{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import math, numpy as np, tensorflow as tf, matplotlib.pyplot as plt, operator\n",
    "from importlib import reload"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Clustering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Clustering techniques are unsupervised learning algorithms that try to group unlabelled data into \"clusters\", using the (typically spatial) structure of the data itself."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import kmeans; reload(kmeans)\n",
    "from kmeans import Kmeans"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The easiest way to demonstrate how clustering works is to simply generate some data and show them in action."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Create data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "n_clusters=6\n",
    "n_samples =250"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "To generate our data, we're going to pick 6 random points, which we'll call centroids, and for each point we're going to generate 250 random points about it.\n",
    "\n",
    "In statistical parlance, we're going to simulate 1500 realizations from 6 different bivariate normal distributions (250 each) with random centroids over the range -35, 35."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "centroids = np.random.uniform(-35, 35, (n_clusters, 2))\n",
    "slices = [np.random.multivariate_normal(centroids[i], np.diag([5., 5.]), n_samples)\n",
    "           for i in range(n_clusters)]\n",
    "data = np.concatenate(slices).astype(np.float32)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Below we can see each centroid marked w/ X, and the coloring associated to each respective cluster."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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W7Q5IhoR0X0XOwLeUtsoxC17ak6kSKPKB51lB3IwLfSmaH3s2OokfYiYMS/wBBo8wLiJW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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1dbc224518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kmeans.plot_data(centroids, data, n_samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true,
    "heading_collapsed": true
   },
   "source": [
    "## K means"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true,
    "hidden": true
   },
   "source": [
    "The goal of clustering is to identify these clusters, defined by their centroids, given the raw data with no labels. Once these centroids have been identified, each point is labelled as belonging to the centroid it is closest to.\n",
    "\n",
    "K means clustering is a simple and popular approach of finding appropriate centroids. It does this by taking random centroids, and iteratively moving them to make the clusters as compact as possible.\n",
    "\n",
    "The algorithm is very simple:\n",
    "- Select the number of clusters N you want to find\n",
    "- Guess N random centroids (more on this below)\n",
    "- While centroids change:\n",
    "    - Create clusters by assigning each point to the nearest centroid\n",
    "    - For each cluster, define the new centroid as the centroid of all points assigned to it\n",
    "    \n",
    "Typically the algorithm is terminated once the change in centroids is negligible or after a certain number of iterations.\n",
    "\n",
    "While guessing random centroids is fine in theory, most implementations use the data itself to identify initial cluster points. This speeds up convergence by initializing centroids in the appropriate regime. Typically, inital points are selected amongst the data and tries to pick them to be as far apart as possible."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "hidden": true
   },
   "outputs": [],
   "source": [
    "k = Kmeans(data, n_clusters)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true,
    "hidden": true
   },
   "outputs": [],
   "source": [
    "sess = tf.InteractiveSession()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true,
    "hidden": true
   },
   "outputs": [],
   "source": [
    "tf.global_variables_initializer().run()\n",
    "initial_centroids = k.find_initial_centroids(n_clusters).eval()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true,
    "hidden": true
   },
   "source": [
    "Inital \"random\" guesses, based on the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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bQIv2IwjC+GKwFv5h4CvA/7QXKqVuAO4H5gFFwC6l1BytdWCQ9xsS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\n/g8qGSk1o0ZSHgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1d5c36f048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kmeans.plot_data(initial_centroids, data, n_samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true,
    "hidden": true
   },
   "outputs": [],
   "source": [
    "curr_centroids = tf.Variable(initial_centroids)\n",
    "nearest_indices = k.assign_to_nearest(curr_centroids)\n",
    "updated_centroids = k.update_centroids(nearest_indices)\n",
    "tf.global_variables_initializer().run()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true,
    "hidden": true
   },
   "source": [
    "Updated centroids after one iteration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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/9fdTUFBAYWEh32n6iA84w5hxTThjx/OrlqOUtNZz6Hgbj42ZIqUU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\n/wF6qmnk4oDwOAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1d5803fcc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kmeans.plot_data(updated_centroids.eval(), data, n_samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor 'Assign:0' shape=(6, 2) dtype=float32_ref>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "curr_centroids.assign(updated_centroids)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "hidden": true
   },
   "outputs": [],
   "source": [
    "with tf.Session().as_default(): new_centroids = k.run()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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dDSTBvndxywjCyEYEf5QQKmc94JvI7Yjy+MTeysRpT5Mw5DntBUEYdETwRyjB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\nEETwBUEQIgQRfEEQhAhBBF8QBCFC+P+Ax2jnoZCIrgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1ce46ed860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kmeans.plot_data(new_centroids, data, n_samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true,
    "hidden": true
   },
   "source": [
    "The result are centroids that have minimized the total distance between all points and their centroids; the centroids are \"optimal\" in this sense.\n",
    "\n",
    "There are some problems with K-means clustering.\n",
    "* Number of clusters needs to be known a priori\n",
    "    * This is an obvious failure of an unsupervised learning algorithm; we want the data to \"speak for itself\"\n",
    "    * Difficult to identify in higher dimensions\n",
    "    \n",
    "* Naive approach only works if the clusters are the same shape\n",
    "    * This is because centroid is identified using euclidean distance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Mean shift"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Mean shift clustering is a newer and less well-known approach.\n",
    "\n",
    "The algorithm is as follows:\n",
    "* Take each data point X\n",
    "* For each x in X, find the distance between point x and every other point in X\n",
    "* Create weights for each point in X by using the Gaussian function of that point's distance to x\n",
    "    * Gaussian function here is the density function of a Normal distribution of distances with mean 0\n",
    "    * This weighting approach penalizes points further away from x\n",
    "    * The rate at which the weights fall to zero is determined by the bandwidth, which is the standard deviation of the Gaussian\n",
    "* Update x as the weighted average of all other points in X, defined by the weights determined in the previous step\n",
    "\n",
    "This will iteratively push points that are close together even closer until they are next to each other."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def gaussian(d, bw):\n",
    "    return np.exp(-0.5*((d/bw))**2) / (bw*math.sqrt(2*math.pi))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "In our implementation, we choose the bandwidth to be 2.5. \n",
    "\n",
    "One easy way to choose bandwidth is to find which bandwidth covers one third of the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def meanshift(data):\n",
    "    X = np.copy(data)\n",
    "    for it in range(5):\n",
    "        for i, x in enumerate(X):\n",
    "            dist = np.sqrt(((x-X)**2).sum(1))\n",
    "            weight = gaussian(dist, 2.5)\n",
    "            X[i] = (np.expand_dims(weight,1)*X).sum(0) / weight.sum()\n",
    "    return X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 824 ms, sys: 20 ms, total: 844 ms\n",
      "Wall time: 792 ms\n"
     ]
    }
   ],
   "source": [
    "%time X=meanshift(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We can see that mean shift clustering has almost reproduced our original clustering. The one exception are the very close clusters, but if we really wanted to differentiate them we could lower the bandwidth.\n",
    "\n",
    "What is impressive is that this algorithm nearly reproduced the original clusters without telling it how many clusters there should be."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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hDHxJKoSBL0mFMPAlqRAGviQVwsCXpEIY+JJUCANfkgph4EtSIQx8SSqEgS9JhTDwJakQ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\nwsCXpEIY+JJUCANfkgph4EtSIf4NdvQQawIGDIwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1ce4654a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kmeans.plot_data(centroids+2, X, n_samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We should be able to accelerate this algorithm with a GPU."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## PyTorch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "GPU-accelerated mean shift implementation in pytorch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import torch_utils; reload(torch_utils)\n",
    "from torch_utils import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The advantage of pytorch is that it's very similar to numpy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def gaussian(d, bw):\n",
    "    return torch.exp(-0.5*((d/bw))**2) / (bw*math.sqrt(2*math.pi))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Torch does not support broadcasting, therefore Jeremy has replaced the distance subtraction line with a subtraction function from his custom pytorch broadcasting library."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def meanshift(data):\n",
    "    X = torch.FloatTensor(np.copy(data))\n",
    "    for it in range(5):\n",
    "        for i, x in enumerate(X):\n",
    "            dist = torch.sqrt((sub(x, X)**2).sum(1))\n",
    "            weight = gaussian(dist, 3)\n",
    "            num = mul(weight, X).sum(0)\n",
    "            X[i] = num / weight.sum()\n",
    "    return X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "This implementation actually takes longer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 2.02 s, sys: 0 ns, total: 2.02 s\n",
      "Wall time: 1.9 s\n"
     ]
    }
   ],
   "source": [
    "%time X = meanshift(data).numpy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "All the computation is happening in the <tt>for</tt> loop, which isn't accelerated by pytorch.\n",
    "\n",
    "Each iteration launches a new cuda kernel, which takes time and slows the algorithm down as a whole."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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MfEkqhIEvSYUw8CWpEAa+JBXCwJekQhj4klQIA1+SCmHgS1IhDHxJKoSBL0mFMPAlqRAG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\nC5d2XTfJAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1c24e81d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kmeans.plot_data(centroids+2, X, n_samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### GPU"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "To truly accelerate the algorithm, we need to be performing updates on a batch of points per iteration, instead of just one as we were doing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def dist_b(a,b):\n",
    "    return torch.sqrt((sub(a.unsqueeze(0),b.unsqueeze(1))**2).sum(2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       " 0.2547  0.7809  0.4620\n",
       " 0.3356  0.8589  0.4897\n",
       "[torch.FloatTensor of size 2x3]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a=torch.rand(2,2)\n",
    "b=torch.rand(3,2)\n",
    "dist_b(b, a).squeeze(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def gaussian(d, bw):\n",
    "    return torch.exp(-0.5*((d/bw))**2) / (bw*math.sqrt(2*math.pi))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def sum_sqz(a,axis): return a.sum(axis).squeeze(axis)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def meanshift(data, bs=500):\n",
    "    n = len(data)\n",
    "    X = torch.FloatTensor(np.copy(data)).cuda()\n",
    "    for it in range(5):\n",
    "        for i in range(0,n,bs):\n",
    "            s = slice(i,min(n,i+bs))\n",
    "            weight = gaussian(dist_b(X, X[s]), 2)\n",
    "            num = sum_sqz(mul(weight, X), 1)\n",
    "            X[s] = div(num, sum_sqz(weight, 1))\n",
    "    return X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Although each iteration still has to launch a new cuda kernel, there are now fewer iterations, and the acceleration from updating a batch of points more than makes up for it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 48 ms, sys: 36 ms, total: 84 ms\n",
      "Wall time: 78.9 ms\n"
     ]
    }
   ],
   "source": [
    "%time X = meanshift(data).cpu().numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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B32/Hj8OXv7zxLUk91OlFW3Xq4Ye3fktSjxj4/XbzzfCnf9rvVkgqgF06klQIA1+SCmHg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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1c24d57358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kmeans.plot_data(centroids+2, X, n_samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## LSH"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "TO-DO: Needs notes?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from sklearn.neighbors import LSHForest, KDTree, BallTree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "n_clusters=6\n",
    "n_samples =2500"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "centroids = np.random.uniform(-35, 35, (n_clusters, 2))\n",
    "slices = [np.random.multivariate_normal(centroids[i], np.diag([5., 5.]), n_samples)\n",
    "           for i in range(n_clusters)]\n",
    "data = np.concatenate(slices).astype(np.float32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[   0, 1918,  905],\n",
       "       [   1,  102, 1294],\n",
       "       [   2, 2345, 1397],\n",
       "       [   3, 2383,  943],\n",
       "       [   4,   15, 1886],\n",
       "       [   5, 2243,  161],\n",
       "       [   6, 2085, 1853],\n",
       "       [   7, 2222, 2177],\n",
       "       [   8,  324, 2008],\n",
       "       [   9,  396, 1659]])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nn = KDTree(data)\n",
    "nearest = nn.query(data[:10], 3, False); nearest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[   0, 1918,  905],\n",
       "       [   1,  102, 1294],\n",
       "       [   2, 2345, 1397],\n",
       "       [   3, 2383,  943],\n",
       "       [   4,   15, 1886],\n",
       "       [   5, 2243,  161],\n",
       "       [   6, 2085, 1853],\n",
       "       [   7, 2222, 2177],\n",
       "       [   8,  324, 2008],\n",
       "       [   9,  396, 1659]])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nn = BallTree(data)\n",
    "nearest = nn.query(data[:10], 3, False); nearest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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HNgDf/S5VRhurvrWMkDSZ+aunmHn/g9wLTLr3h2QJX4JLBujXPWOff6Evm1+H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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1c209e21d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kmeans.plot_data(centroids, data, n_samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def index_b(a,idxs):\n",
    "    ir, ic = idxs.size()\n",
    "    ar, ac = a.size()\n",
    "    return a[idxs.view(ir*ic)].view(ir,ic,ac)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "a = FT([[1,2],[3.,4],[5,6]])\n",
    "b = torch.LongTensor([[0,1], [1,2]])\n",
    "exp = FT([[[1,2], [3,4.]], [[3,4], [5,6]]])\n",
    "assert(torch.equal(index_b(a,b), exp))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def dist_b_n(a,b,pts):\n",
    "    dists = sub(pts,b.unsqueeze(1))**2\n",
    "    return torch.sqrt(dists.sum(2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def meanshift(data, bs=512):\n",
    "    n = len(data)\n",
    "    X = torch.FloatTensor(np.copy(data)).cuda()\n",
    "    for it in range(5):\n",
    "        d = X.cpu().numpy()\n",
    "        nn = BallTree(d)\n",
    "        for i in range(0,n,bs):\n",
    "            s = slice(i,min(n,i+bs))\n",
    "            nearest = torch.LongTensor(nn.query(d[s], 50, False)).cuda()\n",
    "            pts = index_b(X, nearest)\n",
    "            weight = gaussian(dist_b_n(X, X[s], pts), 2)\n",
    "            num = sum_sqz(mul(weight, pts), 1)\n",
    "            X[s] = div(num, sum_sqz(weight, 1))\n",
    "    return X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.45 s, sys: 16 ms, total: 1.46 s\n",
      "Wall time: 1.35 s\n"
     ]
    }
   ],
   "source": [
    "%time data = meanshift(data).cpu().numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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T6ksGSYRtbL1HBc280lLJ/kON3mkPLo04jmaMLeyjEQ652/tRCI0YW9h3Nrw1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\nK6WUQ2jgK6WUQ2jgK6WUQ/w/p8zUEOal5ggAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1c20920400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kmeans.plot_data(centroids+1, data, n_samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}