PyTorch K-Means.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import torch\n",
    "from torch.autograd import Variable\n",
    "from torch import FloatTensor\n",
    "import torch.optim as optim\n",
    "\n",
    "from sklearn.datasets import make_blobs\n",
    "\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "from pylab import rcParams"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def init_clusters_v1(num_dimensions=2, num_clusters=3, random_state=None): \n",
    "    clusters = None\n",
    "    if random_state is None: \n",
    "        clusters = np.random.rand(num_clusters, num_dimensions)\n",
    "    else:\n",
    "        clusters = random_state.rand(num_clusters, num_dimensions)\n",
    "    return Variable(FloatTensor(clusters), requires_grad=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def create_dataset(num_samples=100, num_dimensions=2, num_clusters=3, std=1.0, random_state=None): \n",
    "    X, y = make_blobs(n_samples=num_samples, \n",
    "                      n_features=num_dimensions, \n",
    "                      centers=num_clusters, \n",
    "                      random_state=random_state, \n",
    "                      cluster_std=std)\n",
    "    return Variable(FloatTensor(X), requires_grad=False), Variable(FloatTensor(y), requires_grad=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def calculate_sample_cluster_cost(X, clusters, cost_fn='mean'): \n",
    "    norms = []\n",
    "    \n",
    "    for c in range(clusters.size()[0]):\n",
    "        sub = X - clusters[c].resize(1, 2).expand_as(X)\n",
    "        norm = sub.norm(2, 1)\n",
    "        norms.append(norm)\n",
    "    \n",
    "    norms = torch.cat(norms, 1)\n",
    "    \n",
    "    min_norm, clusters_memberships = norms.min(1)\n",
    "    \n",
    "    cost = None\n",
    "    \n",
    "    if cost_fn is 'mean': \n",
    "        cost = min_norm.mean()\n",
    "    if cost_fn is 'sum': \n",
    "        cost = min_norm.sum()\n",
    "    \n",
    "    return cost, min_norm, clusters_memberships"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def calculate_cluster_cluster_cost(clusters, cost_fn='mean'): \n",
    "    clusters_ = clusters\n",
    "\n",
    "    norms = []\n",
    "\n",
    "    for c in range(clusters.size()[0]):\n",
    "        sub = clusters - clusters[c].resize(1, 2).expand_as(clusters)\n",
    "        #norm = sub.norm(2, 1)\n",
    "        norm = sub**2\n",
    "        norms.append(norm)\n",
    "\n",
    "    cost = None\n",
    "        \n",
    "    if cost_fn is 'mean': \n",
    "        cost = torch.mean(torch.cat(norms) / 2)\n",
    "    if cost_fn is 'sum':\n",
    "        cost = torch.sum(torch.cat(norms) / 2)\n",
    "        \n",
    "    return -cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def kmeans_step(clusters, X, optimizer, cost_fn='mean', alpha=0.0): \n",
    "    \n",
    "    sample_cluster_cost, dist, cluster_assignment = calculate_sample_cluster_cost(X, clusters, cost_fn=cost_fn)\n",
    "    \n",
    "    cluster_cluster_cost = calculate_cluster_cluster_cost(clusters, cost_fn=cost_fn)\n",
    "    \n",
    "    total_cost = 0\n",
    "    \n",
    "    total_cost = sample_cluster_cost \n",
    "    \n",
    "    #total_cost += alpha * cluster_cluster_cost\n",
    "    \n",
    "    optimizer.zero_grad()\n",
    "    \n",
    "    total_cost.backward()\n",
    "    \n",
    "    optimizer.step()\n",
    "    \n",
    "    return total_cost, cluster_assignment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot(X, clusters, figsize=(10, 10)): \n",
    "    rcParams['figure.figsize'] = figsize\n",
    "    \n",
    "    X_ = X.data.numpy()\n",
    "    C_ = clusters.data.numpy()\n",
    "    \n",
    "    plt.plot(\n",
    "        X_[:,0], \n",
    "        X_[:,1], \n",
    "        'yo'\n",
    "    )\n",
    "    plt.plot(\n",
    "        C_[:, 0], \n",
    "        C_[:, 1], \n",
    "        'go'\n",
    "    )\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_clusters = 3\n",
    "num_dimensions = 2\n",
    "cluster_std = 2.0\n",
    "num_samples = 200\n",
    "\n",
    "clusters = init_clusters_v1(num_clusters=num_clusters, \n",
    "                            random_state=np.random.RandomState(30))\n",
    "\n",
    "X, y = create_dataset(num_samples=num_samples, \n",
    "                      num_clusters=num_clusters, \n",
    "                      std=cluster_std, \n",
    "                      random_state=np.random.RandomState(10))\n",
    "\n",
    "optimizer1 = optim.RMSprop([clusters])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
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WsMXojTW0qIyM3/b2rdjbexg3bz6OnZ27cXh4Z1TrBoF+CFuM3lhDi8pIO8a6bhDoR8o5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\nWwAABQlbAAAFCVsAAAUJWwAABf3/TIDNt3b5f/cAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1a32af8bd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(X, clusters)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Od5jS808pvZBz3l30dSpbjeuinDvVkvAUe2YBm5v6miUV78uErcZ1Uc5VEgZY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\n/z+0Iew6WyiNCwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1a2f48a450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "clusters_positions = {}\n",
    "\n",
    "for i in range(clusters.size()[0]):\n",
    "    clusters_positions[i] = {\n",
    "        0: [], \n",
    "        1: []\n",
    "    }\n",
    "\n",
    "for i in range(200):\n",
    "    #optimizer1 = optim.RMSprop([clusters])\n",
    "    optimizer1.zero_grad()\n",
    "    \n",
    "    cost, cluster_assignment = kmeans_step(clusters, X, optimizer1)\n",
    "    \n",
    "    for i in range(clusters.size()[0]):\n",
    "        clusters_positions[i][0].append(clusters.data.numpy()[i, 0])\n",
    "        clusters_positions[i][1].append(clusters.data.numpy()[i, 1])\n",
    "    \n",
    "    \n",
    "plot(X, clusters)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[None, None, None, None]"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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MavexCiEE4G7grRjjDSu5bBDw+xDCQ8CewFcxxk9zV6YyFSMcfTS0bg3DhsE1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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1a2f18f450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lines = plt.plot(clusters_positions[0][0], clusters_positions[0][1])\n",
    "plt.setp(lines, color='red', linewidth=0.5, markersize=2, marker='+')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from ipywidgets import interact, interactive, fixed, interact_manual\n",
    "import ipywidgets as widgets\n",
    "from ipywidgets import FloatSlider"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def step(n_steps=1.0): \n",
    "    optimizer1.zero_grad()\n",
    "    \n",
    "    for i in range(int(n_steps)):\n",
    "        kmeans_step(clusters, X, optimizer1)\n",
    "    \n",
    "    plot(X, clusters)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c0b718b462f644a9822fddc746aaa2af",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "A Jupyter Widget"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "interact_manual(step, n_steps=FloatSlider(min=1, max=20, step=1));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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   "language": "python",
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  "language_info": {
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    "name": "ipython",
    "version": 2
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   "file_extension": ".py",
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