",
       "      <td>2008-02-19</td>\n",
       "      <td>17080</td>\n",
       "      <td>Rebecca</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15501</th>\n",
       "      <td>Mike Clark</td>\n",
       "      <td>fresh</td>\n",
       "      <td>124718</td>\n",
       "      <td>USA Today</td>\n",
       "      <td>The year's first Hollywood movie to burst with...</td>\n",
       "      <td>2000-01-01</td>\n",
       "      <td>13529</td>\n",
       "      <td>He Got Game</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19376</th>\n",
       "      <td>Janet Maslin</td>\n",
       "      <td>fresh</td>\n",
       "      <td>120623</td>\n",
       "      <td>New York Times</td>\n",
       "      <td>The best ant colony movie of the year!</td>\n",
       "      <td>2000-01-01</td>\n",
       "      <td>9749</td>\n",
       "      <td>A Bug's Life</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24872</th>\n",
       "      <td>Michael Wilmington</td>\n",
       "      <td>fresh</td>\n",
       "      <td>166943</td>\n",
       "      <td>Chicago Tribune</td>\n",
       "      <td>One of the year's most heartfelt movies.</td>\n",
       "      <td>2000-01-01</td>\n",
       "      <td>10485</td>\n",
       "      <td>Music of the Heart</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8000</th>\n",
       "      <td>Roger Ebert</td>\n",
       "      <td>fresh</td>\n",
       "      <td>34583</td>\n",
       "      <td>Chicago Sun-Times</td>\n",
       "      <td>Seeing the film over and over again, year afte...</td>\n",
       "      <td>2000-01-01</td>\n",
       "      <td>10056</td>\n",
       "      <td>Casablanca</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15046</th>\n",
       "      <td>Gene Siskel</td>\n",
       "      <td>fresh</td>\n",
       "      <td>119822</td>\n",
       "      <td>Chicago Tribune</td>\n",
       "      <td>One of the year's best.</td>\n",
       "      <td>2000-01-01</td>\n",
       "      <td>12971</td>\n",
       "      <td>As Good as It Gets</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24945</th>\n",
       "      <td>Roger Ebert</td>\n",
       "      <td>fresh</td>\n",
       "      <td>119698</td>\n",
       "      <td>At the Movies</td>\n",
       "      <td>Princess Mononoke is a great achievement and a...</td>\n",
       "      <td>2000-01-01</td>\n",
       "      <td>10144</td>\n",
       "      <td>Mononoke-hime</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9747</th>\n",
       "      <td>Peter Travers</td>\n",
       "      <td>none</td>\n",
       "      <td>103850</td>\n",
       "      <td>Rolling Stone</td>\n",
       "      <td>Tim Robbins inaugurates the fall season with a...</td>\n",
       "      <td>2001-05-12</td>\n",
       "      <td>16319</td>\n",
       "      <td>Bob Roberts</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26361</th>\n",
       "      <td>Lou Lumenick</td>\n",
       "      <td>fresh</td>\n",
       "      <td>125664</td>\n",
       "      <td>New York Post</td>\n",
       "      <td>One of the year's most entertaining movies.</td>\n",
       "      <td>2000-01-01</td>\n",
       "      <td>13765</td>\n",
       "      <td>Man on the Moon</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23791</th>\n",
       "      <td>J. Hoberman</td>\n",
       "      <td>rotten</td>\n",
       "      <td>169547</td>\n",
       "      <td>Village Voice</td>\n",
       "      <td>There's too much dead air around the dialogue ...</td>\n",
       "      <td>2000-01-01</td>\n",
       "      <td>12878</td>\n",
       "      <td>American Beauty</td>\n",
       "      <td>29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9839</th>\n",
       "      <td>Mark Caro</td>\n",
       "      <td>fresh</td>\n",
       "      <td>116209</td>\n",
       "      <td>Chicago Tribune</td>\n",
       "      <td>With its fine acting, sumptuous visuals and le...</td>\n",
       "      <td>2013-02-24</td>\n",
       "      <td>14840</td>\n",
       "      <td>The English Patient</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5312</th>\n",
       "      <td>Jay Carr</td>\n",
       "      <td>fresh</td>\n",
       "      <td>108071</td>\n",
       "      <td>Boston Globe</td>\n",
       "      <td>The result is an instant classic -- rich, dens...</td>\n",
       "      <td>2013-08-01</td>\n",
       "      <td>9432</td>\n",
       "      <td>The Secret Garden</td>\n",
       "      <td>31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18965</th>\n",
       "      <td>Lisa Alspector</td>\n",
       "      <td>fresh</td>\n",
       "      <td>120157</td>\n",
       "      <td>Chicago Reader</td>\n",
       "      <td>This appealing formulaic action adventure (199...</td>\n",
       "      <td>2007-03-07</td>\n",
       "      <td>13402</td>\n",
       "      <td>Soldier</td>\n",
       "      <td>32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5707</th>\n",
       "      <td>Caryn James</td>\n",
       "      <td>fresh</td>\n",
       "      <td>99785</td>\n",
       "      <td>New York Times</td>\n",
       "      <td>[A] surprisingly charming film, which may be t...</td>\n",
       "      <td>2003-05-20</td>\n",
       "      <td>12438</td>\n",
       "      <td>Home Alone</td>\n",
       "      <td>33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5193</th>\n",
       "      <td>Jonathan Rosenbaum</td>\n",
       "      <td>fresh</td>\n",
       "      <td>107969</td>\n",
       "      <td>Chicago Reader</td>\n",
       "      <td>I found it pretty entertaining, as well as pro...</td>\n",
       "      <td>2008-04-09</td>\n",
       "      <td>14232</td>\n",
       "      <td>Rising Sun</td>\n",
       "      <td>34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9074</th>\n",
       "      <td>Roger Ebert</td>\n",
       "      <td>fresh</td>\n",
       "      <td>117802</td>\n",
       "      <td>Chicago Sun-Times</td>\n",
       "      <td>The movie is sweet, funny, observant and goofy...</td>\n",
       "      <td>2000-01-01</td>\n",
       "      <td>14550</td>\n",
       "      <td>Swingers</td>\n",
       "      <td>35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26580</th>\n",
       "      <td>Don Druker</td>\n",
       "      <td>rotten</td>\n",
       "      <td>70903</td>\n",
       "      <td>Chicago Reader</td>\n",
       "      <td>A for effort; C for execution.</td>\n",
       "      <td>2008-05-26</td>\n",
       "      <td>10285</td>\n",
       "      <td>The Way We Were</td>\n",
       "      <td>36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14841</th>\n",
       "      <td>Roger Ebert</td>\n",
       "      <td>rotten</td>\n",
       "      <td>119099</td>\n",
       "      <td>Chicago Sun-Times</td>\n",
       "      <td>The idea is better than the execution.</td>\n",
       "      <td>2000-01-01</td>\n",
       "      <td>13474</td>\n",
       "      <td>Fallen</td>\n",
       "      <td>36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9615</th>\n",
       "      <td>Joe Baltake</td>\n",
       "      <td>fresh</td>\n",
       "      <td>71853</td>\n",
       "      <td>Sacramento Bee</td>\n",
       "      <td>Still has the power to shock and make one laug...</td>\n",
       "      <td>2001-08-01</td>\n",
       "      <td>11450</td>\n",
       "      <td>Monty Python and the Holy Grail</td>\n",
       "      <td>37</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25804</th>\n",
       "      <td>John Anderson</td>\n",
       "      <td>rotten</td>\n",
       "      <td>134154</td>\n",
       "      <td>Newsday</td>\n",
       "      <td>Politically astute, visually breathtaking but ...</td>\n",
       "      <td>2000-01-01</td>\n",
       "      <td>13875</td>\n",
       "      <td>Ride with the Devil</td>\n",
       "      <td>38</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18736</th>\n",
       "      <td>Michael Wilmington</td>\n",
       "      <td>fresh</td>\n",
       "      <td>120889</td>\n",
       "      <td>Chicago Tribune</td>\n",
       "      <td>As rare and odd, and visually breathtaking, as...</td>\n",
       "      <td>2000-01-01</td>\n",
       "      <td>11789</td>\n",
       "      <td>What Dreams May Come</td>\n",
       "      <td>38</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19713</th>\n",
       "      <td>Cody Clark</td>\n",
       "      <td>fresh</td>\n",
       "      <td>120794</td>\n",
       "      <td>Mr. Showbiz</td>\n",
       "      <td>A visually breathtaking film!</td>\n",
       "      <td>2000-01-01</td>\n",
       "      <td>10366</td>\n",
       "      <td>The Prince of Egypt</td>\n",
       "      <td>38</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 9 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                        critic   fresh    imdb              publication                                              quote review_date       rtid                               title  cluster\n",
       "3732                 Lucy Mohl  rotten  109813                 Film.com                        It's a dull day in Bedrock.  2000-01-01      12326                     The Flintstones        0\n",
       "16615              Roger Ebert  rotten   65063        Chicago Sun-Times  Woody Allen's Take the Money and Run has some ...  2004-10-23      16258              Take the Money and Run        1\n",
       "20753  Mary Elizabeth Williams  rotten  137338                Salon.com  Though it has its moments, 200 Cigarettes fail...  2000-01-01      14561                      200 Cigarettes        2\n",
       "3990        James Berardinelli   fresh  111503                ReelViews  An old-fashioned, high-tech, fun time at the m...  2000-01-01      16394                           True Lies        3\n",
       "18994          Moira MacDonald  rotten  985699            Seattle Times  You just can't quite enter the world of this f...  2008-12-29  770671940                            Valkyrie        4\n",
       "1128                Mike Clark   fresh  113247                USA Today  Writer-director Mathieu Kassovitz mines so muc...  2000-01-01   98832611                            La haine        5\n",
       "12349               Joe Leydon  rotten  120389                  Variety  Like the TV series, the pic features makeup an...  2008-05-14      12077        Turbo: A Power Rangers Movie        6\n",
       "24608            Eric Harrison   fresh  332047        Houston Chronicle  At the movie's core is a question that all cou...  2005-04-08         23                         Fever Pitch        7\n",
       "395                Jeff Millar   fresh  112682        Houston Chronicle  The City of Lost Children is a series of assoc...  2000-01-01      13050          La cité des enfants perdus        8\n",
       "5035               Brian Lowry   fresh  107614                  Variety  Although overly sappy in places and probably 2...  2008-07-22      10997                      Mrs. Doubtfire        9\n",
       "24522              Ruthe Stein  rotten  119256  San Francisco Chronicle  Noirish thrillers live or die by their plot tw...  2000-01-01      14170                              Sydney       10\n",
       "26783             Lou Lumenick   fresh  141399            New York Post                      Amusing, light entertainment.  2000-01-01      15866                     Isn't She Great       11\n",
       "10252             Keith Uhlich   fresh   81398        Time Out New York  When has a performer as fully and uniquely sac...  2010-11-03      15121                         Raging Bull       12\n",
       "17931             Geoff Andrew   fresh   58329                 Time Out  It's still thrilling to watch, lush, cool and ...  2006-02-09      10595                              Marnie       12\n",
       "17986                      NaN   fresh  123324                USA Today             Entertaining and nostalgically moving!  2000-01-01      14374           Why Do Fools Fall in Love       12\n",
       "19415          Owen Gleiberman   fresh  140888     Entertainment Weekly             A richly tender and moving experience.  2000-01-01      14037                   Central do Brasil       12\n",
       "11954              Roger Ebert   fresh  116754        Chicago Sun-Times            A thoughtful and moving film about war.  2000-01-01      14448                  Kavkazskiy plennik       12\n",
       "4230              Geoff Andrew   fresh  106226                 Time Out            Scorsese's most poignantly moving film.  2006-02-09      10537                The Age of Innocence       12\n",
       "16383             Mick LaSalle  rotten  166813  San Francisco Chronicle  A mishmash that is sometimes moving, sometimes...  2002-05-24       9502    Spirit: Stallion of the Cimarron       12\n",
       "356               Kevin Thomas   fresh  114057        Los Angeles Times  Parker has shown how involving and moving Shak...  2001-02-13      13094                             Othello       12\n",
       "11318              A.D. Murphy   fresh   73195                  Variety  The fast-moving 124-minute film engenders enor...  2007-06-27      10288                                Jaws       12\n",
       "9201        Jonathan Rosenbaum   fresh   56218           Chicago Reader  powerful experience, alternately corrosive wit...  2008-05-07      12484            The Manchurian Candidate       12\n",
       "10360            Vincent Canby   fresh   97441           New York Times          This is a good, moving, complicated film.  2003-05-20      16760                               Glory       12\n",
       "16558            Vincent Canby   fresh   81283           New York Times  A moving, intelligent and funny film about dis...  2003-05-20      13029                     Ordinary People       12\n",
       "16978          Bosley Crowther   fresh   56193           New York Times  The picture has a rare power, a garbled but of...  2000-01-01      20226                              Lolita       12\n",
       "17633            Vincent Canby  rotten   84649           New York Times  The story manages to be sentimental without be...  2004-08-30       9485                  The Secret of NIMH       12\n",
       "24916         Jonathan Foreman   fresh  144178            New York Post                 Beautifully shot and often moving.  2000-01-01  770684867             Dreaming of Joseph Lees       12\n",
       "3826                 Joe Brown   fresh  107426          Washington Post  Though uneven, the film is engagingly moving a...  2000-01-01      10580                       Little Buddha       12\n",
       "11524             Kevin Thomas   fresh  117571        Los Angeles Times  A bravura, provocative sendup of horror pictur...  2001-02-14      17135                              Scream       12\n",
       "9102            Joseph McBride   fresh   97576                  Variety  What was conceived as a child's dream of a Sat...  2008-05-05      23531  Indiana Jones and the Last Crusade       12\n",
       "...                        ...     ...     ...                      ...                                                ...         ...        ...                                 ...      ...\n",
       "2237                Mike Clark  rotten  114666                USA Today  One of the sleaziest movies of the year and ce...  2000-01-01      16726                  The Tie That Binds       28\n",
       "27398            Kevin Maynard   fresh  185014              Mr. Showbiz  This is certainly the best studio movie of the...  2000-01-01      13257                         Wonder Boys       28\n",
       "26300              Roger Ebert   fresh  151568            At the Movies                      One of the year's best films.  2000-01-01      13407                         Topsy-Turvy       28\n",
       "24235              Roger Ebert   fresh  171804            At the Movies                 One of the best films of the year!  2000-01-01      13339                      Boys Don't Cry       28\n",
       "1527             Amy Biancolli   fresh  483726        Houston Chronicle  Man of the Year isn't Movie of the Year. It mi...  2006-10-13  314387293                     Man of the Year       28\n",
       "1530              Terry Lawson   fresh  483726       Detroit Free Press  No one will mistake Man of the Year for movie ...  2006-10-13  314387293                     Man of the Year       28\n",
       "18952              Roger Ebert   fresh  120789        Chicago Sun-Times    One of the year's best and most original films!  2000-01-01      10341                       Pleasantville       28\n",
       "22764               Rod Dreher  rotten  132347            New York Post                          This year's The Avengers.  2000-01-01      10623                         Mystery Men       28\n",
       "8139             Variety Staff   fresh   32976                  Variety  One of the finest productional efforts of the ...  2008-02-19      17080                             Rebecca       28\n",
       "15501               Mike Clark   fresh  124718                USA Today  The year's first Hollywood movie to burst with...  2000-01-01      13529                         He Got Game       28\n",
       "19376             Janet Maslin   fresh  120623           New York Times             The best ant colony movie of the year!  2000-01-01       9749                        A Bug's Life       28\n",
       "24872       Michael Wilmington   fresh  166943          Chicago Tribune           One of the year's most heartfelt movies.  2000-01-01      10485                  Music of the Heart       28\n",
       "8000               Roger Ebert   fresh   34583        Chicago Sun-Times  Seeing the film over and over again, year afte...  2000-01-01      10056                          Casablanca       28\n",
       "15046              Gene Siskel   fresh  119822          Chicago Tribune                            One of the year's best.  2000-01-01      12971                  As Good as It Gets       28\n",
       "24945              Roger Ebert   fresh  119698            At the Movies  Princess Mononoke is a great achievement and a...  2000-01-01      10144                       Mononoke-hime       28\n",
       "9747             Peter Travers    none  103850            Rolling Stone  Tim Robbins inaugurates the fall season with a...  2001-05-12      16319                         Bob Roberts       28\n",
       "26361             Lou Lumenick   fresh  125664            New York Post        One of the year's most entertaining movies.  2000-01-01      13765                     Man on the Moon       28\n",
       "23791              J. Hoberman  rotten  169547            Village Voice  There's too much dead air around the dialogue ...  2000-01-01      12878                     American Beauty       29\n",
       "9839                 Mark Caro   fresh  116209          Chicago Tribune  With its fine acting, sumptuous visuals and le...  2013-02-24      14840                 The English Patient       30\n",
       "5312                  Jay Carr   fresh  108071             Boston Globe  The result is an instant classic -- rich, dens...  2013-08-01       9432                   The Secret Garden       31\n",
       "18965           Lisa Alspector   fresh  120157           Chicago Reader  This appealing formulaic action adventure (199...  2007-03-07      13402                             Soldier       32\n",
       "5707               Caryn James   fresh   99785           New York Times  [A] surprisingly charming film, which may be t...  2003-05-20      12438                          Home Alone       33\n",
       "5193        Jonathan Rosenbaum   fresh  107969           Chicago Reader  I found it pretty entertaining, as well as pro...  2008-04-09      14232                          Rising Sun       34\n",
       "9074               Roger Ebert   fresh  117802        Chicago Sun-Times  The movie is sweet, funny, observant and goofy...  2000-01-01      14550                            Swingers       35\n",
       "26580               Don Druker  rotten   70903           Chicago Reader                     A for effort; C for execution.  2008-05-26      10285                     The Way We Were       36\n",
       "14841              Roger Ebert  rotten  119099        Chicago Sun-Times             The idea is better than the execution.  2000-01-01      13474                              Fallen       36\n",
       "9615               Joe Baltake   fresh   71853           Sacramento Bee  Still has the power to shock and make one laug...  2001-08-01      11450     Monty Python and the Holy Grail       37\n",
       "25804            John Anderson  rotten  134154                  Newsday  Politically astute, visually breathtaking but ...  2000-01-01      13875                 Ride with the Devil       38\n",
       "18736       Michael Wilmington   fresh  120889          Chicago Tribune  As rare and odd, and visually breathtaking, as...  2000-01-01      11789                What Dreams May Come       38\n",
       "19713               Cody Clark   fresh  120794              Mr. Showbiz                      A visually breathtaking film!  2000-01-01      10366                 The Prince of Egypt       38\n",
       "\n",
       "[100 rows x 9 columns]"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2=df2.sort(\"cluster\")\n",
    "df2.head(100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Text Analysis with the Non-Negative matrix factorization by Projected Gradient (NMF)\n",
    "\n",
    "Well, things are getting a little bit more mathematically challenging from here but there is a good overview over at [Wikipedia](https://en.wikipedia.org/wiki/Non-negative_matrix_factorization). The actual implementation is described [here](http://scikit-learn.org/stable/modules/generated/sklearn.decomposition.NMF.html).\n",
    "\n",
    "For an understanding of the following code, we will try to outline the idea behind NMF - or more precise - what it is used for in this tutorial. Bascially, we want to find out which topics are \"hidden\" in our quotes. The output of the NMF algorithm will be a list of the discovered topics where each topic is represented by a set of unique terms.\n",
    "\n",
    "Depending on the number of topics, the learning will take a while."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
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   "source": [
    "# import the NMF algorithm\n",
    "from sklearn.decomposition import NMF\n",
    "# set a number of topics to be learnt\n",
    "n_topics=10\n",
    "# use NMF with our data\n",
    "nmf = NMF(n_components=n_topics, random_state=1).fit(Xtfidf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "* * * * * * * * * * * * * * * *\n",
      "Topic #0: (first #20 terms)\n",
      "movie great kind enjoyable isn moments bad lot horror makes funniest big going summer year little end kids think tv\n",
      "* * * * * * * * * * * * * * * *\n",
      "Topic #1: (first #20 terms)\n",
      "film great new horror finest moving real beautiful fine emotional war deeply american fascinating noir moments end people family rare\n",
      "* * * * * * * * * * * * * * * *\n",
      "Topic #2: (first #20 terms)\n",
      "good bad pretty natured isn feel performances acting hearted looking time makes better stuff direction idea writing looks example going\n",
      "* * * * * * * * * * * * * * * *\n",
      "Topic #3: (first #20 terms)\n",
      "comedy romantic laughs romance black adventure drama charming screwball melodrama high spirited light bright thriller satire likable teen uneven action\n",
      "* * * * * * * * * * * * * * * *\n",
      "Topic #4: (first #20 terms)\n",
      "like movies feels ve plays seen looks watching bad feel just sounds look tv makes don ll life know little\n",
      "* * * * * * * * * * * * * * * *\n",
      "Topic #5: (first #20 terms)\n",
      "best year movies films far thing years work hollywood disney easily seen ve picture works worst animated series come certainly\n",
      "* * * * * * * * * * * * * * * *\n",
      "Topic #6: (first #20 terms)\n",
      "funny smart isn touching moving fast scary warm sweet frequently surprisingly just gags satire jokes laugh clever pretty darkly laughs\n",
      "* * * * * * * * * * * * * * * *\n",
      "Topic #7: (first #20 terms)\n",
      "fun great lot watch just movies scary dumb wicked watching flawed plain really certainly packed run formulaic kids having terrific\n",
      "* * * * * * * * * * * * * * * *\n",
      "Topic #8: (first #20 terms)\n",
      "story time just director characters make doesn way action work picture little love does new plot thriller long screen old\n",
      "* * * * * * * * * * * * * * * *\n",
      "Topic #9: (first #20 terms)\n",
      "entertaining enormously witty surprisingly intelligent thriller wildly year far movies hitchcock moving supremely mildly point mess man films picture terrifically\n"
     ]
    }
   ],
   "source": [
    "# for clarity, we restrict the displayed number of topic-specif terms\n",
    "n_top_words = 20\n",
    "# get the feature names (as above)\n",
    "feature_names = tfidfvectorizer.get_feature_names()\n",
    "# iterate of all topics found by the NMF algorithm\n",
    "for topic_idx, topic in enumerate(nmf.components_):\n",
    "    print(\"* * * * * * * * * * * * * * * *\")\n",
    "    print(\"Topic #%d: (first #%d terms)\" % (topic_idx, n_top_words))\n",
    "    topic_idxs=topic.argsort()[:-n_top_words - 1:-1] # sort the entries of \"topic\" by size\n",
    "    \n",
    "    # the next line is pretty compact, for an illustration what is happening see below\n",
    "    # take all entries from \"feature_names\" that are found in \"topic_idxs\" and join them in a string separated by \" \"\n",
    "    print(\" \".join([feature_names[i] for i in topic_idxs])) \n",
    "    \n",
    "    # to understand the line above you might want to uncomment the 3 lines below\n",
    "    #print \"\\nSample of the expansion happening above:\"\n",
    "    #print topic_idxs # prints all topic index of the current topic\n",
    "    #print feature_names[topic_idxs[0]] # displays the name of the term addressed at the first element of \"topic_idxs\"\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What to Do Next?\n",
    "\n",
    "* You might want to apply [_stemming_](https://en.wikipedia.org/wiki/Stemming) in combination with stop world elimnation on your natural language texts. Stemming reduces words to a (sometimes) artifical base form, e.g., the terms \"houses\", \"housing\" and \"house\" will be reduced to \"house\" as they are related to the same semantic concept. This might improve the quality of your topic analysis as these 3 terms will end up in the same topic. Without stemming, the terms can occur in different topic what is not what you would expect from a topic analysis. Adding stemming to the tutorial above is a little difficult as it is not directly supported by the _scikit learn_ package but there is an [article](http://scikit-learn.org/stable/modules/feature_extraction.html) to get you started using [_NLTK_](http://www.nltk.org/book/), a natural language processing toolkit for Python.\n",
    "* The [data science lab](https://datasciencelab.wordpress.com/) does also provide some nice examples in Python and can inspire you to start your own projects.\n",
    "* The used $k$-means clustering algorithm is neither the most efficient nor the most stable clustering algorithm regarding outliers in your data. An alternative is the [DBSCAN algorithm](https://en.wikipedia.org/wiki/DBSCAN) that is also [supported by scikit learn](http://scikit-learn.org/stable/modules/generated/sklearn.cluster.DBSCAN.html) and can be used similarly to the clustering above.  \n",
    "* You can try to transfer the things you have learned to other data sets provided by [scikit learn](http://scikit-learn.org/stable/tutorial/basic/tutorial.html#loading-example-dataset).\n",
    "* If you really want to increase you knowledge of typical ML techiques, read about [_support vector machines (SVM)_](https://en.wikipedia.org/wiki/Support_vector_machine). SVMs are widely used in ML for pattern recognition and classification and also supported by [scikit learn](http://scikit-learn.org/stable/modules/svm.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# no longer needed\n",
    "# bitfidfvectorizer = TfidfVectorizer(min_df=2, max_df=0.5, ngram_range=(1,2), stop_words='english')\n",
    "# biXtfidf=bitfidfvectorizer.fit_transform(corpus)\n",
    "# bigs=bitfidfvectorizer.get_feature_names()\n",
    "# print len(bigs)\n",
    "# bigs[10000:10200]"
   ]
  }
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