KNN1.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": 1,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "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": {
    "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": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108e50490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ba8e790>"
      ]
     },
     "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": 3,
   "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": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108e50050>"
      ]
     },
     "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": 5,
   "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": 6,
   "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": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Standard KNN took 1.0s\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: predictiong 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 be caused be the high-dimensional data that we used. We now use low-dimensional data to verify it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(4, 150)\n",
      "(4, 100)\n",
      "(4, 50)\n"
     ]
    }
   ],
   "source": [
    "# The data set is Ronald Fisher's measurements of type, petal width (PW), petal length (PL), sepal width (SW), \n",
    "# and sepal length (SL) for a sample of 150 irises. \n",
    "# Check more information in http://www.math.uah.edu/stat/data/Fisher.html\n",
    "low_dimension_martix = np.loadtxt('../../../data/multiclass/Fisher.txt')\n",
    "\n",
    "Xall_low = low_dimension_martix[:,[1, 2, 3, 4]].transpose()\n",
    "Yall_low = low_dimension_martix[:, 0]\n",
    "\n",
    "Xtrain_low = Xall_low[:, :100]\n",
    "Ytrain_low = Yall_low[:100]\n",
    "\n",
    "Xtest_low = Xall_low[:, 100:]\n",
    "Ytest_low = Yall_low[100:]\n",
    "\n",
    "print Xall_low.shape\n",
    "print Xtrain_low.shape\n",
    "print Xtest_low.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predictions [ 2.  0.  1.  1.  1.]\n",
      "Ground Truth [ 2.  0.  2.  2.  1.]\n",
      "Accuracy = 92.00%\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": 10,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Standard KNN took 0.0065s\n",
      "Covertree KNN took 0.0008s\n",
      "KDTree KNN took 0.0019s\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 now can see the KD-Tree solver is faster than the Standard KNN from above comparison which prove the KD-Tree is more suitable for low-dimensional data. 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": 11,
   "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 with and without Cover Tree. This takes a few seconds:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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": 13,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
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AZ8+epXXr1gQHB9OmTRvCwsLYcJXd1SdPnsynn35KREQEkZGRKcfnzp1L9erVU1ZGBvj3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eAAAP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\nP66yXsE9RfXGAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1103ba190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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11FOMHz8+ab0iRYoQGxsLwNGjRylRosQNbTujUYIj1xWXEAfAtuhtNP2qKZ+u\n/pSoU06NzaT7JtE/rD/ZArO5HKWISCo5cAAaNYKDB1OlueDgYNauXcuGDRsICAhgzJgxKV53xYoV\nN7XNEydO0KpVK/r168ejjz4KQP78+Rk5ciRxcXHJruPr68u4ceNuansZkRIcuaotR7fQaXInKo+u\njMd6KJ+3PPMemMf+Ifspmr2o2+GJiKSN//wHfvkFhg1L9aYbNGhAZGTkZdNOnz5Ns2bNqFatGpUr\nV2b27NlJ8y708ixZsoTGjRvTpUsXypcvz0MPPYS1NtltnD59mjZt2vDggw8yYMCApOn58uWjWbNm\nfPnll8muN2jQIEaMGEF8fPyt7maGoBocucyuv3axLXobrcq0IsQ/hPD94fSo0oOY+BhC/ENoV66d\n2yGKiNycQYNg7dqrz1+2DDyei+9Hj3YePj7QoEHy64SGwgcfpGjz8fHxzJ8/n9atW182PSgoiJkz\nZ5I9e3aOHj1K7dq16dChw9+G+9esWcPGjRspXLgw9erVY/ny5dSvX/9v2xkyZAh9+/Zl8ODBf5v3\n3HPP0aZNG3r37v23ecWLF6d+/fpMmDCBe+65J0X7lJGpB0eSzNs2j3Ifl+PR2Y+S4EmgeI7i7B28\nl+HNhxPiH+J2eCIiaatmTcif30lowHnOnx9q1bqlZs+dO0doaChhYWEUL16cPn36XDbfWssLL7xA\nlSpVaN68OVFRURw6dCiZ8GpStGhRfHx8CA0NZffu3clur2nTpsyePZvDhw//bV6pUqWoVasWkyZN\nSnbd559/nnfeeQfPpYleJpWmPTjGmNbASMAX+NxaO/yK+YHAV0B1IBroZq3dnTjveaAPkAA8Y61d\ncK02jZPqvg50TVxntLX2w7TcP2+x7+Q+imYvSsM7GvJkjSd5ts6z+Pr4ArpujYh4kZT0tAwYAJ99\nBkFBEBcH990Ho0bd0mYv1OBczcSJEzly5AirV6/G39+fEiVKJHv9l8DAwKTXvr6+Vx1K6t69O/Xq\n1aNt27YsXryYbNkur5F84YUX6NKlC40aNfrbumXLliU0NJSpU6emdPcyrDQ7ehljfIFPgDZABeAB\nY0yFKxbrA/xlrS0DjADeSly3AtAdqAi0BkYZY3yv02YvoBhQ3lp7FzA5rfbNW5yIOUHPmT258+M7\n2fXXLrIHZueD1h9QLEcxt0MTEXHHoUPw+OPw22/OcyoVGl/LiRMnyJ8/P/7+/ixevJg///zzltsc\nPHgwzZogPZ8dAAAgAElEQVQ149577/1bUXH58uWpUKECc+fOTXbdF198kXffffeWY3BbWv57XhOI\ntNbutNbG4SQcHa9YpiNwodppOtAssSemIzDZWhtrrd0FRCa2d602BwDDrLUeAGvt3/vm5DIBvgGs\nPrCaIbWHUChbIbfDERFx34wZ8MknULWq8zxjRppv8qGHHiIiIoLKlSvz1VdfUb58+VRp96233qJo\n0aL06NHjb0NOL774Ivv27Ut2vYoVK1KtWrVUicFN5mpV2LfcsDFdgNbW2r6J73sAtay1T12yzIbE\nZfYlvt8B1AJeBX6z1n6dOH0sMD9xtWTbNMZEA+8DnYEjOMNa25OJqx/QD6B48eLVUyNTzky2R2/n\n6flP827Ld6mUvxJxCXEE+Aa4HZaISJrYvHkzd911l9thyE1K7vdnjFltrQ273rreVGARCMQk7vT/\ngGRP5rfWfmatDbPWhuXLly9dA3SbtZaes3ry277f2HFsB4CSGxER8UppWWQchVMTc0HRxGnJLbPP\nGOMH5MApNr7Wulebvg+40Jc4E/jiFuP3Gsv3LCfIL4jqhaszrsM4cgbl1JCUiIh4tev24Bhjyhlj\nfkocTsIYU8UY81IK2g4HyhpjShpjAnCKhudcscwc4JHE112ARdYZM5sDdDfGBBpjSgJlgVXXaXMW\n0CTxdSNgWwpi9HofrvyQ+l/U55UlrwBwV767lNyIiIjXS8kQ1f+A54HzANbadTiJxTVZa+OBp4AF\nwGZgqrV2ozFmmDGmQ+JiY4E8xphIYAjwr8R1NwJTgU3A98CT1tqEq7WZ2NZw4D5jzHrgv0DfFOyb\nV7LWcviMU2PdolQLhtQewuQuOqlMRERuH9ctMjbGhFtraxhj1lhr706cttZaG5ouEaahsLAwGxER\n4XYYqSrqZBSPf/s4m45sYv2A9bpAn4jc1lRknLmldZHxUWNMacAmNtwFOHAzgUraO+85z6qoVTxV\n4ykVEIuIyG0rJQnOk8CnQHljTBQwCOeaM5JB/H7gd9pPas+JmBOUyFmC3QN3M7jOYPx8dKsxEZEb\ntXEjVKrkPKeGgwcP0r17d0qXLk316tVp27Yt27alTZlodHQ0oaGhhIaGUrBgQYoUKZL0/mp3Eb9Z\nL730Eh8kXh363LlzNG3alNdff534+HiMMTz33HNJyw4fPpzXX389ab2sWbNy9OjRpPkXbiqamq6b\n4CReVK85kA/nKsH1L9xOQdx37vw5Wn/dmtUHVrMt2vnABPsHuxyViEjmdOYMtG0LmzZBu3bO+1th\nraVz5840btyYHTt2sHr1av773/8me6+p1JAjRw7Wrl3L2rVrefzxxxk8eHDS+4CAi7361tpUu99U\nbGwsnTt3pm7durz0knMOUnBwMFOnTuXYsWPJrpM7d25GjBiRKtu/mpScRZXTGPMM8B/gDWPMh8YY\n3ePJZd9t/45Dpw8R7B/MjG4z2PzkZmoUqeF2WCIimVrv3nD4MFjr3LXhivti3rDFixfj7+/P448/\nnjStatWqNGjQAGstQ4cOpVKlSlSuXJkpU6YAzr2kvv3226Tle/XqxfTp00lISGDo0KHUqFGDKlWq\n8OmnnwKwZMkSGjRoQIcOHahQ4co7Il0UGRlJhQoVeOihh6hYsSIHDhxg/vz51KlTh2rVqtGtWzfO\nJGZ04eHhNGrUiOrVq9OmTZurJmTnz5+na9euVKxYMamHBiAgIIDevXszcuTIZNfr27cvEydO5MSJ\nEyn8Sd64lIxhfAf8BqwHMv/tRb3AM/Of4aNVHzG07lDebvE29YvXdzskEZEMb9AguMY9LzlwACIj\n4ULHRkwMTJsGa9ZAoatcXSM09Nr38NywYQPVq1dPdt6MGTNYu3Ytf/zxB0ePHqVGjRo0bNiQbt26\nMXXqVNq1a0dcXBw//fQTo0ePZuzYseTIkYPw8HBiY2OpV68eLVu2BOD3339nw4YNlCxZ8po/gy1b\ntvDVV18RFhbG4cOHGT58OD/99BMhISG88cYbjBw5kmeffZaBAwcyZ84c8ubNy8SJE3n55Zf57LPP\n/tbef//7X1q3bs177733t3lPP/00oaGh/OMf//jbvOzZs9OzZ08+/PBDXn755WvGfLNSkuAEWWuH\npMnW5aY0KdGEAlkKMLTeULdDERHxGrt2XUxuLvB4nOlXS3BuxS+//MIDDzyAr68vBQoUoFGjRoSH\nh9OmTRsGDhxIbGws33//PQ0bNiQ4OJiFCxeybt06pk+fDjg36dy+fTsBAQHUrFnzuskNQOnSpQkL\nc05AWrFiBZs2baJu3boAxMXFUb9+fTZv3szGjRtp3rw5AAkJCRQtWjTZ9ho0aMAvv/xCZGQkZcqU\nuWxezpw5efDBB/n4449xbjN5uUGDBlGtWjUGDx6c8h/aDUhJgjPBGPMYMA+IvTDRWpv8wJqkGY/1\nYDB0vqszne/q7HY4IiKZyrV6WgDGjYNnnrm87iYkBD7+GB599Oa2WbFixaSEJKWCgoJo3LgxCxYs\nYMqUKXTv7lx6zlrLRx99RKtWrS5bfsmSJWTJkiVFbV+6nLWW1q1bM2HChMuWWbNmDVWqVGHZsmXX\nba9JkyY8+OCDtGnThmXLllGwYMHL5g8ZMoQaNWrQo0ePy2qAwKnDuf/++xkzZkyKYr9RKTmLKg54\nB/gVWJ348K6Lx2QSq6JWUeDdAvy691e3QxER8Tq9ezuFxUFBzvugILjnnptPbgCaNm1KbGzsZcM7\n69atY9myZTRo0IApU6aQkJDAkSNH+Pnnn6lZsyYA3bp144svvmDZsmW0bt0agFatWjF69GjOnz8P\nwLZt25JqZm5G3bp1Wbp0KTt37gTgzJkzbN++nQoVKhAVFcWqVasAp2dn4zVOKevWrRvPPPMMbdq0\n4eTJk5fNy5s3L507d2b8+PHJrvvss88yatSoVCt4vlRKEpxngTLW2hLW2pKJj1KpHolc189//syR\ns0conbu026GIiHilceMgf34wBgoUgLFjb609YwwzZ87kxx9/pHTp0lSsWJHnn3+eggUL0rlzZ6pU\nqULVqlVp2rQpb7/9dlIPSMuWLVm6dCnNmzdP6vno27cvFSpUoFq1alSqVIn+/fsTHx9/07EVKFCA\nsWPH0q1bN6pWrUrdunXZtm0bgYGBTJ8+nSFDhlClShXuvvtuVq5cec22nn76adq1a0fHjh1JSEi4\nbN7QoUM5fPjwVWNo3759qp/CDim7kvFCoJO19myqb91lme1KxgdPH2TlvpV0LN/R7VBERDKFm7mS\n8caN0K0bTJkCFSumUWCSIrdyJeOU1OCcAdYaYxZzeQ3OMzcaqNyaglkLKrkREUljFSvChg1uRyG3\nKiVDVLOAN4AVXKzBWZ2WQcnfbTqyiUdmPcKOYzvcDkVERCTDu24PjrX2y/QIRK7tx50/8tUfX/F6\nk9evv7CIiMht7qoJjjFmqrX2fmPMehJvtHkJa62tmrahyaUq5KvAMzWfoViOYm6HIiIikuFdqwdn\nYOLzZuDSK8oZ4O00i0iS1bxUc5qXau52GCIiIpnCVWtwrLUHEl+Wsdb+ecljN1A+XaITAPad3Mf/\nrf8/TsaevP7CIiIicvUExxgzIHF46k5jzLpLHruAdekXony3/TsenPEgh06nzd1nRUQk7WTNmjXp\n9XfffUe5cuX4888/efXVVylSpAihoaGULVuWe++9l02bNv1t/fXr1xMaGkpoaCi5c+emZMmShIaG\nJt1KQZJ3rSGqScB84L/Avy6Zfkq3aUhf586fo3L+ypTJXeb6C4uISIb0008/8cwzz7BgwQLuuOMO\nAAYPHpx0M8opU6bQtGlT1q9fT758+ZLWq1y5MmsT7xLaq1cv2rdvT5cuXf7Wfnx8PH5+Kbn6y+3h\nWkNUJ6y1u621D1wxRKXkJp0NrD2QdQPWJXuzMhERyfh+/vlnHnvsMebNm0fp0slfjb5bt260bNmS\nSZMmpbjdH3/8kcaNG9O+fXsqV64MwJdffknNmjUJDQ3liSeeSLoNwvz586lTpw7VqlWjW7duSbd5\nGDp0KBUqVKBKlSo899xzt7inGUdKroMjLjodd5pj55RTioikhsbjG9N4fGO2Ht0KwLsr3qXx+Ma8\nu+JdALYe3Zq0zAX95vaj8fjGzN06F4C5W+fSeHxj+s3tl6JtxsbG0qlTJ2bNmkX58tcuYa1WrRpb\ntmy5oX2KiIhg1KhRbN68mQ0bNjBz5kxWrFjB2rVriY+PZ/LkyRw+fJjhw4fz008/8fvvv1OlShVG\njhzJoUOH+O6779i4cSPr1q3j+eefv6FtZ2RKcDK4GZtnkOftPEkfRhERyVz8/f2pW7cuY1NwY6vr\n3T4pOXXq1KF48eKA06MTHh5OWFgYoaGhLF26lB07drBixQo2bdpE3bp1CQ0NZeLEiezevZvcuXPj\n4+PDY489xsyZM1N8V/LMQIN1GdyKvSvIFZSLsnnKuh2KiEimt6TXksve/6PuP/hH3X8kvb8z751/\nW+azez677P09d97DPXfek+Jt+vj4MHXqVJo1a8abb77JCy+8cNVl16xZQ1hYGCtXrqR///4ADBs2\njA4dOlx1nUuTEmstvXv35j//+c9ly8ycOZPWrVszYcKEv60fERHBDz/8wLRp0xg9ejQLFy5M8b5l\nZEpwMriP237MP+r+Ax+jzjYRkcwqJCSEb7/9lgYNGlCgQAH69Onzt2W++eYbFi5cyHvvvUe+fPmS\nCotvRPPmzenSpQsDBw4kb968REdHc+bMGerWrcvAgQPZuXMnpUqV4syZM+zfv5+CBQsSExND+/bt\nqVu3LnfeeWdq7G6GoAQng/Pz8dPZUyIiXiB37tx8//33NGzYMOksqREjRvD1119z5swZKlWqxKJF\niy47g+pGVa5cmVdeeYXmzZvj8Xjw9/dnzJgx1KhRg7Fjx9KtWzfi4uIAePPNNwkODubee+8lNjYW\nj8fD+++/nyr7mhGYmxnv8xZhYWE2IiLC7TCuasbmGbyz4h2+uf8bCmcr7HY4IiKZzubNm7nrrrvc\nDkNuUnK/P2PMamtt2PXW1bhHBrZo1yLWH1pP/iz53Q5FREQkU9EQVQbWK7QXtYrUws9HvyYREZEb\noSNnBhZWOIywwtfthRMRkWuw1upCqZnQrZbQaIgqg1qxdwXDlg7jRMwJt0MREcm0goKCiI6OvuWD\npaQvay3R0dEEBQXddBvqwcmgvtn0DZ+Ef8I/6/3T7VBERDKtokWLsm/fPo4cOeJ2KHKDgoKCKFq0\n6E2vrwQngyqduzR97u5DkN/NZ68iIrc7f39/SpYs6XYY4gIlOBnUEzWecDsEERGRTEs1OBnQrr92\nER4VToInwe1QREREMiUlOBnQ2DVjqTO2Dufiz7kdioiISKakBCcDijoVRY0iNcgakNXtUERERDIl\n1eBkQF90/ILzCefdDkNERCTTUg9OBhMTH4O1Fn9ff7dDERERybSU4GQw7654l4LvFeTcedXfiIiI\n3CwlOBnM0j+XUjBrQYL9g90ORUREJNNSDU4G82WnLzlw6oDbYYiIiGRqSnAymMLZClM4W2G3wxAR\nEcnUNESVgYz9fSw9ZvbQGVQiIiK3SD04GcisrbPYFr1NZ1CJiIjcIiU4GchDlR/S2VMiIiKpQAlO\nBtK9Une3QxAREfEKqsHJIBbvWsyk9ZPwWI/boYiIiGR6SnAyiFERo3jhpxfwMfqViIiI3CodTTOI\nvMF56VS+k9thiIiIeAXV4GQQo9uPdjsEERERr6EenAxgz4k9RJ+NdjsMERERr5GmCY4xprUxZqsx\nJtIY869k5gcaY6Ykzl9pjClxybznE6dvNca0uoE2PzTGnE6rfUoLLy56kUqjK2GtdTsUERERr5Bm\nCY4xxhf4BGgDVAAeMMZUuGKxPsBf1toywAjgrcR1KwDdgYpAa2CUMcb3em0aY8KAXGm1T2llzYE1\n1C9eH2OM26GIiIh4hbSswakJRFprdwIYYyYDHYFNlyzTEXg18fV04GPjHOU7ApOttbHALmNMZGJ7\nXK3NxOTnHeBBoHMa7leqW/v4Wk7EnHA7DBEREa+RlkNURYC9l7zflzgt2WWstfHACSDPNda9VptP\nAXOstde8Fbcxpp8xJsIYE3HkyJEb2qG0YK3Fz8ePPCF53A5FRETEa3hFkbExpjDQFfjoestaaz+z\n1oZZa8Py5cuX9sFdx5PfPUmbiW3cDkNERMSrpGWCEwUUu+R90cRpyS5jjPEDcgDR11j3atPvBsoA\nkcaY3UBI4rBWhvfTrp/w99HNNUVERFJTWtbghANljTElcZKQ7jj1MZeaAzwC/Ap0ARZZa60xZg4w\nyRjzPlAYKAusAkxybVprNwIFLzRqjDmdWLic4f3vnv8pwREREUllaZbgWGvjjTFPAQsAX2CctXaj\nMWYYEGGtnQOMBSYk9rYcw0lYSFxuKk5BcjzwpLU2ASC5NtNqH9JDwzsauh2CiIiI1zG387VXwsLC\nbEREhGvbHxU+ijNxZxhab6hrMYiIiGQmxpjV1tqw6y3nFUXGmdWnqz/lh50/uB2GiIiI19G9qFxi\nreWecvdQLk85t0MRERHxOkpwXGKM4fWmr7sdhoiIiFfSEJVLlu5eSsR+9+p/REREvJl6cFzyzx//\nSYBvAMseXeZ2KCIiIl5HPTguSPAkkOBJoEmJJm6HIiIi4pXUg+MCXx9fIvpFcDufoi8iIpKW1IPj\nguiz0XisB+fG6SIiIpLalOC44N6p99Lq61ZuhyEiIuK1lOCks7iEOFbuW0nVAlXdDkVERMRrqQYn\nnQX4BrBr4C481uN2KCIiIl5LCY4LCmUr5HYIIiIiXk1DVOns0dmP8tKil9wOQ0RExKspwUlH8Z54\npm2cxvGY426HIiIi4tU0RJWO4j3xfNjmQyrmq+h2KCIiIl5NCU46CvILovfdvd0OQ0RExOtpiCod\njQofxbxt89wOQ0RExOspwUknHuvhpUUvMWvLLLdDERER8XpKcNLJydiTNC/VnLZl27odioiIiNdT\ngpNOcgblZGrXqdx7171uhyIZ1YED0KgRHDzodiQiIpmeEpx0sipqFUfPHnU7DHfpAH5t//kP/PIL\nDBvmdiQiIpmeEpx0YK2lw/91YND3g269scycJOgAnrygIDAGRo8Gj8d5NgaCg92OTEQk01KCkw4O\nnj7I2fNnaXhHw1tvLDMmCcHBOoADWAtRUfDtt/DGG9C1K5QtC7Gxly/n6wvt2sGuXe7EKSLiBYy1\n1u0YXBMWFmYjIiLSZVsJngTiPfEE+gXeXAPBwRAT8/fpQUFw7tytBZdWYmOdg/n//gcLFjgH+AtC\nQmDQIBg8GPLmdS/GtBIfD1u3wtq1lz+OXjJMWaYMhIY6j+XL4fvvwccHEhKc+S1aOD+j1q2d6SJy\nYw4cgO7dYcoUKFjQ7WgklRhjVltrw663nL4100G8Jx5fH9+bT24Adu6EmjUvn1a0KLz1FkRH31qA\nqclaWLECBgyAQoXgvvucA3vlyk6vzYXhmJw54c03oVgx6N0b1qxxO/Lru9rw4KlTToLyySfw2GNQ\nowZkywaVKsHDD8NHH8Fff0HHjs7rZcvgxAnYvh2mTYMXX3R+LgMGwOrVzs+jQgXYuNHpyalYEcaM\ngTNn3NlvkcwqM/Z4e4uMUE5hrb1tH9WrV7fpocyHZexzPzx38w3ExFjbr5+1Tvpgrb+/8xwS4jz7\n+lrbuLG1I0ZYu3Nn6gV+I3bssPbVV60tXdqJKTjY2ocesvb77609f97azp2tfeIJa9eudZ47d7Z2\nwwZrH3/84n7Uq2ft5MnWxsW5sw/X8/jj1hpjbdu21r7xhrVdu1pbtqwz7cLvJndua5s1s/bZZ62d\nMMHa9etvfn/i4qydONHasDCn7Vy5rP3Xv6zdty919+t2t3+/tQ0bWnvggNuRSGrweKwNDLz4mbz0\n4edn7bRp1i5dau3mzdZGR1ubkHBz20nrv5vM/nc5YIC1Pj7OcyoDImwKjvGuJxluPtIjwfnz+J+W\nV7Ejfxt5cw1ERVlbu7bzqypXzjnIXkgSOnWydtUqa1980dqKFS9+iKtUsfbll61dvdr5sKeVY8es\nHTPGSUzAOdA3bWrt+PHWnjyZ8nb++sva99+/mBwVKmTta69ljA/2vn0XE8orH8ZYe++91g4bZu2c\nOdbu3Zs2P2+Px9ply6y97z7nC8PPz9oHH7Q2PDz1t3U7SsMv4nSR2Q+EqeHQIWsnTbK2d29rixe/\n/DOa3Gf3yqSnYEHne7N5c+ezNWiQtW++ae3nnzuf7d9+c/6JO3Xq4mc8rf9uMuvf5dWSy6CgVNtE\nShMc1eCkcQ1OXEIcq6JWUSpXKQpnK3xjKy9fDl26OEMg48c7r69lxw6YPRtmzXLW9XicIaCOHZ1H\no0bg73/T+wJAXJxTK/LVVzB3rvP+rrugZ0946CFnezfL44H58+Hjj51t+PvD/ffD009DrVq3FndK\nnToFS5bAjz/CDz/A5s3O9IAApzYmIQECA6FDB/jww/Qf19+1yxnm+vxzJ9Z69Zw6pk6dnOJkSbnM\nWNeWnCeegE8/hf79YdQot6NJH2fOwM8/O5/TH3+Edeuc6blyQdOm0Ly5M3/KFOezGxfnDB+/9hoc\nPnz1x5EjF1+fOnVjMfn4QJs2zuurHVdTMn3hQue78EqBgc5+Z6TP+Zkz8PvvEB4Oq1Y5zzt3Xr5M\nSAh07gzvvptq35cprcFRgpNORcY3xFqn5mLgQLjjDidhqXiDdyA/cgTmzXMSnoULnS/snDmhbVvn\nYNi6tVMnktJ4wsNhwgT4v/9zan7y5YMHH4QePaBaNaeuJjVt2+bUtHzxhfNFU6MGPPUUdOvmfNBT\ny/nzzgfzhx+cL8qVK50C4aAgaNjQKfRt3tz5ffzvfxe/LN0+mJw86fxsRo50kp4SJZxEsE8fyJHD\nvbgyg2PHYOlSJ0GfMcOph7oge3Zo2RIaNICwMKcAPCTEvVivxVsStJSIj3e+gy4kNL/+6nx2AwOh\nfn3nM9q8Odx998UE4N57nTrAfv3gs8+cmpAZM1K+zXPnLk94Ljx27nROmtizx0lELtQUFit2+T+Q\nV/tOvN70uDin7ePH/57oBAc79XmVK198VKkCBQqkfL9u1vnzsH795cnMxo0XYyxe3PmerlHD+Qf7\n22/T7PsypQmO68NEbj7SY4iq58yedtK6SSlf4dw5p5sVnFqPv/669SDOnLF21ixrH33U2rx5nbYD\nAqxt3doZYtq//+Kyl3Z3795t7euvW3vnnc46gYHWdutm7bx56Vcnc/KktR9/bG358k4M+fI5Q3J7\n995cex6PtRs3WjtypLXt21ubNevFruwaNax9/nlrFy1yfg+XSq6GKCOIj7d2xgzndwbWZstm7cCB\n1kZGuh1ZxnH8uDPMMHiwtaGhF4ctQkKsLVrUee/v7zzfcYczXHGhW93Hx9pKlazt1cv5O/ztN2vP\nnk3f+BMSnM/i/PnOUO5jj1lbv75Tk3XlMECWLE493lNPOX/j331n7fbtTh1cRnS14TWPx9pNm6z9\n8ENrO3SwNnv2i5/T6tWtfe45a3/4If1/Fxc8/rjztxEUlDbDSFe2f9991o4b5/wNN29ubYECl//e\n8+VzygMGDnSG1VautPb06Wtv41pDmwkJ1m7Z4tQRPv20UyYRFHRxe3nyOMePf//b2rlzrT148PL1\n0/j7EtXguJ/gHDx10PIq9q1f3krZCnv3OgdZcGpobrb47Vri4639+Wdrhwy5WPMC1taq5Yw5d+3q\nfIkUKnRxXsOGzofm+PHUjyelPB7nC61DByc+X18n1qVLL46JX+0Du3+/tV99ZW3PntYWLnxxv8qU\ncb5Ipk93ig0zu4gIax9++OLBulOniz+f26kg8tQpp7j9n/90Pk8+PhcT9CZNnJqpZcusjY29+hdx\nVJS1s2c7X+Bt2zoHkEtrNqpWtbZPH2tHj3ZqoWJirh5PSn82cXHOQf2bb5x/LB56yNpq1Zyk5dKD\nWe7cTt1b377W1qlzeYJWpoyTAFxICC6NuWxZZ18GDnSStQULnJMS4uNvPfabdWmdSVRU8p/T0qWt\n7d/fKQ4+ejRt4rhRaf0PT0raP3zY2p9+svaDD5y/xRo1Lp6wcSEZLF3a+R54+WVrp051CqsvJLsX\nfvaPP+4ce2bMcE5iaNbM2hw5LrYTEmJtgwbOiROTJzu1SGlZ25kCKU1wNESVhkNUB08f5KOVH9G9\nUncqF6h87YV//tm58Nu5c059S6dOaRZXEmth0yZnCOzll5MfHw4MTL4b3E27djndnWPHOqdfV63q\nDF+tXAnjxsGjjzpjvheGnTZudNbLk+diV3bz5s6wjjfav9/5+YwZ4wwnVqvmdKEvWZJ2Q2tu1oGc\nO+cMWSxaBIsXO93n8fHg5we1a0OTJs6jTh1n+OZmWAv79kFEhHMqf0SE87hwiQZ/f2e4ICzs4qNi\nRaeL/sqfzZkzsGWLU9916SMy0on7gmLFnPq2Kx/58l1c5mrDMNY6wynbtyf/OHv2YhsBAVC6tHPR\nySsfb77ptHu132tCgjMEERvrPC68vt5zz57OkEdy8uaFZs2cz2izZlCy5M39zm5HHo8zhLZ+/eWP\n7duTr+u5kp+fM+RVs6Yz1FSzpvM3l5HqflANTopkiBoca52i2iFDnC+ZmTOdP6j0duCA80X83XfO\nl1AaFIalurNnYdIk58v9an/HLVpcrKOpWvX2umDe2bNOYnO1A0mpUk4CGxDgPF943Mj7f/7z8oPy\nBQEBzkE7a1bnceFq1jfr0gu25crlJLOLFzuPX391/mZ9fJzEomlTJ6GpVw+yZLn5bV6PtfDnn39P\neo4fT3kbvr7OBR+vTGLKl3d+bmkV94EDySc+kZHX/4cmZ86LycqFi1LeKh8f5/P59tvO7+92+pym\nh3PnnM/j+vXO52X27IvXp/H1dWrNhg1zfvY3+09AOkppguOXHsHcrsatGUetIrWomP8qBcLnzsHj\njwxwKfsAABdRSURBVDs9Nh06OEW82bOnb5AXFCrkJDL/3969R0lR3XkA//5mmAcM74e85DHySALG\nlYdE0Sgcc4IC0WgSNQ+XOJiceGKyrhAD6hHds1GyJnKOCayJYVzjIYp5aHDFRHbVI5GM62BEGTUy\nyCAQXgKCjDLP3/7xqzpd3VM90zPT1dVV8/2cc09XV1VX39tVXfWrW7duuQ1sT52yvORrcANYEHb9\n9dZwetEiO9i1tNhZyEUX2Z1Gca2lyUSfPnYAXrLEzuobGuy3KS8HZsywHZv3rLqhwWoXjh1LvE+d\n3tCQ2UGtsdECdpeIHbD79UsEPd7U0fjVq62DxJkzrZHwxx/bMs8+2xpXz51rDYNz+f8Rse1r/PjE\nHY6qdgZdXW0NmX//e6tJcecfN87uDHTPjCdOtGAwl0SAUaMsXXRR8rTWVnucSFUVcO+91gFnc7Nt\nK+PGWdA4aFBykOsOZ/rqDq9YYScobkPUc8+1ExHKvt69rSZ3+nTbV4pYzZz728+aZfvRmGGAE5Bj\nHx/D9Ruux51z7vQPcHbvturlV1+1Wxdvvz38s5aDBy3g8lZ3R8GoUXageO45C84aG4HJk3t2cOMa\nOdLuqmpqSvw2n/tc9y4jpV6WWLoUWLfOLtM0NVnvy9ddZ3e/nTzZNnnHHzxo3Rt4x7dXlb5vn70W\nFdkZ6ODBXS9HEEQssJswwe74U00+kFx6qfU+nq8KCuzS2Jgx9n/aujWx3cybl93Lj/X10dzfxEFU\n9/WdxAAnIPtP7sfZI87GnPFz2k58/nk7i2tstFtVFy7Mef58eW+hXL06vHx0RQ/5w3ZJtn+bwkI7\nI3Qfllpfb4+Z8C7/yiu7tmxVqz10A6Bdu4CVK62NWkND8qXTfAtu/ER5uww671He30RdD/nt2QYn\nl21wVIFVq6zdwic+Ye1tJk/O3fcTRdENNyTXgoTdBxERhYoP2wzZzqM70aqeqvaPPrKefpcssV6F\nq6oY3BBlwq1JqKqy1zAf3kdEkcFLVFlWUwN85Wv12PGlT+LWz96Ku+beZdXsV1xh3YnffTewbFn2\ne/4liqseUp1ORNnFACeL6uutIfp78iqgzZg27Dzri+Waa6zh5MaN9ogEIiIiChQvUWVRRQVw6GAr\nsPuzKLl/H9ZdO8ICmlGj7LZRBjdEREQ5wQAnSyor7dlipxrsJ204OgobX5uEyhk/t46VvH2CEBER\nUaAY4GTJ8sWHUF8PoLAB+N4k4KxH8BHKsPyVLwXXIykRERH5YoCTJffcV4yywlPA6FeAIbVAYz/0\nLmzAylU57qWUiIiIGOBkS8W/DsSC8dtR8v5Y4MmHgLoLMaz3SVx308Cws0ZERNTjMMDJosopP8Xw\ngjLItkUY2FqK904OwYYNYeeKiIio52GAk0VlGx7FxqohmDJF8PzLfXDWWdYvWWceLkxERETdxwAn\ny6ZOBbZvt4ccV1bag4SXLAk7V0RERD0LA5wAzZgB/OAHFuhs2hR2boiIiHoOBjgBW7HCnqv5rW/Z\nw5GJiIgoeIEGOCJyiYj8XURqRWSZz/QSEVnvTH9ZRMZ7pi13xv9dROZ1tEwRWeeM3y4ilSJSFGTZ\nMlVaajU4770HLF8edm6IiIh6hsACHBEpBLAawKUApgD4qohMSZltMYBjqjoRwCoAP3Y+OwXANQCm\nArgEwBoRKexgmesAfBLApwH0BnB9UGXrrNmzge9/H/j5z4HNm8PODRERUfwFWYMzC0Ctqr6rqo0A\nHgNweco8lwN42Bn+HYCLRUSc8Y+paoOq7gJQ6ywv7TJVdaM6APwfgNMDLFun/ehHQHk5sHgx8PHH\nYeeGiIgo3oIMcEYD2ON5v9cZ5zuPqjYDOA5gSDuf7XCZzqWpawH8yS9TIvJtEakWkerDhw93skhd\nV1YGPPggsGMHcOedOftaIiKiHimOjYzXAHhRVX0vBqnqL1V1pqrOHDZsWE4zdvHF1tj4Jz8BXnkl\np19NRETUowQZ4OwDMMbz/nRnnO88ItILwAAAR9r5bLvLFJEVAIYBuDkrJQjAvfcCI0cCFRVAY2PY\nuSEionxUUwOceaa9UtcEGeC8AmCSiJSLSDGs0XDqgws2AFjkDH8ZwHNOG5oNAK5x7rIqBzAJ1q4m\n7TJF5HoA8wB8VVVbAyxXtwwYAPziF9YZ4N13h50bIiLKN/X1wPz5wJtvAgsW2HvqvMACHKdNzY0A\n/gzgLQCPq2qNiPybiFzmzLYWwBARqYXVuixzPlsD4HEAb8La0nxXVVvSLdNZ1gMAhgP4q4i8JiJ3\nBFW27lqwAPj6163h8euvh50bIgoSz8SpsyoqrBd8VeDgQbs5hTpPrMKkZ5o5c6ZWV1eH8t1HjgBT\npgBjxgBVVUCvXqFkgygSamqAq68G1q+3x6FERX29/c/37AHGjrVylJWFnSvKZ6tXA0uXAqdOJcb1\n7m3djFRUhJevfCIiW1V1ZkfzxbGRcSQMGWIb7NatwH33hZ0birso1yJEubqeZ+LhCnK77+qyVe0E\n9+WXgXXrgLvuAq69FjjvPGDYMODGG5ODG8C6Flm82J5x+JWvALfeCjz0EPCXv9h21ZV6iqD3Cfmw\nz2ENTkg1OIBtlF/+MvD008C2bfZIB6Jsi3otwtVXAxs22E6/tBS4/HLgsceyt/xs1A6pAv/4h3UD\n4aZNm+x/7d3FFhQAF15ogVp5OXDGGZYGDAg3/2EsO2hBbvcdLdsNaGtr26adO4EPPkjMK2I1+RMn\nWjp6FHjqKaChITFPcTFw0UVAUZFtW7t2Ac3Nien9+9tnJ02yNHlyYnjIkNz+NrlYfqY1OAxwQgxw\nAODAAdsQpkwBXnzRdoBE2RR0gBCE5mbgrbeAVauARx5J3pkXFdmJwRe/CIwYAQwfbq/9+9vBojM6\nsyNWtdoYbxCzYwfwzjt24Proo8S8JSWW55aWtssRaXvGPXhwcsBzxhmJ92PHWpm7m//OykVgHGQA\nle3tvrUVaGqydO21wDPPWBBSXAycdZZ1A+INZLw1jYWFwPjxiSBm4kRgwgR7LS+3/HUm783NQF1d\n221xxw4b3+q5zWbQoESw4ya39ieofULQ+xwGOBnIhwAHAH79a2DRIuD++4HvfS/s3FAcNDUBf/ub\nXf783e+SD7SFhVaD8I1v2EFl0qT0B9BccIOZ6mq7ZLt1q9V8dLbH75ISC3S8QU/qqzvct699xm9H\nvGZNInBJPXicOJH4vl69LABJPXhMmmRn5A8/bI9o8R7o+vSxS9NXXGFn4e++m3h1U12drT9XQYEt\nzy/4uftu4NlngzmQBH2Q6k4A1dpqDy/+4AP/9NxzVjPuDYwLC4FPfcq2ATdQ8UuNjf7jWzu4N7ew\n0Na9G7h407hxnfuPdee3aWy0bcov+HnvvfSXswYOBIYOtXXdUSopST9tyxZ7/qK3BqpPH+BnP8te\nGyIGOBnIlwBH1doYbN4MvPGG7byIOuPoUduxbNkCvPSSdSSZaYBQVGSXR6dOTU4TJmTe+D3TM/Hm\nZmtL4wYyqcFM377A9OnAjBmW6uqAe+5pGySsXAnMnWs1oAcP+r8eOAAcPuy/Qy8rs4abR4+2f+Aq\nKLCDk7fK303jx3f8+3QlSGhpsctdfsHPrl1WrnRELIAbPtxqFoqKkl/TDaeO27bN8u3tq6u42Gou\n5s61g3lBQfJrR+NSp//wh8ALLyRqQWbNso5Q0wUt3nT8eMcBh59evYBzzrEypia37O2l4mILKk+e\nbLvs006zbS9bgqjdOnUKGD3atvtUpaXAlVfaPJmmzqyDbP4+DHAykC8BDmCR9ZlnAp/5jJ2Rdbaq\nnaIv0x2aqtUuuMHMli1WAwLYDnzaNOD88+0hr3v2AHfc0TZAuO8+29HX1CSnXbsS85WUWOBz5pnJ\ngU95uR2kXOnONlODmepqO3C6DShTg5mZMy1wSL1M252ahOZm4P33/YOfNWuSzzJdffsCv/mN5aW8\n3H6HrgriMk99vQV+559vB/pUJSXAvHmJ2gi3RsL72t64fNG3r9UqdCU98QRw003+tWfXXde9fFVW\npq+Z6+6ycyFb+Ve1/1dDQ3LQ8+ijFgR6G0pn+/dhgJOBfApwAOCBB4AbbgB+9SvebdHTtHcgPHXK\ngoOXXkoENEeO2LRBgyyQmT3bDnjnnGM7E6/OBAj19RYspQY+u3cn5ikttap+N+B5+mmrMWposLPc\nceOsYaM3mOnXLzmYmTHDP5jp7G/THbk6UAXVziSI/LsHrbVrgSVLktsV9e4NrFhhl9daW62myX31\nDvuNS52+aJF/cDZkiAXv/ft3v+uMIC+xRbFdm1fQ+c+XNjhQ1R6bZsyYofmkpUV1zhzV/v1V9+4N\nOzeUS1ddpVpaqgqolpSozp6tevPNqueeq1pUZOMB1cmTVb/5TdUHH1StqbFtpiMnT6qOHasqojpu\nnL3vrBMnVKuqVNeutXzNm6d6+umJfKWmyZNtvnXrVN9+O7N8tmf7dtWpU+01m7y/e2mp6tVXZ3f5\nQQsy/0Eue+1a1bKy5G2mTx/VysrsfUc2tvswlp0LQec/6OUDqNYMjvGhBxlhpnwLcFRVa2tVe/dW\nXbhQtbU17NxES1AHwSCW39ysunu36gsvqFZUJAcxbiosVD3/fNVbblF98knVQ4fyI+9ew4b5Bzin\nnZbd7wkKD1ThLFs1N8FlkPuEoPc3QYvS/jJVpgEOL1Hl0SUq16pVwM03WydQX/ta2LmJhnzr16Gl\nBdi/39q01NUlkvt+z57kOzz8DBtmtyXns6i3RwCi3dcLEN1+cKLePxOFh21wMpCvAU5LC3DBBXZb\n35tvWutzal+urylfdpk11PULXurqrNF4aoPNkSPtzpvycnt1U3U18O//ntzeIUpBQtTbI1B4oh5c\nUjgY4GQgXwMcwAKbadOsM7P168POTXZka2emanfG7Npl6be/Bf74x+QakYICCx5GjLDhggK7M80d\nTjfOb55du+wuIL9O27xGjEgOXLzBzNixbTvz8opykMAzcSLKJQY4GcjnAAewp43ffjvwhz/YnQu5\nENQZVWcPgh9+mAhgUlNdnX8/FKmKi61b/NbWRFJNfu83LvV9ba1/cNOvH/D44xbAjBtnd5l0VdSD\nBJ6JE1GuMMDJQL4HOE1N1vnVgQNWozNoULDfF+RBNrWGYuFCuyzjBiypQYx7G7Srb1+rDfFLmzcD\nt9wSXDuQqN9OTEQUJwxwMpDvAQ5g3e2fc471IPrQQ8F+V2cvk6hau5HjxxPJ7WXUm/76V3vOVnuN\naouLE5d0UtP48dY/RnudH0a9XwciIsoMA5wMRCHAAYDbbrOeIf/0J+uhNAhr1gBLlyZ3719UZE+w\nHT3aP3A5frzjO4EKChI3D6fq3986iSsvtwa43XnQaL7dRUVERMFggJOBqAQ4p05ZL7D19dagtqKi\n85cxWlqAvXuTn2vjTe+/7/85EXvQ38CBwIABySmTcWVlVvMUh0s8vIRERBQ+BjgZiEqAA9hlntmz\nrS1Kfb1/LcIHH/gHL247F29tS69e1jDWfTrxkSPAU0+1fQJstoIQXuIhIqJsYICTgSgFOIA9+PCd\nd2y4qMie9vzpTycCmWPHkucfOjQRwKSm0aPbPuslyCCEl3iIiCgbMg1wuvk4M8qVykq7xORqagLe\nftuCmmnT7Cnk3gCmvNzauHT2O9wgZPhwe+BetpSVARs3Ji7xMLghIqIgMcCJiOXLk3u6dakCzzyT\nne8IOgiZOhXYvj27yyQiIvLTjftWKJfuuadtwNGnD7ByZXa/xw1C2IiWiIiijAFORFRUAAsWJLr7\nLy0FvvCFaDyriIiIKNcY4ERIZaU9eFMk+21kiIiI4oQBToS4bWSmTLEO8thQl4iIyB8bGUcMG+oS\nERF1jDU4REREFDsMcIiIiCh2GOAQERFR7DDAISIiothhgENERESxwwCHiIiIYocBDhEREcWOqGrY\neQiNiBwGsDvsfOTAUADvh52JHGFZ46snlZdljaeeVFYguPKOU9VhHc3UowOcnkJEqlV1Ztj5yAWW\nNb56UnlZ1njqSWUFwi8vL1ERERFR7DDAISIiothhgNMz/DLsDOQQyxpfPam8LGs89aSyAiGXl21w\niIiIKHZYg0NERESxwwCHiIiIYocBTkyIyBgReV5E3hSRGhH5F5955ojIcRF5zUl3hJHXbBCROhF5\nwylHtc90EZH7RaRWRF4Xkelh5LO7ROQTnvX1moicEJGbUuaJ9HoVkUoROSQi2z3jBovIJhHZ4bwO\nSvPZRc48O0RkUe5y3TVpynqviLztbKdPiMjANJ9td5vPN2nKeqeI7PNsq/PTfPYSEfm78/9dlrtc\nd02asq73lLNORF5L89morVffY01e/mdVlSkGCcBIANOd4X4A3gEwJWWeOQD+O+y8Zqm8dQCGtjN9\nPoBnAAiAcwG8HHaes1DmQgAHYJ1cxWa9ArgQwHQA2z3j/gPAMmd4GYAf+3xuMIB3nddBzvCgsMvT\nhbJ+HkAvZ/jHfmV1prW7zedbSlPWOwEs7eBzhQB2AjgDQDGAban7snxLfmVNmf5TAHfEZL36Hmvy\n8T/LGpyYUNX9qvqqM/whgLcAjA43V6G6HMCv1VQBGCgiI8POVDddDGCnqsaq921VfRHA0ZTRlwN4\n2Bl+GMAXfT46D8AmVT2qqscAbAJwSWAZzQK/sqrqs6ra7LytAnB6zjMWgDTrNROzANSq6ruq2gjg\nMdj2kLfaK6uICICrADya00wFpJ1jTd79ZxngxJCIjAcwDcDLPpPPE5FtIvKMiEzNacaySwE8KyJb\nReTbPtNHA9jjeb8X0Q/4rkH6nWRc1qtruKrud4YPABjuM08c13EFrObRT0fbfFTc6FyOq0xzGSNu\n6/WzAA6q6o400yO7XlOONXn3n2WAEzMi0hfA7wHcpKonUia/Cru88U8AfgbgyVznL4suUNXpAC4F\n8F0RuTDsDAVJRIoBXAbgtz6T47Re21Cr2459fxYichuAZgDr0swSh23+PwFMAHA2gP2wSzdx91W0\nX3sTyfXa3rEmX/6zDHBiRESKYBvcOlX9Q+p0VT2hqied4Y0AikRkaI6zmRWqus95PQTgCVi1ttc+\nAGM87093xkXVpQBeVdWDqRPitF49DrqXFJ3XQz7zxGYdi8g3ASwE8HXn4NBGBtt83lPVg6raoqqt\nAB6EfxnitF57AbgSwPp080RxvaY51uTdf5YBTkw413nXAnhLVe9LM88IZz6IyCzY+j+Su1xmh4iU\niUg/dxjWSHN7ymwbAPyzczfVuQCOe6pPoyjtWWBc1muKDQDcOywWAfijzzx/BvB5ERnkXOr4vDMu\nUkTkEgC3ALhMVT9KM08m23zeS2kHdwX8y/AKgEkiUu7UXF4D2x6i6HMA3lbVvX4To7he2znW5N9/\nNuwW2UzZSQAugFUJvg7gNSfNB/AdAN9x5rkRQA3sroQqALPDzncXy3qGU4ZtTnluc8Z7yyoAVsPu\nxngDwMyw892N8pbBApYBnnGxWa+wwG0/gCbYNfnFAIYA+F8AOwD8D4DBzrwzAfzK89kKALVOui7s\nsnSxrLWwdgnu//YBZ95RADY6w77bfD6nNGV9xPk/vg47II5MLavzfj7s7pydUS2rM/6/3P+pZ96o\nr9d0x5q8+8/yUQ1EREQUO7xERURERLHDAIeIiIhihwEOERERxQ4DHCIiIoodBjhEREQUOwxwiCg2\nROSkZ3i+iLwjIuPCzBMRhaNX2BkgIso2EbkYwP0A5mnMHk5KRJlhgENEseI8y+dBAPNVdWfY+SGi\ncLCjPyKKDRFpAvAhgDmq+nrY+SGi8LANDhHFSROALbDHAhBRD8YAh4jipBXAVQBmicitYWeGiMLD\nNjhEFCuq+pGILACwWUQOqurasPNERLnHAIeIYkdVj4rIJQBeFJHDqroh7DwRUW6xkTERERHFDtvg\nEBERUewwwCEiIqLYYYBDREREscMAh4iIiGKHAQ4RERHFDgMcIiIiih0GOERERBQ7/w+6p5SDav/e\n2AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11506d950>"
      ]
     },
     "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\", \"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": {
    "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": 14,
   "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": 15,
   "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": 16,
   "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 0x10ffb6ed0>"
      ]
     },
     "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
}