Clustering.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import random\n",
    "from collections import defaultdict\n",
    "from scipy.sparse import csr_matrix\n",
    "from sklearn.utils import shuffle\n",
    "from sklearn.metrics import calinski_harabaz_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def csr_read(fname, ftype=\"csr\", nidx=1):\n",
    "    r\"\"\" \n",
    "        Read CSR matrix from a text file. \n",
    "        \n",
    "        \\param fname File name for CSR/CLU matrix\n",
    "        \\param ftype Input format. Acceptable formats are:\n",
    "            - csr - Compressed sparse row\n",
    "            - clu - Cluto format, i.e., CSR + header row with \"nrows ncols nnz\"\n",
    "        \\param nidx Indexing type in CSR file. What does numbering of feature IDs start with?\n",
    "    \"\"\"\n",
    "    \n",
    "    with open(fname) as f:\n",
    "        lines = f.readlines()\n",
    "    \n",
    "    if ftype == \"clu\":\n",
    "        p = lines[0].split()\n",
    "        nrows = int(p[0])\n",
    "        ncols = int(p[1])\n",
    "        nnz = long(p[2])\n",
    "        lines = lines[1:]\n",
    "        assert(len(lines) == nrows)\n",
    "    elif ftype == \"csr\":\n",
    "        nrows = len(lines)\n",
    "        ncols = 0 \n",
    "        nnz = 0 \n",
    "        for i in xrange(nrows):\n",
    "            p = lines[i].split()\n",
    "            if len(p) % 2 != 0:\n",
    "                raise ValueError(\"Invalid CSR matrix. Row %d contains %d numbers.\" % (i, len(p)))\n",
    "            nnz += len(p)/2\n",
    "            for j in xrange(0, len(p), 2): \n",
    "                cid = int(p[j]) - nidx\n",
    "                if cid+1 > ncols:\n",
    "                    ncols = cid+1\n",
    "    else:\n",
    "        raise ValueError(\"Invalid sparse matrix ftype '%s'.\" % ftype)\n",
    "    val = np.zeros(nnz, dtype=np.float)\n",
    "    ind = np.zeros(nnz, dtype=np.int)\n",
    "    ptr = np.zeros(nrows+1, dtype=np.long)\n",
    "    n = 0 \n",
    "    for i in xrange(nrows):\n",
    "        p = lines[i].split()\n",
    "        for j in xrange(0, len(p), 2): \n",
    "            ind[n] = int(p[j]) - nidx\n",
    "            val[n] = float(p[j+1])\n",
    "            n += 1\n",
    "        ptr[i+1] = n \n",
    "    \n",
    "    assert(n == nnz)\n",
    "    \n",
    "    return csr_matrix((val, ind, ptr), shape=(nrows, ncols), dtype=np.float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def csr_idf(matrix, copy=False, **kargs):\n",
    "    r\"\"\" Scale a CSR matrix by idf. \n",
    "    Returns scaling factors as dict. If copy is True, \n",
    "    returns scaled matrix and scaling factors.\n",
    "    \"\"\"\n",
    "    if copy is True:\n",
    "        matrix = matrix.copy()\n",
    "    nrows = matrix.shape[0]\n",
    "    nnz = matrix.nnz\n",
    "    ind, val, ptr = matrix.indices, matrix.data, matrix.indptr\n",
    "    # document frequency\n",
    "    df = defaultdict(int)\n",
    "    for i in ind:\n",
    "        df[i] += 1\n",
    "    # inverse document frequency\n",
    "    for k,v in df.items():\n",
    "        df[k] = np.log(nrows / float(v))  ## df turns to idf - reusing memory\n",
    "    # scale by idf\n",
    "    for i in range(0, nnz):\n",
    "        val[i] *= df[ind[i]]\n",
    "        \n",
    "    return df if copy is False else matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def csr_l2normalize(matrix, copy=False, **kargs):\n",
    "    r\"\"\" Normalize the rows of a CSR matrix by their L-2 norm. \n",
    "    If copy is True, returns a copy of the normalized matrix.\n",
    "    \"\"\"\n",
    "    if copy is True:\n",
    "        matrix = matrix.copy()\n",
    "    nrows = matrix.shape[0]\n",
    "    nnz = matrix.nnz\n",
    "    ind, val, ptr = matrix.indices, matrix.data, matrix.indptr\n",
    "    # normalize\n",
    "    for i in range(nrows):\n",
    "        rsum = 0.0    \n",
    "        for j in range(ptr[i], ptr[i+1]):\n",
    "            rsum += val[j]**2\n",
    "        if rsum == 0.0:\n",
    "            continue  # do not normalize empty rows\n",
    "        rsum = float(1.0/np.sqrt(rsum))\n",
    "        for j in range(ptr[i], ptr[i+1]):\n",
    "            val[j] *= rsum\n",
    "            \n",
    "    if copy is True:\n",
    "        return matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def initialCentroids(matrix):\n",
    "    matrixShuffled = shuffle(matrix, random_state=0)\n",
    "    return matrixShuffled[:2,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def similarity(matrix, centroids):\n",
    "    similarities = matrix.dot(centroids.T)\n",
    "    return similarities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def findClusters(matrix, centroids):\n",
    "    \n",
    "    clusterA = list()\n",
    "    clusterB = list()\n",
    "    \n",
    "    similarityMatrix = similarity(matrix, centroids)\n",
    "    \n",
    "    for index in range(similarityMatrix.shape[0]):\n",
    "        similarityRow = similarityMatrix[index]\n",
    "        \n",
    "        #Sort the index of the matrix in ascending order of value and get the index of the last element\n",
    "        #This index will be the cluster that the row in input matrix will belong to\n",
    "        similaritySorted = np.argsort(similarityRow)[-1]\n",
    "        \n",
    "        if similaritySorted == 0:\n",
    "            clusterA.append(index)\n",
    "        else:\n",
    "            clusterB.append(index)\n",
    "        \n",
    "    return clusterA, clusterB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def recalculateCentroid(matrix, clusters):\n",
    "    centroids = list()\n",
    "    \n",
    "    for i in range(0,2):\n",
    "        cluster = matrix[clusters[i],:]\n",
    "        clusterMean = cluster.mean(0)\n",
    "        centroids.append(clusterMean)\n",
    "        \n",
    "    centroids_array = np.asarray(centroids)\n",
    "    \n",
    "    return centroids_array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def kmeans(matrix, numberOfIterations):\n",
    "    \n",
    "    centroids = initialCentroids(matrix)\n",
    "    \n",
    "    for _ in range(numberOfIterations):\n",
    "        \n",
    "        clusters = list()\n",
    "        \n",
    "        clusterA, clusterB = findClusters(matrix, centroids)\n",
    "        \n",
    "        if len(clusterA) > 1:\n",
    "            clusters.append(clusterA)\n",
    "        if len(clusterB) > 1:\n",
    "            clusters.append(clusterB)\n",
    "            \n",
    "        centroids = recalculateCentroid(matrix, clusters)\n",
    "        \n",
    "    return clusterA, clusterB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def calculateSSE(matrix, clusters):\n",
    "    \n",
    "    SSE_list = list()\n",
    "    SSE_array = []\n",
    "    \n",
    "    for cluster in clusters:\n",
    "        members = matrix[cluster,:]\n",
    "        SSE = np.sum(np.square(members - np.mean(members)))\n",
    "        SSE_list.append(SSE)\n",
    "        \n",
    "    SSE_array = np.asarray(SSE_list)\n",
    "    dropClusterIndex = np.argsort(SSE_array)[-1]\n",
    "            \n",
    "    return dropClusterIndex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def bisecting_kmeans(matrix, k, numberOfIterations):\n",
    "    \n",
    "    clusters = list()\n",
    "    \n",
    "    initialcluster = list()\n",
    "    for i in range(matrix.shape[0]):\n",
    "        initialcluster.append(i)\n",
    "    \n",
    "    clusters.append(initialcluster)\n",
    "    \n",
    "    while len(clusters) < k:\n",
    "\n",
    "        dropClusterIndex = calculateSSE(matrix, clusters)\n",
    "        droppedCluster = clusters[dropClusterIndex]\n",
    "        \n",
    "        clusterA, clusterB = kmeans(matrix[droppedCluster,:], numberOfIterations)\n",
    "        del clusters[dropClusterIndex]\n",
    "        \n",
    "        actualClusterA = list()\n",
    "        actualClusterB = list()\n",
    "        for index in clusterA:\n",
    "            actualClusterA.append(droppedCluster[index])\n",
    "            \n",
    "        for index in clusterB:\n",
    "            actualClusterB.append(droppedCluster[index])\n",
    "        \n",
    "        clusters.append(actualClusterA)\n",
    "        clusters.append(actualClusterB)\n",
    "    \n",
    "    labels = [0] * matrix.shape[0]\n",
    "\n",
    "    for index, cluster in enumerate(clusters):\n",
    "        for idx in cluster:\n",
    "            labels[idx] = index + 1\n",
    "    return labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Read CSR matrix from the input file\n",
    "csrMatrix = csr_read('train.dat', ftype=\"csr\", nidx=1)\n",
    "\n",
    "#Scale the CSR matrix by idf (Inverse Document Frequency)\n",
    "csrIDF = csr_idf(csrMatrix, copy=True)\n",
    "\n",
    "#Normalize the rows of a CSR matrix by their L-2 norm.\n",
    "csrL2Normalized = csr_l2normalize(csrIDF, copy=True)\n",
    "\n",
    "#Obtain a dense ndarray representation of the CSR matrix.\n",
    "denseMatrix = csrL2Normalized.toarray()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For K= 3 Calinski Harabaz Score is 63.080976\n",
      "For K= 5 Calinski Harabaz Score is 47.311063\n",
      "For K= 7 Calinski Harabaz Score is 46.035433\n",
      "For K= 9 Calinski Harabaz Score is 43.216868\n",
      "For K= 11 Calinski Harabaz Score is 38.217769\n",
      "For K= 13 Calinski Harabaz Score is 34.761864\n",
      "For K= 15 Calinski Harabaz Score is 34.206359\n",
      "For K= 17 Calinski Harabaz Score is 32.649491\n",
      "For K= 19 Calinski Harabaz Score is 30.837459\n",
      "For K= 21 Calinski Harabaz Score is 30.097737\n"
     ]
    }
   ],
   "source": [
    "kValues = list()\n",
    "scores = list()\n",
    "\n",
    "for k in range(3, 22, 2):\n",
    "    labels = bisecting_kmeans(denseMatrix, k, 10)\n",
    "    \n",
    "    if (k == 7):\n",
    "        # write result to output file\n",
    "        outputFile = open(\"output.dat\", \"w\")\n",
    "        for index in labels:\n",
    "            outputFile.write(str(index) +'\\n')\n",
    "        outputFile.close()\n",
    "\n",
    "    score = calinski_harabaz_score(denseMatrix, labels)\n",
    "    kValues.append(k)\n",
    "    scores.append(score)\n",
    "    \n",
    "    print (\"For K= %d Calinski Harabaz Score is %f\" %(k, score))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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FKxp4E7hbVXt8ykFEaoA9wEEgrKqLRKQQeBiYBtQAl6hqc3fpBD0iALj8vndZ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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xea46e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.plot(kValues, scores)\n",
    "plt.xticks(kValues, kValues)\n",
    "plt.xlabel('Number of Clusters k')\n",
    "plt.ylabel('Calinski and Harabaz Score')\n",
    "plt.title('Trend of Average Distance to Centroid/Diameter')\n",
    "plt.grid(linestyle='dotted')\n",
    "\n",
    "plt.savefig('plot.png')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}