assets/notebooks/K-Means.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a7261cd4",
   "metadata": {},
   "source": [
    "# Clustering"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db63aba9",
   "metadata": {},
   "source": [
    "<img src=\"../images/kmeans.png\" alt=\"\" width=\"600\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c63859d3",
   "metadata": {},
   "source": [
    "Clustering is the process of examining a collection of \"points\" and grouping the points into \"clusters\" according to some **distance measure**. The goal is that the points in the same cluster have a small distance from one another, while points in different clusters are at a larger distance from one another.\n",
    "\n",
    "### Points, Spaces, and Distances\n",
    "A dataset suitable for clustering is a collection of _points_, which are just objects belonging to some _space_. In its most general sense, a space is just a universal set of points, from which the points in the dataset are drawn. All spaces for which we can perform a clustering have a distance measure, giving a distance between any two points in the space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ce93eeff",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import pandas\n",
    "import pandas as pd\n",
    "pd.set_option('display.max_columns', None)\n",
    "\n",
    "# Import seaborn\n",
    "import seaborn as sns\n",
    "%matplotlib inline\n",
    "\n",
    "# Apply the default theme\n",
    "sns.set_theme()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39a95c9e",
   "metadata": {},
   "source": [
    "## K-Means Algorithm (Step-by-step)\n",
    "K-Means is the best known algorithm in a family of clustering algorithms known as _point-assignment algorithms_. K-Means requires a Euclidean space and assumes the number of clusters, _k_, is known in advance. It is, however, possible to deduce _k_ by trial and error. \n",
    "\n",
    "In order to explain the K-Means algorithm, we will start by creating a low dimension \"demo\" dataset that has a clear number of clusters (K=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "dac7656c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[2.5, 1.1], [1.5, 2], [2, 3], [4, 6], [4, 4], [4.5, 5], [3.5, 5.1]]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create demo data\n",
    "points = [\n",
    "    [2.5, 1.1],\n",
    "    [1.5, 2],\n",
    "    [2, 3],\n",
    "    [4, 6],\n",
    "    [4, 4],\n",
    "    [4.5, 5],\n",
    "    [3.5, 5.1]\n",
    "]\n",
    "points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d7c36c35",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>cluster</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>P-0</th>\n",
       "      <td>2.5</td>\n",
       "      <td>1.1</td>\n",
       "      <td>N/A</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P-1</th>\n",
       "      <td>1.5</td>\n",
       "      <td>2.0</td>\n",
       "      <td>N/A</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P-2</th>\n",
       "      <td>2.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>N/A</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P-3</th>\n",
       "      <td>4.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>N/A</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P-4</th>\n",
       "      <td>4.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>N/A</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P-5</th>\n",
       "      <td>4.5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>N/A</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P-6</th>\n",
       "      <td>3.5</td>\n",
       "      <td>5.1</td>\n",
       "      <td>N/A</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       x    y cluster\n",
       "P-0  2.5  1.1     N/A\n",
       "P-1  1.5  2.0     N/A\n",
       "P-2  2.0  3.0     N/A\n",
       "P-3  4.0  6.0     N/A\n",
       "P-4  4.0  4.0     N/A\n",
       "P-5  4.5  5.0     N/A\n",
       "P-6  3.5  5.1     N/A"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# identify columns and index\n",
    "columns = [\"x\", \"y\"]\n",
    "index = [f\"P-{i}\" for i in range(len(points))]\n",
    "\n",
    "# create data frame\n",
    "demodf = pd.DataFrame(\n",
    "    points, \n",
    "    columns=columns, \n",
    "    index=index\n",
    ")\n",
    "\n",
    "# add blank label column\n",
    "demodf['cluster'] = 'N/A'\n",
    "\n",
    "# display demo data\n",
    "demodf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "289e1946",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 822.35x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def kmeans_plot(df, cf=None):\n",
    "    \n",
    "    df_tmp = df.copy()\n",
    "    df_tmp['centriod'] = False\n",
    "    \n",
    "    if cf is not None:\n",
    "        cf_tmp = cf.copy()\n",
    "        cf_tmp['centriod'] = True\n",
    "    \n",
    "    vf = pd.concat([df_tmp, cf_tmp]) if cf is not None else df_tmp\n",
    "    \n",
    "    # visualize demo + centriod data\n",
    "    scatter = sns.relplot(\n",
    "        data=vf, \n",
    "        x=\"x\", \n",
    "        y=\"y\",\n",
    "        hue='cluster',\n",
    "        style='centriod',\n",
    "        kind=\"scatter\",\n",
    "        height=7,\n",
    "        aspect=1.5,\n",
    "        s=300\n",
    "    ).set(\n",
    "        title=\"Demo Data\"\n",
    "    )\n",
    "\n",
    "    # label points with index\n",
    "    for i, point in vf.iterrows():\n",
    "        scatter.ax.text(point['x']+.1, point['y'], i)\n",
    "        \n",
    "kmeans_plot(demodf)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b427da7",
   "metadata": {},
   "source": [
    "### Step 1\n",
    "* Pick K value (how many clusters you want)\n",
    "* Choose initial centriods from points (can be random for larger data. here we pick two obivous candidates)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0afb8824",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>cluster</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>C-1</th>\n",
       "      <td>2.5</td>\n",
       "      <td>1.1</td>\n",
       "      <td>C-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C-2</th>\n",
       "      <td>3.5</td>\n",
       "      <td>5.1</td>\n",
       "      <td>C-2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       x    y cluster\n",
       "C-1  2.5  1.1     C-1\n",
       "C-2  3.5  5.1     C-2"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k=2\n",
    "\n",
    "initial_centriods = [ \n",
    "    [2.5, 1.1, 'C-1'],  # P-0\n",
    "    [3.5, 5.1, 'C-2'],  # P-6\n",
    "]\n",
    "\n",
    "centriods = pd.DataFrame(\n",
    "    initial_centriods, \n",
    "    columns=['x', 'y', 'cluster'],\n",
    "    index=['C-1', 'C-2']\n",
    ")\n",
    "\n",
    "centriods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "bc07d641",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 822.35x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kmeans_plot(demodf, centriods)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c4c18ab",
   "metadata": {},
   "source": [
    "### Step 2\n",
    "* Determine the centriod closest to each point\n",
    "* Assign the point to a cluster"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ade22d1",
   "metadata": {},
   "source": [
    "Let's use the $\\textit{L}_{1}\\textit{-norm}$, or $\\textit{Manhattan distance}$. \n",
    "\n",
    "<br />\n",
    "\n",
    "$$\n",
    "d([x_{1},x_{2},...,x_{n}], [y_{1},y_{2},...,y_{n}]) = \\sum_{i=1}^{n} |x_{i} - y_{i}|\n",
    "\\\\\n",
    "$$\n",
    "\n",
    "<br />"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "41e13471",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 2D array of points\n",
    "points = demodf[['x', 'y']].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "1d440397",
   "metadata": {},
   "outputs": [],
   "source": [
    "# demodf[['x', 'y']].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "fec64837",
   "metadata": {},
   "outputs": [],
   "source": [
    "# point of C-1\n",
    "c_1 = centriods.loc['C-1'].values[:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "0f1df85d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# point of C-2\n",
    "c_2 = centriods.loc['C-2'].values[:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "739e08b2",
   "metadata": {},
   "outputs": [],
   "source": [
    "def manhattan_distance(a, c):\n",
    "    dist = []\n",
    "    for row in a:\n",
    "        x_dist = abs(row[0] - c[0])\n",
    "        y_dist = abs(row[1] - c[1])\n",
    "        dist.append(x_dist + y_dist)\n",
    "        \n",
    "    return dist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "dfdde3f4",
   "metadata": {},
   "outputs": [],
   "source": [
    "demodf['C-1'] = manhattan_distance(points, c_1)\n",
    "demodf['C-2'] = manhattan_distance(points, c_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "b1cd5fca",
   "metadata": {},
   "outputs": [
    {
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       "       x    y cluster  C-1  C-2\n",
       "P-0  2.5  1.1     N/A  0.0  5.0\n",
       "P-1  1.5  2.0     N/A  1.9  5.1\n",
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       "P-4  4.0  4.0     N/A  4.4  1.6\n",
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       "P-6  3.5  5.1     N/A  5.0  0.0"
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     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "demodf"
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  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "1a136cd1",
   "metadata": {},
   "outputs": [],
   "source": [
    "def label_cluster(row):\n",
    "    if row['C-1'] < row['C-2']:\n",
    "        return 'C-1'\n",
    "    return 'C-2'\n",
    "\n",
    "demodf['cluster'] = demodf.apply(label_cluster, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "e4b8ab35",
   "metadata": {},
   "outputs": [
    {
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      ],
      "text/plain": [
       "       x    y cluster  C-1  C-2\n",
       "P-0  2.5  1.1     C-1  0.0  5.0\n",
       "P-1  1.5  2.0     C-1  1.9  5.1\n",
       "P-2  2.0  3.0     C-1  2.4  3.6\n",
       "P-3  4.0  6.0     C-2  6.4  1.4\n",
       "P-4  4.0  4.0     C-2  4.4  1.6\n",
       "P-5  4.5  5.0     C-2  5.9  1.1\n",
       "P-6  3.5  5.1     C-2  5.0  0.0"
      ]
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     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
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   "source": [
    "demodf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "084f7cdb",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "d3dc27c1",
   "metadata": {},
   "source": [
    "### K-Means Algorithm Step 3\n",
    "* Update centriod position\n",
    "* Repeat procedure until convergence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "af94a21c",
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "       x    y cluster\n",
       "C-1  2.5  1.1     C-1\n",
       "C-2  3.5  5.1     C-2"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "centriods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "21fb482b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "x    2.000000\n",
       "y    2.033333\n",
       "dtype: float64"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "demodf[demodf['cluster'] == 'C-1'][['x', 'y']].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "9ba3633c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "x    2.000000\n",
       "y    2.033333\n",
       "dtype: float64"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_center_1 = demodf[ demodf['cluster'] == 'C-1' ][['x', 'y']].mean()\n",
    "new_center_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "10bb6e46",
   "metadata": {},
   "outputs": [],
   "source": [
    "centriods.loc['C-1', 'x'] = new_center_1[0]\n",
    "centriods.loc['C-1', 'y'] = new_center_1[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "aec7e1dd",
   "metadata": {},
   "outputs": [],
   "source": [
    "new_center_2 = demodf[ demodf['cluster'] == 'C-2' ][['x', 'y']].mean()\n",
    "centriods.loc['C-2', 'x'] = new_center_2[0]\n",
    "centriods.loc['C-2', 'y'] = new_center_2[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "c00f7960",
   "metadata": {},
   "outputs": [
    {
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       "       x         y cluster\n",
       "C-1  2.0  2.033333     C-1\n",
       "C-2  4.0  5.025000     C-2"
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     "execution_count": 21,
     "metadata": {},
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  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a13dbf0a",
   "metadata": {},
   "outputs": [],
   "source": []
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  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "e567d93b",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 822.35x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kmeans_plot(demodf, centriods)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0c2b0296",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "f5cfd291",
   "metadata": {},
   "source": [
    "## K-Means Algorithm (scikit-learn)\n",
    "https://scikit-learn.org/stable/index.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "bcc90639",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import make_blobs\n",
    "\n",
    "# create dataset https://scikit-learn.org/stable/modules/generated/sklearn.datasets.make_blobs.html\n",
    "blobs, _ = make_blobs(\n",
    "    n_samples=150, \n",
    "    n_features=2,\n",
    "    centers=3, \n",
    "    cluster_std=0.5,\n",
    "    shuffle=True, \n",
    "    random_state=0\n",
    ")\n",
    "\n",
    "type(blobs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "d5b71fbc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2.60509732, 1.22529553],\n",
       "       [0.5323772 , 3.31338909],\n",
       "       [0.802314  , 4.38196181],\n",
       "       [0.5285368 , 4.49723858],\n",
       "       [2.61858548, 0.35769791]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# print the first five points\n",
    "blobs[:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d272115",
   "metadata": {},
   "source": [
    "### Create DataFrame from 2d ndarray\n",
    "This step is not strictly necessary (in fact, we'll just use the 2D ndarray for fitting our model). Converting to a DataFrame allows us to use our pandas and seaborn knowledge."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "3f950eca",
   "metadata": {},
   "outputs": [],
   "source": [
    "blobs_df = pd.DataFrame(blobs, columns=['x', 'y'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "f233713a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.605097</td>\n",
       "      <td>1.225296</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.532377</td>\n",
       "      <td>3.313389</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.802314</td>\n",
       "      <td>4.381962</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.528537</td>\n",
       "      <td>4.497239</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.618585</td>\n",
       "      <td>0.357698</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          x         y\n",
       "0  2.605097  1.225296\n",
       "1  0.532377  3.313389\n",
       "2  0.802314  4.381962\n",
       "3  0.528537  4.497239\n",
       "4  2.618585  0.357698"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "blobs_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "832c53e3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 756x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scatter = sns.relplot(\n",
    "    data=blobs_df, \n",
    "        x=\"x\", \n",
    "        y=\"y\",\n",
    "        kind=\"scatter\",\n",
    "        height=7,\n",
    "        aspect=1.5,\n",
    "        s=300\n",
    "    ).set(\n",
    "        title=\"Blob Data\"\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bdcec041",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "f160bdc3",
   "metadata": {},
   "source": [
    "### Working with sklearn.cluster.KMeans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "1a5e8329",
   "metadata": {},
   "outputs": [],
   "source": [
    "# https://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.html\n",
    "from sklearn.cluster import KMeans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "b99d6e69",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KMeans(n_clusters=3)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "km = KMeans(\n",
    "    n_clusters = 3, \n",
    ")\n",
    "\n",
    "km"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "c254869a",
   "metadata": {},
   "outputs": [],
   "source": [
    "result = km.fit(blobs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "2dcf29bd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.06521743,  0.96137409],\n",
       "       [-1.5947298 ,  2.92236966],\n",
       "       [ 0.9329651 ,  4.35420712]])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result.cluster_centers_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "59848896",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 2, 2, 2, 0, 2, 2, 0, 1, 2, 0, 1, 1, 2, 2, 1, 1, 0, 1, 0, 2, 0,\n",
       "       2, 2, 1, 0, 0, 2, 1, 0, 1, 1, 1, 1, 2, 0, 0, 0, 2, 2, 1, 1, 2, 0,\n",
       "       0, 0, 1, 2, 1, 2, 0, 2, 2, 0, 0, 1, 2, 0, 1, 2, 1, 1, 1, 1, 2, 1,\n",
       "       2, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 1, 1, 2, 0, 0, 2, 2, 0, 0, 0, 1,\n",
       "       1, 0, 0, 2, 0, 2, 0, 2, 1, 1, 0, 0, 0, 0, 1, 0, 0, 2, 1, 2, 2, 2,\n",
       "       1, 2, 0, 1, 2, 1, 2, 2, 1, 1, 2, 0, 2, 2, 0, 0, 1, 0, 1, 1, 1, 1,\n",
       "       0, 1, 1, 1, 2, 1, 0, 1, 2, 2, 0, 0, 1, 1, 1, 1, 0, 0], dtype=int32)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result.labels_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "e440f53c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# assign the newly minted cluster labels to the DataFrame we creaed earlier\n",
    "blobs_df[\"cluster\"] = pd.Series(result.labels_).astype(\"str\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "fdc26894",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>cluster</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.605097</td>\n",
       "      <td>1.225296</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.532377</td>\n",
       "      <td>3.313389</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.802314</td>\n",
       "      <td>4.381962</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.528537</td>\n",
       "      <td>4.497239</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.618585</td>\n",
       "      <td>0.357698</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          x         y cluster\n",
       "0  2.605097  1.225296       0\n",
       "1  0.532377  3.313389       2\n",
       "2  0.802314  4.381962       2\n",
       "3  0.528537  4.497239       2\n",
       "4  2.618585  0.357698       0"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "blobs_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "d7460892",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 801.725x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scatter = sns.relplot(\n",
    "    data=blobs_df, \n",
    "    x=\"x\", \n",
    "    y=\"y\",\n",
    "    hue=\"cluster\",   # color by cluster\n",
    "    kind=\"scatter\",\n",
    "    height=7,\n",
    "    aspect=1.5,\n",
    "    s=300\n",
    ").set(\n",
    "    title=\"Blob Data\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "148cf6cb",
   "metadata": {},
   "source": [
    "## Picking the Right Value of _k_\n",
    "We may not know the correct value of _k_ to use in a k-means clustering. However, if we can measure the quality of the clustering for variouss values of _k_, we can usually guess what the right value of _k_ is. If we take a measure of appropriateness for clusters, such as average radius or diameter, we expect that value will grow slowly as long as the number of clusters remains at or above the true number of clusters. However, as soon as we try to form fewer clusters than there really are, the measure will rise precipitously. \n",
    "\n",
    "The K-Means algorithm aims to choose centroids that minimize the _inertia_, or within-cluster sum-of-squares. We want to choose a value of _k_ that also minimizes _inertia_, but not at the expense of choosing an unnaturally large number of clusters. _Inertia_ can be recognized as a measure of how internally coherent clusters are. It suffers from various drawbacks:\n",
    "\n",
    "* Inertia makes the assumption that clusters are convex and isotropic, which is not always the case. It responds poorly to elongated clusters, or manifolds with irregular shapes.\n",
    "\n",
    "* Inertia is not a normalized metric: we just know that lower values are better and zero is optimal. But in very high-dimensional spaces, Euclidean distances tend to become inflated (this is an instance of the so-called “curse of dimensionality”)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "35aa6c02",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "72.47601670996697"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result.inertia_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "0a88d05a",
   "metadata": {},
   "outputs": [],
   "source": [
    "dist = []\n",
    "dfs = []\n",
    "for i in range(1, 8):\n",
    "    km = KMeans(n_clusters = i, init=\"random\",\n",
    "           n_init = 10, max_iter=300,\n",
    "           tol=1e-04, random_state=0)\n",
    "    result = km.fit(blobs)\n",
    "    \n",
    "    dist.append(result.inertia_)\n",
    "    \n",
    "    blobs_df[\"cluster\"] = pd.Series(result.labels_).astype(\"str\")\n",
    "    dfs.append(blobs_df.copy())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "5ff645f6",
   "metadata": {},
   "outputs": [],
   "source": [
    "idf = pd.DataFrame({\n",
    "    \"k\":range(1, 8),\n",
    "    \"distortion\":dist\n",
    "})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "55351797",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scatter = sns.relplot(\n",
    "    data=idf, \n",
    "    x=\"k\", \n",
    "    y=\"distortion\",\n",
    "    kind=\"line\",\n",
    "    height=7,\n",
    ").set(\n",
    "    title=\"Distortion\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "632d426b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "IPython.OutputArea.auto_scroll_threshold = 9999;\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%javascript\n",
    "IPython.OutputArea.auto_scroll_threshold = 9999;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "79a1f2b7",
   "metadata": {},
   "outputs": [],
   "source": [
    "for idx, df in enumerate(dfs, 1):\n",
    "\n",
    "    scatter = sns.relplot(\n",
    "        data=df, \n",
    "        x=\"x\", \n",
    "        y=\"y\",\n",
    "        hue=\"cluster\",   # color by cluster\n",
    "        kind=\"scatter\",\n",
    "        height=7,\n",
    "        aspect=1.5,\n",
    "        s=300\n",
    "    ).set(\n",
    "        title=f\"Blob Data ({idx})\"\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5f35b01f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ce79a261",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "12b68f7e",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}