MikeLing/KNN.ipynb

## KNN.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# K-Nearest Neighbors (KNN)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### by Chiyuan Zhang and S&ouml;ren Sonnenburg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook illustrates the <a href=\"http://en.wikipedia.org/wiki/K-nearest_neighbors_algorithm\">K-Nearest Neighbors</a> (KNN) algorithm on the USPS digit recognition dataset in Shogun. Further, the effect of <a href=\"http://en.wikipedia.org/wiki/Cover_tree\">Cover Trees</a> on speed is illustrated by comparing KNN with and without it. Finally, a comparison with <a href=\"http://en.wikipedia.org/wiki/Support_vector_machine#Multiclass_SVM\">Multiclass Support Vector Machines</a> is shown. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The basics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The training of a KNN model basically does nothing but memorizing all the training points and the associated labels, which is very cheap in computation but costly in storage. The prediction is implemented by finding the K nearest neighbors of the query point, and voting. Here K is a hyper-parameter for the algorithm. Smaller values for K give the model low bias but high variance; while larger values for K give low variance but high bias.\n",
    "\n",
    "In `SHOGUN`, you can use [CKNN](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CKNN.html) to perform KNN learning. To construct a KNN machine, you must choose the hyper-parameter K and a distance function. Usually, we simply use the standard  [CEuclideanDistance](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CEuclideanDistance.html), but in general, any subclass of [CDistance](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CDistance.html) could be used. For demonstration, in this tutorial we select a random subset of 1000 samples from the USPS digit recognition dataset, and run 2-fold cross validation of KNN with varying K."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we load and init data split:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(256, 9298)\n",
      "(256, 5000)\n",
      "(256, 1000)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "from scipy.io import loadmat, savemat\n",
    "from numpy    import random\n",
    "from os       import path\n",
    "\n",
    "mat  = loadmat('../../../data/multiclass/usps.mat')\n",
    "Xall = mat['data']\n",
    "Yall = np.array(mat['label'].squeeze(), dtype=np.double)\n",
    "\n",
    "# map from 1..10 to 0..9, since shogun\n",
    "# requires multiclass labels to be\n",
    "# 0, 1, ..., K-1\n",
    "Yall = Yall - 1\n",
    "\n",
    "random.seed(0)\n",
    "\n",
    "subset = random.permutation(len(Yall))\n",
    "\n",
    "Xtrain = Xall[:, subset[:5000]]\n",
    "Ytrain = Yall[subset[:5000]]\n",
    "\n",
    "Xtest = Xall[:, subset[5000:6000]]\n",
    "Ytest = Yall[subset[5000:6000]]\n",
    "\n",
    "Nsplit = 2\n",
    "all_ks = range(1, 21)\n",
    "\n",
    "print Xall.shape\n",
    "print Xtrain.shape\n",
    "print Xtest.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us plot the first five examples of the train data (first row) and test data (second row)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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     },
     "output_type": "display_data",
     "metadata": {}
    },
    {
     "data": {
      "image/png": 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     },
     "output_type": "display_data",
     "metadata": {}
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import pylab as P\n",
    "def plot_example(dat, lab):\n",
    "    for i in xrange(5):\n",
    "        ax=P.subplot(1,5,i+1)\n",
    "        P.title(int(lab[i]))\n",
    "        ax.imshow(dat[:,i].reshape((16,16)), interpolation='nearest')\n",
    "        ax.set_xticks([])\n",
    "        ax.set_yticks([])\n",
    "        \n",
    "        \n",
    "_=P.figure(figsize=(17,6))\n",
    "P.gray()\n",
    "plot_example(Xtrain, Ytrain)\n",
    "\n",
    "_=P.figure(figsize=(17,6))\n",
    "P.gray()\n",
    "plot_example(Xtest, Ytest)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we import shogun components and convert the data to shogun objects:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predictions [ 9.  7.  1.  0.  7.]\n",
      "Ground Truth [ 9.  7.  1.  0.  7.]\n",
      "Accuracy = 97.30%\n"
     ]
    }
   ],
   "source": [
    "from modshogun import MulticlassLabels, RealFeatures\n",
    "from modshogun import KNN, EuclideanDistance\n",
    "\n",
    "labels = MulticlassLabels(Ytrain)\n",
    "feats  = RealFeatures(Xtrain)\n",
    "k=3\n",
    "dist = EuclideanDistance()\n",
    "knn = KNN(k, dist, labels)\n",
    "labels_test = MulticlassLabels(Ytest)\n",
    "feats_test  = RealFeatures(Xtest)\n",
    "knn.train(feats)\n",
    "pred = knn.apply_multiclass(feats_test)\n",
    "print \"Predictions\", pred[:5]\n",
    "print \"Ground Truth\", Ytest[:5]\n",
    "\n",
    "from modshogun import MulticlassAccuracy\n",
    "evaluator = MulticlassAccuracy()\n",
    "accuracy = evaluator.evaluate(pred, labels_test)\n",
    "\n",
    "print \"Accuracy = %2.2f%%\" % (100*accuracy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot a few missclassified examples - I guess we all agree that these are notably harder to detect."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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     },
     "output_type": "display_data",
     "metadata": {}
    }
   ],
   "source": [
    "idx=np.where(pred != Ytest)[0]\n",
    "Xbad=Xtest[:,idx]\n",
    "Ybad=Ytest[idx]\n",
    "_=P.figure(figsize=(17,6))\n",
    "P.gray()\n",
    "plot_example(Xbad, Ybad)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the question is - is 97.30% accuracy the best we can do? While one would usually re-train KNN with different values for k here and likely perform Cross-validation, we just use a small trick here that saves us lots of computation time: When we have to determine the $K\\geq k$ nearest neighbors we will know the nearest neigbors for all $k=1...K$ and can thus get the predictions for multiple k's in one step:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1000, 13)\n"
     ]
    }
   ],
   "source": [
    "knn.set_k(13)\n",
    "multiple_k=knn.classify_for_multiple_k()\n",
    "print multiple_k.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have the prediction for each of the 13 k's now and can quickly compute the accuracies:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy for k=1 is 97.20%\n",
      "Accuracy for k=2 is 97.20%\n",
      "Accuracy for k=3 is 97.30%\n",
      "Accuracy for k=4 is 96.70%\n",
      "Accuracy for k=5 is 96.70%\n",
      "Accuracy for k=6 is 96.60%\n",
      "Accuracy for k=7 is 96.40%\n",
      "Accuracy for k=8 is 96.50%\n",
      "Accuracy for k=9 is 96.20%\n",
      "Accuracy for k=10 is 96.20%\n",
      "Accuracy for k=11 is 96.00%\n",
      "Accuracy for k=12 is 96.30%\n",
      "Accuracy for k=13 is 96.20%\n"
     ]
    }
   ],
   "source": [
    "for k in xrange(13):\n",
    "    print \"Accuracy for k=%d is %2.2f%%\" % (k+1, 100*np.mean(multiple_k[:,k]==Ytest))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So k=3 seems to have been the optimal choice."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Speed comparisons with different KNN solvers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In SHOGUN, you can use Cover Trees to speed up the nearest neighbor searching process in KNN and the KD-Trees solver is also alternative, which is faster than the other two solvers only on low-dimesional data. Just call set_use_covertree on the KNN machine to switch between different solvers. We also show the prediction time comparison with and without Cover Tree and KD-Trees in this tutorial. So let's just have a comparison utilizing the data above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Standard KNN took 1.1s\n",
      "Covertree KNN took 0.9s\n",
      "KDTree KNN took 3.0s\n"
     ]
    }
   ],
   "source": [
    "from modshogun import Time, KNN_COVER_TREE, KNN_BRUTE, KNN_KDTREE\n",
    "start = Time.get_curtime()\n",
    "knn.set_k(3)\n",
    "knn.set_knn_solver_type(KNN_BRUTE)\n",
    "pred = knn.apply_multiclass(feats_test)\n",
    "print \"Standard KNN took %2.1fs\" % (Time.get_curtime() - start)\n",
    "\n",
    "\n",
    "start = Time.get_curtime()\n",
    "knn.set_k(3)\n",
    "knn.set_knn_solver_type(KNN_COVER_TREE)\n",
    "pred = knn.apply_multiclass(feats_test)\n",
    "print \"Covertree KNN took %2.1fs\" % (Time.get_curtime() - start)\n",
    "\n",
    "\n",
    "start = Time.get_curtime()\n",
    "knn.set_k(3)\n",
    "knn.set_knn_solver_type(KNN_KDTREE)\n",
    "pred = knn.apply_multiclass(feats_test)\n",
    "print \"KDTree KNN took %2.1fs\" % (Time.get_curtime() - start)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Obviously applying KNN is very costly: for each prediction you have to compare the object against all training objects. While the implementation in `SHOGUN` will use all available CPU cores to parallelize this computation it might still be slow when you have big data sets. We can see it been significantly speed up by Cover Trees solver, but the result of KD-Trees solver is not so ideally. So, let's do a more systematic comparison. For that a helper function is defined to run the evaluation for KNN:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def evaluate(labels, feats, use_cover_tree=False, use_KD_Tree=False):\n",
    "    from modshogun import MulticlassAccuracy, CrossValidationSplitting\n",
    "    import time\n",
    "    split = CrossValidationSplitting(labels, Nsplit)\n",
    "    split.build_subsets()\n",
    "    \n",
    "    accuracy = np.zeros((Nsplit, len(all_ks)))\n",
    "    acc_train = np.zeros(accuracy.shape)\n",
    "    time_test = np.zeros(accuracy.shape)\n",
    "    for i in range(Nsplit):\n",
    "        idx_train = split.generate_subset_inverse(i)\n",
    "        idx_test  = split.generate_subset_indices(i)\n",
    "\n",
    "        for j, k in enumerate(all_ks):\n",
    "            #print \"Round %d for k=%d...\" % (i, k)\n",
    "\n",
    "            feats.add_subset(idx_train)\n",
    "            labels.add_subset(idx_train)\n",
    "\n",
    "            dist = EuclideanDistance(feats, feats)\n",
    "            knn = KNN(k, dist, labels)\n",
    "            knn.set_store_model_features(True)\n",
    "            if use_cover_tree:\n",
    "                knn.set_knn_solver_type(KNN_COVER_TREE)\n",
    "            elif use_KD_Tree:\n",
    "                knn.set_knn_solver_type(KNN_KDTREE)\n",
    "            else:\n",
    "                knn.set_knn_solver_type(KNN_BRUTE)\n",
    "            knn.train()\n",
    "\n",
    "            evaluator = MulticlassAccuracy()\n",
    "            pred = knn.apply_multiclass()\n",
    "            acc_train[i, j] = evaluator.evaluate(pred, labels)\n",
    "\n",
    "            feats.remove_subset()\n",
    "            labels.remove_subset()\n",
    "            feats.add_subset(idx_test)\n",
    "            labels.add_subset(idx_test)\n",
    "\n",
    "            t_start = time.clock()\n",
    "            pred = knn.apply_multiclass(feats)\n",
    "            time_test[i, j] = (time.clock() - t_start) / labels.get_num_labels()\n",
    "\n",
    "            accuracy[i, j] = evaluator.evaluate(pred, labels)\n",
    "\n",
    "            feats.remove_subset()\n",
    "            labels.remove_subset()\n",
    "    return {'eout': accuracy, 'ein': acc_train, 'time': time_test}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Evaluate KNN with and without Cover Tree. This takes a few seconds:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Evaluating KNN...\n",
      "Done!\n"
     ]
    }
   ],
   "source": [
    "labels = MulticlassLabels(Ytest)\n",
    "feats  = RealFeatures(Xtest)\n",
    "print(\"Evaluating KNN...\")\n",
    "wo_ct = evaluate(labels, feats, use_cover_tree=False, use_KD_Tree=False)\n",
    "wi_ct = evaluate(labels, feats, use_cover_tree=True)\n",
    "wd_ct = evaluate(labels, feats, use_KD_Tree=True)\n",
    "print(\"Done!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generate plots with the data collected in the evaluation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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UBBKMMU4ReQNIMcb801Wg/CvwoDHmqIhMBmKNMWOu1d7N2IMTFASJV5fgEOhz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MzMiuMCx8zMzIrjAsfMzMyK4wLHzMzMiuMCx8zMzIrjAsfMzMyK818mvyVeAYOtNgAAAABJRU5E\nrkJggg==\n"
     },
     "output_type": "display_data",
     "metadata": {}
    },
    {
     "data": {
      "image/png": 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Yn6j1ci1umHMDCckJlPYvzdwBc7mk7iUKNiLifXbtgk6dYPfuAmkuKCiIVatW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\nEZHcUYAjIiIiufP/vLeAhSCom5wAAAAASUVORK5CYII=\n"
     },
     "output_type": "display_data",
     "metadata": {}
    }
   ],
   "source": [
    "import matplotlib\n",
    "\n",
    "fig = P.figure(figsize=(8,5))\n",
    "P.plot(all_ks, wo_ct['eout'].mean(axis=0), 'r-*')\n",
    "P.plot(all_ks, wo_ct['ein'].mean(axis=0), 'r--*')\n",
    "P.plot(all_ks, wi_ct['eout'].mean(axis=0), 'b-*')\n",
    "P.plot(all_ks, wi_ct['ein'].mean(axis=0), 'b--*')\n",
    "P.plot(all_ks, wd_ct['eout'].mean(axis=0), 'g-*')\n",
    "P.plot(all_ks, wd_ct['ein'].mean(axis=0), 'g--*')\n",
    "P.legend([\"Test Accuracy\", \"Training Accuracy\"])\n",
    "P.xlabel('K')\n",
    "P.ylabel('Accuracy')\n",
    "P.title('KNN Accuracy')\n",
    "P.tight_layout()\n",
    "\n",
    "fig = P.figure(figsize=(8,5))\n",
    "P.plot(all_ks, wo_ct['time'].mean(axis=0), 'r-*')\n",
    "P.plot(all_ks, wi_ct['time'].mean(axis=0), 'b-d')\n",
    "P.plot(all_ks, wd_ct['time'].mean(axis=0), 'g:')\n",
    "P.xlabel(\"K\")\n",
    "P.ylabel(\"time\")\n",
    "P.title('KNN time')\n",
    "P.legend([\"Plain KNN\", \"CoverTree KNN\", \"KD-Trees\"], loc='center right')\n",
    "P.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although simple and elegant, KNN is generally very resource costly. Because all the training samples are to be memorized literally, the memory cost of KNN *learning* becomes prohibitive when the dataset is huge. Even when the memory is big enough to hold all the data, the prediction will be slow, since the distances between the query point and all the training points need to be computed and ranked. The situation becomes worse if in addition the data samples are all very high-dimensional. Leaving aside computation time issues, k-NN is a very versatile and competitive algorithm. It can be applied to any kind of objects (not just numerical data) - as long as one can design a suitable distance function. In pratice k-NN used with bagging can create improved and more robust results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparison to Multiclass Support Vector Machines"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In contrast to KNN - multiclass Support Vector Machines (SVMs) attempt to model the decision function separating each class from one another. They compare examples utilizing similarity measures (so called Kernels) instead of distances like KNN does. When applied, they are in Big-O notation computationally as expensive as KNN but involve another (costly) training step. They do not scale very well to cases with a huge number of classes but usually lead to favorable results when applied to small number of classes cases. So for reference let us compare how a standard multiclass SVM performs wrt. KNN on the mnist data set from above."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us first train a multiclass svm using a Gaussian kernel (kind of the SVM equivalent to the euclidean distance)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from modshogun import GaussianKernel, GMNPSVM\n",
    "\n",
    "width=80\n",
    "C=1\n",
    "\n",
    "gk=GaussianKernel()\n",
    "gk.set_width(width)\n",
    "\n",
    "svm=GMNPSVM(C, gk, labels)\n",
    "_=svm.train(feats)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's apply the SVM to the same test data set to compare results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy = 100.00%\n"
     ]
    }
   ],
   "source": [
    "out=svm.apply(feats_test)\n",
    "evaluator = MulticlassAccuracy()\n",
    "accuracy = evaluator.evaluate(out, labels_test)\n",
    "\n",
    "print \"Accuracy = %2.2f%%\" % (100*accuracy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the SVM performs way better on this task - let's apply it to all data we did not use in training."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy = 94.69%\n"
     ]
    },
    {
     "data": {
      "image/png": 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     },
     "output_type": "display_data",
     "metadata": {}
    }
   ],
   "source": [
    "Xrem=Xall[:,subset[6000:]]\n",
    "Yrem=Yall[subset[6000:]]\n",
    "\n",
    "feats_rem=RealFeatures(Xrem)\n",
    "labels_rem=MulticlassLabels(Yrem)\n",
    "out=svm.apply(feats_rem)\n",
    "\n",
    "evaluator = MulticlassAccuracy()\n",
    "accuracy = evaluator.evaluate(out, labels_rem)\n",
    "\n",
    "print \"Accuracy = %2.2f%%\" % (100*accuracy)\n",
    "\n",
    "idx=np.where(out.get_labels() != Yrem)[0]\n",
    "Xbad=Xrem[:,idx]\n",
    "Ybad=Yrem[idx]\n",
    "_=P.figure(figsize=(17,6))\n",
    "P.gray()\n",
    "plot_example(Xbad, Ybad)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The misclassified examples are indeed much harder to label even for human beings."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2.0
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}