KNN2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# K-Nearest Neighbors (KNN)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "#### by Chiyuan Zhang and Sören Sonnenburg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "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": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## The basics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "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": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "First we load and init data split:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(256, 9298)\n",
      "(256, 5000)\n",
      "(256, 1000)\n",
      "[ 6.  5.  4. ...,  4.  0.  1.]\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\n",
    "print Yall"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Let us plot the first five examples of the train data (first row) and test data (second row)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e855d10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x116c57d10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "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": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Then we import shogun components and convert the data to shogun objects:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "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": {
    "deletable": true,
    "editable": true
   },
   "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": 27,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e899110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "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": {
    "deletable": true,
    "editable": true
   },
   "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": 28,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "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": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We have the prediction for each of the 13 k's now and can quickly compute the accuracies:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "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": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "So k=3 seems to have been the optimal choice."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Speed comparisons of different KNN solvers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "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": 30,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Standard KNN took 1.1s\n",
      "Covertree KNN took 0.8s\n",
      "KDTree KNN took 3.2s\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": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "KNN predictions are very costly: predicate a new point's class requires computing distances to all training samples. While Shogun exploits multi-core infrastructure, KNN quickly becomes infeasible for large datasets. We can see that the Cover Tree is faster than standard KNN. In contrast, the KD-Trees solver is much slower. This is likely to by caused be the high-dimensional data that we used. We now use low-dimensional data to verify it. In this experiment, we use the Letter Recognition Data Set to test it. For more information about data set, see http://archive.ics.uci.edu/ml/datasets/Letter+Recognition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(16, 8000)\n",
      "(16, 2000)\n"
     ]
    }
   ],
   "source": [
    "Yall_low = np.genfromtxt('../../../../shogun-data/multiclass/letter-recognition.dat', delimiter=',', usecols=(0,), dtype=\"string\")\n",
    "Xall_low = np.genfromtxt('../../../../shogun-data/multiclass/letter-recognition.dat', delimiter=',', usecols=(range(1,17))).transpose()\n",
    "\n",
    "# cover alphabet to numbers\n",
    "Yall_low = np.array([ord(data) - 64 for data in Yall_low], dtype=np.double)\n",
    "\n",
    "Xtrain_low = Xall_low[:, :8000]\n",
    "Ytrain_low = Yall_low[:8000]\n",
    "\n",
    "Xtest_low = Xall_low[:, 8000:]\n",
    "Ytest_low = Yall_low[8000:]\n",
    "\n",
    "print Xtrain_low.shape\n",
    "print Xtest_low.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predictions [ 13.  22.  25.  24.  22.]\n",
      "Ground Truth [ 13.  22.  25.  24.  22.]\n",
      "Accuracy = 91.25%\n"
     ]
    }
   ],
   "source": [
    "labels_low = MulticlassLabels(Ytrain_low)\n",
    "feats_low  = RealFeatures(Xtrain_low)\n",
    "k=3\n",
    "dist_low = EuclideanDistance()\n",
    "knn_low = KNN(k, dist_low, labels_low)\n",
    "labels_test_low = MulticlassLabels(Ytest_low)\n",
    "feats_test_low  = RealFeatures(Xtest_low)\n",
    "knn_low.train(feats_low)\n",
    "pred_low = knn_low.apply_multiclass(feats_test_low)\n",
    "print \"Predictions\", pred_low[:5]\n",
    "print \"Ground Truth\", Ytest_low[:5]\n",
    "\n",
    "evaluator_low = MulticlassAccuracy()\n",
    "accuracy_low = evaluator_low.evaluate(pred_low, labels_test_low)\n",
    "\n",
    "print \"Accuracy = %2.2f%%\" % (100*accuracy_low)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Standard KNN took 1.3214s\n",
      "Covertree KNN took 0.3118s\n",
      "KDTree KNN took 0.6500s\n"
     ]
    }
   ],
   "source": [
    "start = Time.get_curtime()\n",
    "knn_low.set_k(3)\n",
    "knn_low.set_knn_solver_type(KNN_BRUTE)\n",
    "pred_low = knn_low.apply_multiclass(feats_test_low)\n",
    "print \"Standard KNN took %2.4fs\" % (Time.get_curtime() - start)\n",
    "\n",
    "\n",
    "start = Time.get_curtime()\n",
    "knn_low.set_k(3)\n",
    "knn_low.set_knn_solver_type(KNN_COVER_TREE)\n",
    "pred_low = knn_low.apply_multiclass(feats_test_low)\n",
    "print \"Covertree KNN took %2.4fs\" % (Time.get_curtime() - start)\n",
    "\n",
    "\n",
    "start = Time.get_curtime()\n",
    "knn_low.set_k(3)\n",
    "knn_low.set_knn_solver_type(KNN_KDTREE)\n",
    "pred_low = knn_low.apply_multiclass(feats_test_low)\n",
    "print \"KDTree KNN took %2.4fs\" % (Time.get_curtime() - start)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We can see that the KD-tree solver now is faster than standard KNN on this 16-dimensional dataset. The cover tree solver is still fastest. Next, let's do a more systematic comparison of Shogun's KNN implementations. We begin by defining a helper function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def evaluate(labels, feats, knn_solver_type=KNN_BRUTE):\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 knn_solver_type is KNN_COVER_TREE:\n",
    "                knn.set_knn_solver_type(KNN_COVER_TREE)\n",
    "            elif knn_solver_type is KNN_KDTREE:\n",
    "                knn.set_knn_solver_type(KNN_KDTREE)\n",
    "            elif knn_solver_type is KNN_BRUTE:\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": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Evaluate KNN using all possible solvers. This takes a few seconds. And we are going back to the initial dataset(the USPS digit recognition dataset) now:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "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, KNN_BRUTE)\n",
    "wi_ct = evaluate(labels, feats, KNN_COVER_TREE)\n",
    "wd_ct = evaluate(labels, feats, KNN_KDTREE)\n",
    "print(\"Done!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Generate plots with the data collected in the evaluation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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2gIgsAT4H+gLHgKvAqMJtaUqpWUDRdaCZIlL5hd5q8vOqb7FardhNdaRW3r38/OG3NRWK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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f049350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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HUkpSlsb/ym+vUHl0ZT5a9hEAAxoN4Os+X/NFT2dvJl8fXyU3kqcowRGRPCvFpqQ9b/9p\neyI+iGDxrsUAjPpjFPXH1ufhHx8GYPuR7dR6txY136nJiYQTANzy1S2Ejg5NW+Pl2/XfUm5UOZp/\n2Dyt3sqjK1P8v8VZsGMBAE/8/ASBLwSmjYXZdGgT5j8G32d9ORJ3BIDrPr+OoBeDeHPRmwB8s+4b\nSr5a8qx6671Xj8qjK7Nw50IA9p3cR91SdalarCoADco0oHut7mcN7hXJS5TOi0ietPPoTnpM7sFr\n17xG+9D2TOo5icSUROqXrg/A7Q1up3lIc8oXLg9AmaAyfH7j51hrCfQLBODfrf7NrfVvJaKcM2M1\nolwEY7uMpVD+Qmn3eaXjK8QnxVM92Jk51LlaZ4IDg6lVohYAxQKK8VTbp0ixKWnbDVxf83rCSobR\noHQDAEIKh9A7rPdZg4DbVGzDycSTFA0oCsDr17yOMSbbvl8i3kbr4GgdHJE8qcfkHvy89Wem3TSN\nyCqRbocjIpmkdXBERNIRmxhLoF8gY7uM5cCpA5pFJJJLaQyOiOQZHyz5gNrv1ib6WDSlg0oruRHJ\nxZTgiEiecDj2MI///Di1S9amSP4ibocjItlMXVQikqvFJ8UTlxRHscBi/H7X74QWDcXP18/tsEQk\nmynBEZFc61DsIXpM7oHB8PMdP2sPJJE8RF1UIpJrLduzjKjdUQxsPBAfo487kbxELTgikuusO7iO\n6sHViawSydZhWylVsJTbIYlIDtN/aUQkV/l23bc0er8RL/32EoCSG5E8SgmOiOQqf+/7mzql6nBP\no3vcDkVEXKQER0S8XopN4ZetvwDwZNsnWXDnAkoHlXY5KhFxkxIcEfFqcUlx3PTlTXT4rANLdi/B\nGJO2p5OI5F1KcETEq+XzyUdCcgKjrhlFo7KN3A5HRDyEZlGJiFfaGLOR3cd30y60Hd/0/UbTwEXk\nLEpwRMTrLN2zlGsmXEPRgKKsu3cd+Xz0USYiZ9N/eUTE61QoXIEm5Zsw+9bZSm5EJF1KcETEK1hr\nefevd9l+ZDslC5ZkVr9ZVAuu5nZYIuKhlOCIiFd4et7T3DvrXsYsHuN2KCLiBdS2KyKusdZijAFg\n86HNHDx1kEpFK1EmqAwr963kpy0/UTSgKHc2vJPra15PUkoSz3d43uWoRcQbqAVHRK6ItZZNhzYR\ntTsq7fXbf77N878+z65juwB4P+p9ukzswusLXwfg771/U+yVYvg/70+KTQHgpqk30Xx8c75Z9w0A\ni6IX8eCcBxn952gAIspF8GLki5otJSKZohYcEbkkSSlJ/L33bwrlL0SN4jUYv2w898y4h7CSYawe\nuhpjDP/+6d/EJcXRrlI7yhcuz6HYQ+w7sY+4pDjA2R/qtvq3UTh/YZJTkvHx9eHVq18lLimOeqXq\nAdCvfj961+lNIf9Cbr5dEfFSxlrrdgyuiYiIsFFRUW6HIeLRYhNj+XPXn0SUiyDIP4jeX/Zm6pqp\n3Nf0Pt7q/Bbbj2znh80/UL90fZqHNAfgUOwhgvyD8Pf1dzl6EcltjDFLrLURFyuXrW29xphOxpj1\nxphNxpjH0jmf3xgzOfX8n8aY0DPOjUg9vt4Yc+3F6jTGRBpjlhpjlhtjfjPGaHqFyGWIORXDbzt+\nAyA5JZmyr5flqk+vYsH2BQAMajyIiTdO5LHWzj+/SkUrMbDxwLTkBiA4MFjJjYi4Ktu6qIwxvsC7\nwNVANLDYGDPdWrvmjGJ3A4ettdWMMX2BV4A+xpgwoC9QBygH/GSMqZF6zYXqfA+4wVq71hgzFHgC\n6J9d708kt9hxdAfH449Tp1Qdft/xO60/bo2/rz9HHztKQL4AXun4CiGFQ2hVsRUAHat0dDliEZGL\ny84WnKbAJmvtFmttAjAJuOGcMjcAn6Y+nwpEGmdKxQ3AJGttvLV2K7Aptb6M6rRA4dTnRYDd2fS+\nRLxWik1h1f5V7D+5H4Bn5j1DpTcr8ciPjwDQoEwDXujwAj/e9mPaAnqDIgbRpUYXCucvfMF6RUQ8\nTXYOMi4P7DzjdTTQ7EJlrLVJxpijQPHU44vOubZ86vML1TkA+N4YEwscA5qTDmPMQGAgQMWKFS/t\nHYl4uTYft2HhzoW81ekt7mt2H9dVv47igcVpH9oegCD/IEa2GelukCIiWSA3zbccDlxnrQ0BPgZG\npVfIWjvOWhthrY0oWbJkjgYoktMOnDxA/2/6szFmI+CMn/n4ho/pUbsHAE3LN+W+ZvdRr3Q9N8MU\nEcly2dmCswuocMbrkNRj6ZWJNsbkw+lairnItecdN8aUBBpYa/9MPT4ZmJ0Vb0LEm/Wc0pNF0YuI\nrBxJ9eLVub3B7W6HJCKSI7IzwVkMVDfGVMZJTvoCt5xTZjpwB/AH0Av42VprjTHTgYnGmFE4g4yr\nA38B5gJ1HgaKGGNqWGs34AxCXpuN703EY+08upPYpFhqFK/BG9e+gb+vv1poRCTPybYEJ3VMzb3A\nD4Av8JG1drUx5lkgylo7HRgPTDDGbAIO4SQspJabAqwBkoB/WWuTAdKrM/X4PcBXxpgUnITnrux6\nbyKeatraafT/pj+NyjZiXv95NC7X2O2QRERcoYX+tNCf5ALJKcn4+viyfO9yRswdwZjrxlC5WGW3\nwxIRyXIesdCfiGSvxOREXlrwEk0/bEp8UjzhZcKZ1W+WkhsRyfOU4Ih4se1Ht/Of+f+hctHKnEo8\n5XY4IiIeQwmOiJeJTYzlxQUvcjLhJNWCq7Fq6Cqm3jSVYoHF3A5NRMRjaDdxES+SYlNo/XFrlu5Z\nSpViVehbty/VgrXtmojIuZTgiHiBo3FHASgSUISHWjxE6YKliawS6XJUIiKeS11UIh5u9qbZ1BlT\nh4fmPATALfVuUXIjInIRSnBEPNyBkwcIDgxmYOOBbociIuI1lOCIeBhrLRP+nsCgGYMAuLX+rSwZ\nuISm5Zu6HJmIiPdQgiPiYX7f+Tu3f3M7K/ev5ETCCYwx+Pn6uR2WiIhXUYIj4gEOxR7iy9VfYq2l\ndcXWfHfzdyy4cwFB/kFuhyYi4pWU4Ii44HDsYRZFLwKcdW3Kvl6Wm6bexA+bfwCgS40u+Pr4uhmi\niIhX0zRxkRxwNO4oR+KOUKloJeZumcvVE66mUP5CxPw7hkC/QN697l1ql6hNywot3Q5VRCRXUAuO\nSDY4Fn+MEwknAHjh1xcI/m8wD//4MAANyzbk6XZPM73vdAwGgAGNBtCqYiuMMa7FLCKSmyjBEckC\nJxNOpj3vMbkHxV4pxpTVUwBoHtKcJ9s+yfDmwwEIDgzm6fZP0y60nbqhRESyibqoRC5Dckoyvj6+\nHDx1kK4TuxK1O4odw3dQrlA5mpRrQr1S9dKmdUdWidTCfCIiOUwJjsglWLB9AY/+9CiJKYksvmcx\nwYHBFC9QnMdaP5bW3TSyzUiXoxQRESU4Ihn4e+/ffLz8Y6oUq8L9ze6ngF8BAK6pcg3WWnyMDzNv\nmelylCIici4lOCLnWLV/FYXzF6ZikYrM2DCDsVFjGdpkKACNyzVm4d0LXY5QREQuRoOMRc7Qb1o/\n6r1Xj3f+egeAfzX5F/se3seoa0e5HJmIiFwKJTiSZ1lrefvPt2n+YXMW7nRaZbrX7M47nd/h4ZbO\nlO5igcUoElDEzTBFROQyqItK8pRDsYeYvn46t9W/DV8fX75c8yXxyfGcSjwFQO86vV2OUEREsoIS\nHMn1klKSyOeTj+PxxwkZFUJsUixVilWhbaW2fN/ve+33JCKSC6mLSnKtHUd30HdqXyqPrkxCcgKF\n8hfijWvfIOqeKNpUbAOg5EZEJJdSC47kGskpyczbNo+tR7YyoNEACucvzG87fqNbjW4cjz9O8QLF\nGRQxyO0wRUQkByjBEa9nrcUYw5drvuTmr26mbFBZ+of3p2hAUXYM34GPUUOliEheo09+8VrL9y6n\n79S+9JvWD4DutbozpdcUNt+/mXw+Tu6u5EZEJG/Sp794laNxR9l0aBMA0ceimbN5DiGFQ7DWEpAv\ngN51ehPoF+hylCIi4jZ1UYnX+HjZx9w36z6ahTRj7u1z6VytM9EPRqdtnyAiInKaEhzxWHFJcUxZ\nPYViAcXoVrMbtUrUok+dPgxpMgQAXx9fCvgouRERkfMpwRGPc3rQ8ONzH2fUolH0CutFt5rdaFGh\nBS0qtHA7PBER8QIagyMe48fNP9Lpf50Y9Yez79PQJkOZe/tcpvSa4nJkIiLibZTgiKv2ntjLgZMH\nAJi/fT6r9q+ioH9BAKoGV6VD5Q4YY9wMUUREvJASHHHNv3/8NxXeqMCbi94E4LHWj7HtgW0Mjhjs\ncmQiIuLtlOBIjolPiuedv95hzYE1AFQLrsb9Te+nf3h/wNk24fT6NSIiIldCf00kx9wy7RamrZ3G\nix1eJKxkGAMbD3Q7JBERyaWU4Ei2Oz0r6pGWj9C3Tl961+ntdkgiIpLLKcGRbPXh0g+ZuHIis2+d\nTfOQ5jQPae52SCKShyQmJhIdHU1cXJzbocglCggIICQkBD8/v8u6XgmOZJsNMRsY/N1gIqtEEpsY\ni7+vv9shiUgeEx0dTaFChQgNDdWMTC9irSUmJobo6GgqV658WXUowZEsd+DkAYoFFqNG8RrM7z+f\n5iHN8fXxdTssEcmD4uLilNx4IWMMxYsX58CBA5ddh2ZRSZb6a9dfNHy/ISPnjgSgVcVWSm5ExFVK\nbrzTlf7clOBIlpq/bT5+vn70q9fP7VBERCQPU4IjVywxOZHvNnwHwMMtH2b5oOU0KNPA5ahERDyD\nr68v4eHh1K1bl969e3Pq1CkAgoKCLnpty5YtL+le/fv3Z+rUqQAcOnSIhg0b8vHHH7Nt2zaMMbz9\n9ttpZe+9914++eSTtOvKly9PfHw8AAcPHiQ0NPSS7u1plODIFTkWf4yrJ1xNty+6sWLfCowxFAko\n4nZYIiKXb88eaNcO9u7NkuoCAwNZvnw5q1atwt/fn7Fjx2b62oULF17WPY8ePcq1117LwIEDufPO\nOwEoVaoUo0ePJiEhId1rfH19+eijjy7rfp5ICY5ckSD/IMoEleF/Pf5H/dL13Q5HROTKPfcc/PYb\nPPtsllfdpk0bNm3adNaxEydOEBkZSaNGjahXrx7ffvtt2rnTrTzz5s2jffv29OrVi1q1atGvXz+s\ntene48SJE3Tu3JlbbrmFIUOGpB0vWbIkkZGRfPrpp+le98ADD/DGG2+QlJR0pW/TI2gWlVyWz1d8\nTtGAonSp0YVJvSa5HY6IyMU98AAsX37h8wsWQErKP6/fe895+PhAmzbpXxMeDm++manbJyUlMWvW\nLDp16nTW8YCAAL7++msKFy7MwYMHad68Oddff/15g2yXLVvG6tWrKVeuHK1ateL333+ndevW593n\nwQcfZMCAAQwfPvy8c48++iidO3fmrrvuOu9cxYoVad26NRMmTKBbt26Zek+eTC04csnGLx3PrV/f\nyril49wORUQk6zRtCqVKOQkNOF9LlYJmza6o2tjYWMLDw4mIiKBixYrcfffdZ5231jJy5Ejq169P\nx44d2bVrF/v27UsnvKaEhITg4+NDeHg427ZtS/d+HTp04Ntvv2X//v3nnatSpQrNmjVj4sSJ6V47\nYsQIXn31VVLOTPS8lFpwJNNOb7nQo3YPoo9FM7LNSLdDEhHJvMy0tAwZAuPGQUAAJCRAz54wZswV\n3fb0GJwL+fzzzzlw4ABLlizBz8+P0NDQdFdezp8/f9pzX1/fC3Yl9e3bl1atWnHdddfxyy+/UKhQ\nobPOjxw5kl69etGuXbvzrq1evTrh4eFMmTIls2/PY6kFRzLl771/0+SDJmw9vJXgwGCebv80fr6X\nt3y2iIjH2rcPBg+GRYucr1k00DgjR48epVSpUvj5+fHLL7+wffv2K65z+PDhREZGcuONN543qLhW\nrVqEhYUxY8aMdK99/PHHee211644BrcpwZGLSk5Jpu9Xfdl7Yi9H4o64HY6ISPaZNg3efRcaNHC+\nTpuW7bfs168fUVFR1KtXj88++4xatWplSb2vvPIKISEh3Hbbbed1OT3++ONER0ene12dOnVo1KhR\nlsTgJnOhUdh5QUREhI2KinI7DI+VnJLMkbgjFC9QnJX7VlKyYEnKBJVxOywRkUxbu3YttWvXdjsM\nuUzp/fx+qrTvAAAgAElEQVSMMUustREXuzZbW3CMMZ2MMeuNMZuMMY+lcz6/MWZy6vk/jTGhZ5wb\nkXp8vTHm2ovVaRwvGGM2GGPWGmPuz873ltsdjj1Ml4ld6Px5ZxKTE6lXup6SGxER8RrZluAYY3yB\nd4HOQBhwszEm7JxidwOHrbXVgDeAV1KvDQP6AnWATsAYY4zvRersD1QAallrawOau3wF1ses5/ed\nvzOw8UCNtREREa9z0QTHGFPDGDPXGLMq9XV9Y8wTmai7KbDJWrvFWpuAk3DccE6ZG4DTKw5NBSKN\nM/H/BmCStTbeWrsV2JRaX0Z1DgGetdamAFhrz58fJxmy1vLDph9ISE6geUhztg3bxoBGA9wOS0RE\n5JJlpgXnA2AEkAhgrV2B07pyMeWBnWe8jk49lm4Za20ScBQonsG1GdVZFehjjIkyxswyxlRPLyhj\nzMDUMlFXsg17btR9cnc6fd6J0YtGA1C8QHGXIxIREbk8mUlwClhr/zrnmCeu45wfiEsdePQBkO6G\nGtbacdbaCGttRMmSJXM0QE8UtTuKAyedRO/qKlfzVqe3GNZ8mMtRiYiIXJnMJDgHjTFVAQtgjOkF\n7MnEdbtwxsScFpJ6LN0yxph8QBEgJoNrM6ozGjg9n+9rQBsjXcTQmUNp8kETRv0xCoB7m97Lfc3u\nw9/X3+XIRERErkxmEpx/Ae8DtYwxu4AHcMa7XMxioLoxprIxxh+nW2v6OWWmA3ekPu8F/GydeevT\ngb6ps6wqA9WBvy5S5zfAVanP2wEbMhFjnrMxZiM7jzq9fM3KN+PZ9s8yos0Il6MSEfEcq1dD3brO\n16ywd+9e+vbtS9WqVWncuDHXXXcdGzZkz5+omJgYwsPDCQ8Pp0yZMpQvXz7t9YV2Eb9cTzzxBG+m\nrg4dGxtLhw4deP7550lKSsIYw6OPPppW9uWXX+b5559Puy4oKIiDBw+mnT+9qWhWumiCkzqgtyNQ\nEmeGUmtr7bZMXJcE3Av8AKwFplhrVxtjnjXGXJ9abDxQ3BizCXgQeCz12tXAFGANMBv4l7U2+UJ1\nptb1MtDTGLMSeAnQ6NhzPDf/OWq/W5tn5j0DwB3hd/BkuycpnL+wu4GJiHiIkyfhuutgzRro0sV5\nfSWstfTo0YP27duzefNmlixZwksvvZTuXlNZoUiRIixfvpzly5czePBghg8fnvba3/+f1nlrbZbt\nNxUfH0+PHj1o2bIlTzzhzEEKDAxkypQpHDp0KN1rgoODeeONN7Lk/heSmVlURVPXlHkOeMEY85Yx\n5q3MVG6t/d5aW8NaW9Va+0LqsaestdNTn8dZa3tba6tZa5taa7ecce0LqdfVtNbOyqjO1ONHrLVd\nrLX1rLUtrLV/Z/7bkHvtPr6bzYc2A1CvdD3ubXovL0a+6HJUIiKe6a67YP9+sNbZteGcfTEv2S+/\n/IKfnx+DBw9OO9agQQPatGmDtZZHHnmEunXrUq9ePSZPngw4e0nNnDkzrXz//v2ZOnUqycnJPPLI\nIzRp0oT69evz/vvvAzBv3jzatGnD9ddfT1jYuaux/GPTpk2EhYXRr18/6tSpw549e5g1axYtWrSg\nUaNG9OnTh5OpGd3ixYtp164djRs3pnPnzhdMyBITE+nduzd16tRJa6EB8Pf356677mL06NHpXjdg\nwAA+//xzjh49msnv5KXLzGab3wOLgJWA928vmoeMWzKOYbOH0bFKR2bcPIPutbrTvVZ3t8MSEXHF\nAw9ABntesmcPbNoEpxs24uLgyy9h2TIoWzb9a8LDM97Dc9WqVTRu3Djdc9OmTWP58uX8/fffHDx4\nkCZNmtC2bVv69OnDlClT6NKlCwkJCcydO5f33nuP8ePHU6RIERYvXkx8fDytWrXimmuuAWDp0qWs\nWrWKypUrZ/g9WLduHZ999hkRERHs37+fl19+mblz51KgQAFeeOEFRo8ezUMPPcSwYcOYPn06JUqU\n4PPPP+fJJ59k3Lhx59X30ksv0alTJ15//fXzzt13332Eh4fz8MMPn3eucOHC3H777bz11ls8+eST\nGcZ8uTKT4ARYax/MlrtLljsSd4R9J/ZRs0RNahavyU11buKptk+5HZaIiMfbuvWf5Oa0lBTn+IUS\nnCvx22+/cfPNN+Pr60vp0qVp164dixcvpnPnzgwbNoz4+Hhmz55N27ZtCQwMZM6cOaxYsYKpU6cC\nziadGzduxN/fn6ZNm140uQGoWrUqERHOLgcLFy5kzZo1tGzZEoCEhARat27N2rVrWb16NR07dgQg\nOTmZkJCQdOtr06YNv/32G5s2baJatWpnnStatCi33HIL77zzDs4Sd2d74IEHaNSoEcOHD8/8N+0S\nZCbBmWCMuQf4Dog/fdBam37Hmrhm2tpp3D39bqoHV+fPAX/SLrQd7ULbuR2WiIhHyKilBeCjj+D+\n+88ed1OgALzzDtx55+Xds06dOmkJSWYFBATQvn17fvjhByZPnkzfvs7Sc9Za3n77ba699tqzys+b\nN4+CBQtmqu4zy1lr6dSpExMmTDirzLJly6hfvz4LFiy4aH1XXXUVt9xyC507d2bBggWUKXP2lj4P\nPvggTZo04bbbbjtrDBA443Buuukmxo4dm6nYL1VmZlElAK8CfwBLUh/aodJDxCXFsfbAWgCqB1en\ndcXWvN/1/XSzZRERubC77nIGFgcEOK8DAqBbt8tPbgA6dOhAfHz8Wd07K1asYMGCBbRp04bJkyeT\nnJzMgQMH+PXXX2natCkAffr04eOPP2bBggV06tQJgGuvvZb33nuPxMREADZs2JA2ZuZytGzZkvnz\n57NlizP89eTJk2zcuJGwsDB27drFX385S+AlJCSwOoMpZX369OH++++nc+fOHDt27KxzJUqUoEeP\nHnzyySfpXvvQQw8xZsyYLBvwfKbMJDgPAdWstaHW2sqpjypZHolcsvnb5lPtrWp0+6IbSSlJ1Ctd\njxk3z6Bh2YZuhyYi4pU++ghKlQJjoHRpGD/+yuozxvD111/z008/UbVqVerUqcOIESMoU6YMPXr0\noH79+jRo0IAOHTrw3//+N60F5JprrmH+/Pl07NgxreVjwIABhIWF0ahRI+rWrcugQYNISrr8dXdL\nly7N+PHj6dOnDw0aNKBly5Zs2LCB/PnzM3XqVB588EHq169Pw4YN+fPPPzOs67777qNLly7ccMMN\nJCcnn3XukUceYf/+9HdPKl26NF27ds3yKewAxll2JoMCxswBultrT2X53V0WERFho6K8qzEqOSWZ\nDTEbqF2yNjuO7uCOb+7gqbZPcVXlqy5+sYhIHrN27Vpq1659SdesXg19+sDkyVCnTjYFJpmS3s/P\nGLMkddeCDGVmDM5JYLkx5hfOHoNz/6UGKldu8HeD+Xb9t2wZtoWKRSryyx2/uB2SiEiuUqcOrFrl\ndhRypTKT4HyT+hCXWWtZGL2QyCqRFPTL3IAyERGRvOiiCY619tOcCEQuzhjDqiGrOJV4SoOIRURE\nMnDBBMcYM8Vae1Pq1gfnDtSx1toG2RuanCsxORE/Xz8K+qv1RkREJCMZteAMS/26FnjkjOMG+G+2\nRSQX1GdqH+KT45l5y8yLFxYREcnDLjhN3Fq7J/VpNWvt9jMe24BaORKdpEmxKczfPp/SBUu7HYqI\niIjHu2CCY4wZkto9VdMYs+KMx1ZgRc6FKAAGw0+3/cTDLc/f00NERDxXUFBQ2vPvv/+eGjVqsH37\ndp555hnKly9PeHg41atX58Ybb2TNmjXnXb9y5UrCw8MJDw8nODiYypUrEx4enraVgqQvoy6qicAs\n4CXgsTOOH9c2DTnPGKMF/EREvNjcuXO5//77+eGHH6hUqRIAw4cPT9uMcvLkyXTo0IGVK1dSsmTJ\ntOvq1avH8tRdQvv370/Xrl3p1avXefUnJSWRL19mJkfnDRl1UR211m6z1t58TheVkhsXjPhpBK/+\n/qrbYYiIyGX49ddfueeee/juu++oWrVqumX69OnDNddcw8SJEzNd708//UT79u3p2rUr9erVA+DT\nTz+ladOmhIeHM3To0LRtEGbNmkWLFi1o1KgRffr0Sdvm4ZFHHiEsLIz69evz6KOPXuE79RyZ2apB\nXJZiU/hg6QesOXh+06WIiGRe+0/a0/6T9qw/uB6A1xa+RvtP2vPawtcAWH9wfVqZ0wbOGEj7T9oz\nY/0MAGasn0H7T9ozcMbATN0zPj6e7t27880331CrVsZDWBs1asS6desu6T1FRUUxZswY1q5dy6pV\nq/j6669ZuHAhy5cvJykpiUmTJrF//35efvll5s6dy9KlS6lfvz6jR49m3759fP/996xevZoVK1Yw\nYsSIS7q3J1NblhdISE7gwRYP0qRcE7dDERGRS+Tn50fLli0ZP348o0ePzrDsxbZPSk+LFi2oWLEi\n4LToLF68mIgIZyeD2NhYKlSoQIECBVizZg0tW7YEnA00W7duTXBwMD4+Ptxzzz106dKFrl27XvL9\nPZUSHC8QkC+AkW1Guh2GiIjXm9d/3lmvH2758FmTN2qWqHlemXHdxp31ulvNbnSr2S3T9/Tx8WHK\nlClERkby4osvMnLkhT/Ply1bRkREBH/++SeDBg0C4Nlnn+X666+/4DUFC/6zNpq1lrvuuovnnnvu\nrDJff/01nTp1YsKECeddHxUVxY8//siXX37Je++9x5w5czL93jyZEhwv8MXKLwgtGkqLCi3cDkVE\nRC5DgQIFmDlzJm3atKF06dLcfffd55X56quvmDNnDq+//jolS5ZMG1h8KTp27EivXr0YNmwYJUqU\nICYmhpMnT9KyZUuGDRvGli1bqFKlCidPnmT37t2UKVOGuLg4unbtSsuWLalZs2ZWvF2PoATHw6XY\nFO6ffT9dqndRgiMi4sWCg4OZPXs2bdu2TZsl9cYbb/C///2PkydPUrduXX7++eezZlBdqnr16vH0\n00/TsWNHUlJS8PPzY+zYsTRp0oTx48fTp08fEhISAHjxxRcJDAzkxhtvJD4+npSUFEaNGpUl79UT\nmMvp78stIiIibFRUlNthZOjgqYP0mNyDQY0HcWv9W90OR0TEq6xdu5batWu7HYZcpvR+fsaYJdba\niItdqxYcD1eiQAkW3LnA7TBERES8iqaJe7gNMRtITE50OwwRERGvogTHg1lrafVRKwZ/N9jtUERE\nvFZeHorhza7056YEx4NtObyFQ7GHaF2xtduhiIh4pYCAAGJiYpTkeBlrLTExMQQEBFx2HRqD48Gq\nBlcl5t8x5PPRj0lE5HKEhIQQHR3NgQMH3A5FLlFAQAAhISGXfb3+cnoway1FA4q6HYaIiNfy8/Oj\ncuXKbochLlAXlYey1lL73dq8uehNt0MRERHxOkpwPNTag2tZH7OewvkLux2KiIiI11EXlYcKKRzC\nlF5TNMBYRETkMijB8VCF8xemd53ebochIiLildRF5YGstdwz/R5+3vqz26GIiIh4JSU4HmjdwXV8\nuOxDth7e6nYoIiIiXkkJjgfyMT7cGX4nHSp3cDsUERERr6QxOB6oZomafHTDR26HISIi4rXUguNh\nrLVMXDmRvSf2uh2KiIiI11KC42HWx6yn37R+fLfhO7dDERER8VpKcDzMzqM7KRNUhvah7d0ORURE\nxGtpDI6Hubrq1ex+cLfbYYiIiHg1teB4EGst+0/uxxiDMcbtcERERLyWEhwPsiFmA6VfK82kVZPc\nDkVERMSrKcHxIL9u/xWARmUbuRyJiIiId9MYHA9yV8O7aFq+KdWDq7sdioiIiFdTguNBfH18aVCm\ngdthiIiIeD11UXmIDTEbiBgXwaLoRW6HIiIi4vWU4HiIedvmsWTPEooFFHM7FBEREa+nBMdDtK3U\nlteufo0axWu4HYqIiIjX0xgcD1GrRC1qlajldhgiIiK5glpwPMC2I9t48ucn2Xl0p9uhiIiI5ArZ\nmuAYYzoZY9YbYzYZYx5L53x+Y8zk1PN/GmNCzzg3IvX4emPMtZdQ51vGmBPZ9Z6yw4+bf+T5Bc9z\nMvGk26GIiIjkCtmW4BhjfIF3gc5AGHCzMSbsnGJ3A4ettdWAN4BXUq8NA/oCdYBOwBhjjO/F6jTG\nRABeN0o3ODCYbjW6UbN4TbdDERERyRWyswWnKbDJWrvFWpsATAJuOKfMDcCnqc+nApHG2YTpBmCS\ntTbeWrsV2JRa3wXrTE1+XgX+nY3vKVv0DOvJ9Juna/8pERGRLJKdCU554MxBJdGpx9ItY61NAo4C\nxTO4NqM67wWmW2v3ZFH8OeLAyQMs3LmQxOREt0MRERHJNXLFIGNjTDmgN/B2JsoONMZEGWOiDhw4\nkP3BXcT09dNp9VErNh/e7HYoIiIiuUZ2Jji7gApnvA5JPZZuGWNMPqAIEJPBtRc63hCoBmwyxmwD\nChhjNqUXlLV2nLU2wlobUbJkyct7Z1lo25FtlCtUTuNvREREslB2JjiLgerGmMrGGH+cQcPTzykz\nHbgj9Xkv4GdrrU093jd1llVloDrw14XqtNbOtNaWsdaGWmtDgVOpA5c93nMdnmPL/Vs0/kZERCQL\nZVuCkzqm5l7gB2AtMMVau9oY86wx5vrUYuOB4qmtLQ8Cj6VeuxqYAqwBZgP/stYmX6jO7HoP2S0h\nOYEUm0L+fPkzf9GePdCuHezdm32BiYiIeDnjNJjkTRERETYqKsq1+3+07CMemvMQK4esJKRwSOYu\nGjoU3n8fBg2CMWOyN0AREREPY4xZYq2NuFi5XDHI2FvN2zYPf19/yhc6d3JZOgIDwRh47z1ISXG+\nGuMcFxERkbMowXHRa9e8xjd9vsnc+JstW6BHj39e588P/frB1q3ZF6CIiIiX0mabLipVsBSlCpbK\nXOGyZWH9+n9ex8c7SU6ZMtkTnIiIiBdTC45Lpq6ZSt+pfTkWfyxzF6xfD2vWQN26MGGCc+zHH7Mv\nQBERES+mBMclMzbM4OetP1PIv1DmLnj8cQgKgp9+gltvhWeegZ07YcqUbI1TRETEG6mLyiU9avWg\nWflmmRt/s2gRfPWVk9SULu0ce/xxmDULBg+GVq2gfCYGKouIiOQRmibu4jTxTLHWWfdm/XrYtAkK\nndHis3EjhIdDy5bwww/gowY5ERHJ3TRN3IP9tuM3Pl3+aeY22Jw5ExYsgKefPju5AaheHd54w+m2\nevui23CJiIjkGWrBcaEFp/83/Zm5cSb7Ht6Hj8kgx0xOhgYNnBlTa9aAn9/5ZayF6693BhwvXQph\nYdkXuIiIiMvUguPBggOD6VW7V8bJDcBnn8Hq1fDii+knN+As9vfhh1C4sLMuTkJC1gcsIiLiZdSC\n46ljcGJjoUYNKFfOGWR8scHI06fDDTfAY4/BSy/lTIyXas8e6NsXJk/W+j0iInJZ1ILjobYf2c6+\nE/suXvDttyE6Gl555eLJDTjdVAMGOOUXLLjyQLPDc8/Bb7/Bs8+6HYmIiORyasHJ4RacO7+9k+82\nfMf+h/dfeIr4oUNQtaozO2rmzMxXfuKEM6sqKQlWrHC6rTxBYCDExZ1/PCDAaakSERHJJLXgeKi/\n9/5N20ptM17/5qWX4OhRePnlS6s8KMhZ5XjnTrj//isLNCtt3gz16p19rFQpmDfPlXBERCT3U4KT\nw6IGRvFBtw8uXGDHDqd76vbbz08KMqNFCxg5Ej791Fkc0G3Wwuuvw8qVzuuAAKfL7fBhiIyEceOc\nMiIiIllICU4OstbiY3wIDgy+cKGnnnK+Xsk4laeegogIGDTIGdjrluRkuOceGDUKqlSBIUOcAdND\nhkCHDtC8uRNjly6we7d7cYqISK6jBCcHDZwxkGsmXHPhAitWOFPD77sPKla8/Bv5+cH//genTsFd\nd7nTQpKQALfcAuPHwxNPOKswjxnjrOvz7rswezbMmeO0Vs2b52wiOnGiWnNERCRLKMHJQXO3zqWg\nf8ELF3jsMShSBEaMuPKb1awJr73mJBJjxlx5fZfi1Cno3t3ZCPTVV53ZU+mNOfLxgXvvheXLnXj7\n9YPeveHAgZyNV0REch0lODnEWsvEnhMZ2Xpk+gV++cXZPHPECAjOoAvrUgwZAp06wcMPw7p1WVPn\nxRw7Bp07O4nV++87976YGjWc6eMvveSs51O3rvNVss6ePc6eZnv3uh2JiEiOUIKTQ4wxNA9pTpPy\nTc4/aS08+iiEhDjdU1l3U/joIyhYEG69NftXOT540Blbs3Ch0900cGDmr/X1dVqwoqKgbFln0cI7\n73Rmk8mV0xpEIpLHKMHJIa/+/iqv/v5q+ienToXFi50/QoGBWXvjsmWdmUpLljj1Z5ddu5wWgtWr\n4ZtvnBWLL0f9+vDXX/D44854pHr1YO7crI01LwkMdBLd996DlBTnqzFZ/3smIuJhlODkkLFLxrIw\neuH5JxITnWnddevCbbdlz81vvBH693f2tFqYTgxXassWaNPGmeI+a5YzK+pK+PvD8887sQYGQseO\nTsvWqVNZE29ekZLiDPD29T37eLFiznY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MVY86wy8AyBWRnilOZlKoaqXTPwDg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\npyWlUz6tq/sAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10eeb6bd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "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 of brute solver\", \"Training Accuracy of brute solver\", \n",
    "          \"Test Accuracy of cover tree solver\", \"Training Accuracy of cover tree solver\", \n",
    "          \"Test Accuracy of kdtree solver\", \"Training Accuracy of kdtree solver\"])\n",
    "\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": {
    "deletable": true,
    "editable": true
   },
   "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": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Comparison to Multiclass Support Vector Machines"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "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": {
    "deletable": true,
    "editable": true
   },
   "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": 37,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "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": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Let's apply the SVM to the same test data set to compare results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "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": {
    "deletable": true,
    "editable": true
   },
   "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": 39,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy = 94.69%\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a103590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "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": {
    "deletable": true,
    "editable": true
   },
   "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
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}