PR2018_Lab1.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "qTYuaFIH4myA"
   },
   "source": [
    "# **Αναγνώριση Προτύπων**\n",
    "\n",
    "\n",
    "**1η Εργαστηριακή Άσκηση**\n",
    "\n",
    "**Οπτική Αναγνώριση Ψηφίων**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "SyHnuVRV5hMh"
   },
   "source": [
    "# Παρατηρήσεις:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "9aIuMrCr90DU"
   },
   "source": [
    "* Πιθανώς να χρειαστεί upgrade στις απαιτούμες βιβλιοθήκες, προκειμένου να τρέξει ο κώδικας."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 325
    },
    "colab_type": "code",
    "id": "Km5fpgS7BDXv",
    "outputId": "bc4ea45d-2f06-44b1-d23d-2b189e4ba328"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already up-to-date: pip in /usr/local/lib/python3.5/dist-packages (18.1)\n",
      "Requirement already up-to-date: scikit-learn in /usr/local/lib/python3.5/dist-packages (0.20.0)\n",
      "Requirement already satisfied, skipping upgrade: numpy>=1.8.2 in /home/nikol/.local/lib/python3.5/site-packages (from scikit-learn) (1.15.3)\n",
      "Requirement already satisfied, skipping upgrade: scipy>=0.13.3 in /usr/local/lib/python3.5/dist-packages (from scikit-learn) (1.1.0)\n",
      "Requirement already up-to-date: numpy in /home/nikol/.local/lib/python3.5/site-packages (1.15.3)\n"
     ]
    }
   ],
   "source": [
    "!pip3 install --upgrade pip #upgrade pip package installer\n",
    "!pip3 install scikit-learn --upgrade #upgrade scikit-learn package\n",
    "!pip3 install --user numpy --upgrade #upgrade numpy package"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "9xoBLWZSBFk2"
   },
   "source": [
    "* Δηλώνονται οι απαιτούμενες βιβλιοθήκες."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "RHGmPEbV97TR"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import sklearn\n",
    "import random\n",
    "import math\n",
    "\n",
    "from scipy.spatial import distance\n",
    "from sklearn.base import BaseEstimator, ClassifierMixin\n",
    "from sklearn.model_selection import KFold\n",
    "from sklearn.model_selection import cross_val_score\n",
    "from sklearn.model_selection import learning_curve\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.naive_bayes import GaussianNB\n",
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "from sklearn import svm\n",
    "from sklearn.ensemble import VotingClassifier, BaggingClassifier"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "z5qN7XsT9-39"
   },
   "source": [
    "* Euclidean distance classifier implemented as scikit-learn estimator\n",
    "Used in STEP 12,13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "0I9ljAbM-DBE"
   },
   "outputs": [],
   "source": [
    "class EuclideanClassifier(BaseEstimator, ClassifierMixin):\n",
    "    \"\"\"Classify samples based on the distance from the mean feature value\"\"\"\n",
    "    def __init__(self):\n",
    "        self.X_mean_ = None\n",
    "\n",
    "    def fit(self, X, y):\n",
    "        \"\"\" Calculates self.X_mean_ based on the mean\n",
    "        feature values in X for each class. \"\"\"\n",
    "        mean_pixels_d = [None] * 10\n",
    "        var_pixels_d = [None] * 10\n",
    "        for label in range(0,10):\n",
    "            indices_d = [i for i, x in enumerate(y) if x == label]\n",
    "            pixels_d = []\n",
    "            for i in indices_d:\n",
    "                pixels_d.append(X[i,:])\n",
    "            mean_pixels_d[label] = np.mean(pixels_d,axis=0)\n",
    "        mean_pixels_d = np.reshape(mean_pixels_d, (10,X.shape[1]))\n",
    "        self.X_mean_ = mean_pixels_d\n",
    "        return self\n",
    "\n",
    "    def predict(self, X):\n",
    "        \"\"\" Make predictions for X based on the\n",
    "        euclidean distance from self.X_mean_ \"\"\"\n",
    "        len_samples = X.shape[0]\n",
    "        len_features = X.shape[1]\n",
    "        mean_pixels_d = self.X_mean_[:,0:len_features]\n",
    "        digit_matched = [None] * len_samples\n",
    "        for i in range(0,len_samples):\n",
    "            features_d = X[i,:]\n",
    "            eudist_d_all = []\n",
    "            for label in range(0,10):\n",
    "                eudist_d = distance.euclidean(features_d, mean_pixels_d[label])\n",
    "                eudist_d_all.append(eudist_d)\n",
    "            digit_matched[i] = float(np.argmin(eudist_d_all))\n",
    "        digit_matched = np.asarray(digit_matched)\n",
    "        return digit_matched\n",
    "\n",
    "    def score(self, X, y):\n",
    "        \"\"\" Return accuracy score on the predictions\n",
    "        for X based on ground truth y \"\"\"\n",
    "        digit_matched = self.predict(X)\n",
    "        len_samples = X.shape[0]\n",
    "        hits_clas = 0\n",
    "        for i in range(0,len_samples):\n",
    "            hits_clas = hits_clas + (digit_matched[i] == y[i])\n",
    "            srate_eudist = hits_clas / len_samples\n",
    "        return srate_eudist\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "yTYByBMQSFmD"
   },
   "source": [
    "* Naive Bayes classifier implemented as scikit-learn estimator Used in STEPS 15, 16"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "wxkZdDc-SF5t"
   },
   "outputs": [],
   "source": [
    "# Naive Bayes classifier implemented as scikit-learn estimator\n",
    "class BayesClassifier(BaseEstimator, ClassifierMixin):\n",
    "    \"\"\"Classify samples based on Gaussian naive bayes\"\"\"\n",
    "    def __init__(self):\n",
    "        self.X_mean_ = None\n",
    "        self.X_var_ = None\n",
    "        self.X_apriori_ = None\n",
    "\n",
    "    def fit(self, X, y, v):\n",
    "        \"\"\" Calculates self.X_mean_,self.X_var_ based on the mean and variance\n",
    "        feature values in X for each class. Also calculates a priori probabilities self.X_apriori_ of digits 0-9.\"\"\"\n",
    "        mean_pixels_d = [None] * 10\n",
    "        if v == 0:\n",
    "            var_pixels_d = [None] * 10\n",
    "        else:\n",
    "            var_pixels_d = np.ones((10,X.shape[1]))\n",
    "\n",
    "        for label in range(0,10):\n",
    "            indices_d = [i for i, x in enumerate(y) if x == label]\n",
    "            pixels_d = []\n",
    "            for i in indices_d:\n",
    "                pixels_d.append(X[i,:])\n",
    "            mean_pixels_d[label] = np.mean(pixels_d,axis=0)\n",
    "            if v==0:\n",
    "                var_pixels_d[label] = np.var(pixels_d,axis=0)\n",
    "\n",
    "        mean_pixels_d = np.reshape(mean_pixels_d, (10,X.shape[1]))\n",
    "        var_pixels_d = np.reshape(var_pixels_d, (10,X.shape[1]))\n",
    "        self.X_mean_ = mean_pixels_d\n",
    "        self.X_var_ = var_pixels_d\n",
    "        \n",
    "        frequencies = np.bincount(y_train.astype(int))\n",
    "        self.X_apriori_ = np.divide(frequencies,y_train.shape[0])\n",
    "        return self\n",
    "\n",
    "    def calcGaussian(self,x,mean,var):\n",
    "        a = np.power(np.subtract(x,mean),2)\n",
    "        b = np.multiply(var,2)\n",
    "        c = np.divide(np.multiply(a,-1),b)\n",
    "        c = np.exp(c)\n",
    "        d = np.multiply(var,2*math.pi)\n",
    "        d = np.power(d,1/2)\n",
    "        e = np.divide(c,d)\n",
    "        return e\n",
    "\n",
    "    def predict(self, X):\n",
    "        \"\"\" Make predictions for X based on Gaussian probability\n",
    "        with self.X_mean_ and self.X_var_\"\"\"\n",
    "        len_samples = X.shape[0]\n",
    "        len_features = X.shape[1]\n",
    "        mean_pixels_d = self.X_mean_[:,0:len_features]\n",
    "        var_pixels_d = self.X_var_[:,0:len_features]\n",
    "        digit_matched = [None] * len_samples\n",
    "        for i in range(0,len_samples):\n",
    "            features_d = X_test[i,:]\n",
    "            prob = []\n",
    "            for label in range(0,10):\n",
    "                mean = mean_pixels_d[label]\n",
    "                var = var_pixels_d[label]\n",
    "\n",
    "                indices_var0 = [j for j, x in enumerate(var_pixels_d[label]) if x == 0]\n",
    "                mean = np.delete(mean,indices_var0)\n",
    "                var = np.delete(var,indices_var0)\n",
    "                features = np.delete(features_d,indices_var0)\n",
    "\n",
    "                prob_d = np.prod(self.calcGaussian(features,mean,var)) * self.X_apriori_[label]\n",
    "                prob.append(prob_d)\n",
    "            digit_matched[i] = float(np.argmax(prob))\n",
    "        digit_matched = np.asarray(digit_matched)\n",
    "        return digit_matched\n",
    "\n",
    "    def score(self, X, y):\n",
    "        \"\"\" Return accuracy score on the predictions\n",
    "        for X based on ground truth y \"\"\"\n",
    "        digit_matched = self.predict(X)\n",
    "        len_samples = X.shape[0]\n",
    "        hits_clas = 0\n",
    "        for i in range(0,len_samples):\n",
    "            hits_clas = hits_clas + (digit_matched[i] == y[i])\n",
    "            srate_eudist = hits_clas / len_samples\n",
    "        return srate_eudist"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "TLrOvQQ8_KNH"
   },
   "source": [
    "# ** MAIN PROGRAM STARTS HERE **\n",
    "*Απαιτείται η εκτέλεση του κώδικα στις **Παρατηρήσεις**, ώστε να είναι δυνατή η εκτέλεση του κυρίως προγράμματος*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "4OUWMLxj_N-J"
   },
   "source": [
    "# STEP 1\n",
    "\n",
    "Πραγματοποιείται η ανάγνωση των δεδομένων από τα αρχεία train.txt, test.txt του φακέλου pr_lab1_2016_2017_data με τη χρήση της np.loadtxt() με όρισμα το path κάθε αρχείου txt και δημιουργούνται οι numpy arrays train_set, test_set. Στη συνέχεια δημιουργούνται οι numpy arrays X_train (train_set[:,1:] - δείγματα εκπαίδευσης χωρίς τα labels), y_train (train_set[:,0] - αντίστοιχα labels για τον X_train) και X_test, y_test ομοίως."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "GxPPNnc3_Slk"
   },
   "outputs": [],
   "source": [
    "# load the txt files into 2D arrays using np library\n",
    "train_set = np.loadtxt('train.txt')\n",
    "test_set = np.loadtxt('test.txt')\n",
    "\n",
    "# create X_train, y_train arrays\n",
    "X_train = train_set[:,1:]\n",
    "y_train = train_set[:,0]\n",
    "\n",
    "# create X_test, y_test arrays\n",
    "X_test = test_set[:,1:]\n",
    "y_test = test_set[:,0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ZeQYnhqw_Vrf"
   },
   "source": [
    "# STEP 2\n",
    "Λαμβάνονται τα χαρακτηριστικά του δείγματος που βρίσκεται στη θέση 131 των train δεδομένων (ως X_train[131,:]) και με τη συνάρτηση np.reshape() και διαστάσεις (16,16) μετασχηματίζεται καταλλήλως ο πίνακας χαρακτηριστικών για να εμφανιστεί με την συνάρτηση plt.imshow().\n",
    "\n",
    "Το αποτέλεσμα εμφανίζεται στην παρακάτω εικόνα.\n",
    "\n",
    "Όπως παρατηρούμε αντιστοιχεί στο ψηφίο 9 το οποίο συμπίπτει και με την ετικέτα του.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 386
    },
    "colab_type": "code",
    "id": "kUIEhVxF_XEy",
    "outputId": "7569c3b4-3309-48e9-860f-d2dda6c8682e"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa04dd0cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# take the features of the digit 131 - row 131 in X_train\n",
    "features_131 = X_train[131,:]\n",
    "features_131 = np.reshape(features_131, (16,16))\n",
    "\n",
    "fig = plt.figure(1)\n",
    "plt.imshow(features_131)\n",
    "fig.suptitle('Digit at place 131 of train data')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "kGmrku1c_YzM"
   },
   "source": [
    "# STEP 3\n",
    "\n",
    "Επιλέγεται 1 τυχαίο δείγμα από κάθε label συνολικά για τα 10 δείγματα με τη συνάρτηση random.randint() και κατάλληλους ελέγχους και σχεδιάζονται όλα μαζί ακολουθώντας της διαδικασία του βήματος 2 (μετασχηματισμός σε μορφή (16,16)) σε ένα figure με subplots. Για το σκοπό αυτό υλοποιείται και καλείται η συνάρτηση subplt_samples_all(rsample) η οποία λαμβάνει ως όρισμα μια λίστα με στοιχεία τους numpy πίνακες χαρακτηριστικών σε διαστάσεις (16,16) και εμφανίζει καταλλήλως τις εικόνες των ψηφίων με τη χρήση των συναρτήσεων fig.add_subplot(), plt.imshow() με fig = plt.figure().\n",
    "\n",
    "Το αποτέλεσμα εμφανίζεται στην παρακάτω εικόνα.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 256
    },
    "colab_type": "code",
    "id": "y-KhzA-o_ddO",
    "outputId": "4efc466d-03f7-4ab4-d4a2-c9f33529e40b"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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H1hi9T8657B0ALktZx5Tt+i/84A96btmKJACK2pUAkHzezGrz5EP3yrradMjeg3n79WcB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\nA2alcvXY78b6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa02da46a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#function that takes the arrays of features for each digit and subplots them\n",
    "\n",
    "def subplt_samples_all (rsample):\n",
    "    for i in range(0,10):\n",
    "        fig.add_subplot(1,10,i+1)\n",
    "        plt.imshow(rsample[i])\n",
    "    return\n",
    "\n",
    "# select random sample for each label\n",
    "rsample = [None] * 10\n",
    "rsample_flag = [False] * 10\n",
    "\n",
    "for i in range (0,10):\n",
    "\tsize_train = len(X_train)\n",
    "\tx = random.randint(0,size_train)\n",
    "\ty = int(y_train[x])\n",
    "\twhile rsample_flag[y]:\n",
    "\t\tx = random.randint(0,size_train)\n",
    "\t\ty = int(y_train[x])\n",
    "\trsample_flag[y] = True\t\n",
    "\trsample[y] = np.reshape(X_train[x,:], (16,16))\n",
    "\n",
    "fig = plt.figure(2)\n",
    "subplt_samples_all (rsample)\n",
    "fig.suptitle('Random samples for each label of train data')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "PFq9cOWC_eLI"
   },
   "source": [
    "# STEP 4\n",
    "\n",
    "Για να υπολογίσουμε τη μέση τιμή των χαρακτηριστικών του pixel (10, 10) για το ψηφίο «0» με βάση τα train δεδομένα, υπολογίζουμε καταρχήν από τον y_train με τη συνάρτηση enumerate() τις θέσεις των δειγμάτων με label 0 (αποθηκεύονται στη λίστα indices_0).  Για καθένα από τα δείγματα που βρήκαμε παίρνουμε την τιμή του pixel (10,10) αφού μετασχηματίσουμε τον πίνακα σε διαστάσεις (16,16). Οι τιμές αυτές αποθηκεύονται σε μια λίστα (pixels10_d0) και κατόπιν με τη χρήση της συνάρτησης np.mean() επιστρέφεται η μέση τους τιμή. \n",
    "\n",
    "Η μέση τιμή του pixel (10, 10) για το ψηφίο «0» που εμφανίζεται είναι:\n",
    "\n",
    "`Mean value of features of pixel(10,10) for digit 0 is -0.5041884422110553`\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 35
    },
    "colab_type": "code",
    "id": "vPTnfgCc_guf",
    "outputId": "d614a155-6d7a-4720-fb00-cc58436c6174"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean value of features of pixel(10,10) for digit 0 is -0.504188442211\n"
     ]
    }
   ],
   "source": [
    "# mean value of pixel(10,10) for digit 0 in train set\n",
    "pixels10_d0 = []\n",
    "indices_0 = [i for i, x in enumerate(y_train) if x == 0]\n",
    "for i in indices_0:\n",
    "    pixels10_d0.append(np.reshape(X_train[i,:], (16,16))[10,10])\n",
    "\n",
    "mean_pixel10_d0 = np.mean(pixels10_d0)\n",
    "print(\"Mean value of features of pixel(10,10) for digit 0 is\",mean_pixel10_d0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "E85XDE_f_jJT"
   },
   "source": [
    "# STEP 5\n",
    "\n",
    "Στο βήμα αυτό ακολουθείται ακριβώς η ίδια διαδικασία με το βήμα 4, με τη διαφορά ότι στις τελικές τιμές που επιλέγονται για το pixel(10,10) υπολογίζεται η διασπορά. Συγκεκριμένα, στις τιμές τις λίστας (pixels10_d0) που δημιουργείται στο προηγούμενο ερώτημα εφαρμόζεται η συνάρτηση np.var() η οποία υπολογίζει τη διασπορά.\n",
    "\n",
    "Η διασπορά του pixel (10, 10) για το ψηφίο «0» που εμφανίζεται είναι:\n",
    "\n",
    "`Variance of features of pixel(10,10) for digit 0 is 0.5245221428814929`\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "-mfX8KZY_ktW",
    "outputId": "d3a7fdba-bb17-4767-90ac-5127b02e032e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variance of features of pixel(10,10) for digit 0 is 0.524522142881\n"
     ]
    }
   ],
   "source": [
    "# variance of pixel(10,10) for digit 0 in train set\n",
    "var_pixel10_d0 = np.var(pixels10_d0)\n",
    "print(\"Variance of features of pixel(10,10) for digit 0 is\",var_pixel10_d0)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "AcKn5wPH_mgg"
   },
   "source": [
    "# STEP 6\n",
    "\n",
    "Για τον υπολογισμό της μέσης τιμής και διασποράς των χαρακτηριστικών κάθε pixel για το ψηφίο «0» με βάση τα train δεδομένα υλοποιείται η συνάρτηση mv_var_digit (indices_d) η οποία λαμβάνει ως είσοδο τις θέσεις εμφάνισης ενός συγκεκριμένου ψηφίου (0-10) στον πίνακα X_train και επιστρέφει τις μέσες τιμές και διασπορές των χαρακτηριστικών του σε μορφή numpy πινάκων με διαστάσεις (16,16). Στο εσωτερικό της συνάρτησης ακολουθείται η ίδια διαδικασία για τον υπολογισμό της μέσης τιμής, διασποράς που ακολουθήθηκε στα βήματα 5,6 με τη διαφορά ότι δεν επιλέγεται 1 pixel για κάθε δείγμα αλλά το σύνολο των χαρακτηριστικών του. Αυτό έχει ως αποτέλεσμα να δημιουργείται μια λίστα (pixels_d) με στοιχεία τους numpy πίνακες χαρακτηριστικών διαστάσεων (16,16). Στη λίστα αυτή εφαρμόζονται με την ίδια λογική οι συναρτήσεις np.mean(), np.var() με παράμετρο axis = 0 για να υπολογιστεί μέση τιμή, διασπορά των χαρακτηριστικών κάθε pixel. Έτσι επιστρέφονται οι πίνακες (16,16) mean_pixels_d, var_pixels_d που χρησιμοποιούνται στη συνέχεια.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "0L6JmCVb_qOz"
   },
   "outputs": [],
   "source": [
    "#function that takes the indices of appareance of a digit and returns the mean value and variance of all pixels for the digit in train set\n",
    "\n",
    "def mv_var_digit (indices_d):\n",
    "    pixels_d = []\n",
    "    for i in indices_d:\n",
    "        pixels_d.append(np.reshape(X_train[i,:], (16,16)))\n",
    "    mean_pixels_d = np.mean(pixels_d,axis=0)\n",
    "    var_pixels_d = np.var(pixels_d,axis=0)\n",
    "    return (mean_pixels_d,var_pixels_d)\n",
    "\n",
    "  # mean value and variance of all pixels for digit 0 in train set\n",
    "(mean_pixels_d0,var_pixels_d0) = mv_var_digit(indices_0)\n",
    "#print(\"Mean value of features of all pixels for digit 0 is\",mean_pixels_d0)\n",
    "#print(\"Variance of features of all pixels for digit 0 is\",var_pixels_d0)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "S2erdWhb_sI7"
   },
   "source": [
    "# STEP 7\n",
    "\n",
    "Ο πίνακας με τις μέσες τιμές των χαρακτηριστικών κάθε pixel για το ψηφίο «0» με βάση τα train δεδομένα που υπολογίστηκε στο βήμα 6, χρησιμοποιείται  για το σχεδιασμό του «0» με τη συνάρτηση plt.imshow().\n",
    "\n",
    "Το αποτέλεσμα εμφανίζεται στην παρακάτω εικόνα.\n",
    "\n",
    "\n",
    "Παρατηρούμε ότι εμφανίζεται αρκετά ξεκάθαρα το ψηφίο 0. Αυτό οφείλεται στο ότι παίρνοντας την μέση τιμή κάθε pixel έχουμε ως αποτέλεσμα ορισμένες ατέλειες δειγμάτων να εξαλείφονται και να τονίζονται περισσότερο περιοχές που περιλαμβάνονται στα περισσότερα δείγματα του dataset - αντιστοιχούν δηλαδή στα πιο συνηθισμένα γραμμένα στο χέρι μηδενικά. Επίσης, παρατηρούμε ότι σε ορισμένες περιοχές εμφανίζεται blurring ενώ άλλες είναι πιο φωτεινές γεγονός που σημαίνει ότι σε αυτές οι μέσες τιμές των χαρακτηριστικών ήταν μικρότερες και μεγαλύτερες αντίστοιχα."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 386
    },
    "colab_type": "code",
    "id": "Il7U6hah_tpu",
    "outputId": "27b73997-78e6-463a-f7bd-7dbf84f98ff8"
   },
   "outputs": [
    {
     "data": {
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lJ/0fWQs0svhqtE2fWjhmw5xy57fvnLOjcMzzJj9Wqq0VO6eVirvx4WcXjulecmCptiau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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa02586400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# draw digit 0 using the mean value of each pixel\n",
    "\n",
    "fig = plt.figure(3)\n",
    "plt.imshow(mean_pixels_d0)\n",
    "fig.suptitle('Digit \"0\" of train data based on its mean values')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "_IuZAq5d_vb0"
   },
   "source": [
    "# STEP 8\n",
    "Ο πίνακας με τις διασπορές των χαρακτηριστικών κάθε pixel για το ψηφίο «0» με βάση τα train δεδομένα που υπολογίστηκε στο βήμα 6, χρησιμοποιείται  για το σχεδιασμό του «0» με τη συνάρτηση plt.imshow().\n",
    "\n",
    "Το αποτέλεσμα εμφανίζεται στην παρακάτω εικόνα.\n",
    "\n",
    "Και εδώ το ψηφίο 0 είναι αναγνωρίσιμο ωστόσο παρατηρούμε ότι έχει τονιστεί πιο φωτεινά η περιοχή εσωτερικά και εξωτερικά του περιγράμματός του και λιγότερο η ενδιάμεση περιοχή. Στην περιοχή των 2 περιγραμμάτων που είναι πιο φωτεινή έχουμε μεγαλύτερη διασπορά γεγονός που σημαίνει ότι τα χαρακτηριστικά των δειγμάτων διέφεραν περισσότερο σε αυτές τις περιοχές (λιγότερα μηδενικά σχεδιάστηκαν σε αυτές), ενώ στην ενδιάμεση περιοχή διέφεραν λιγότερο (δηλαδή περισσότερα μηδενικά είχαν σχεδιαστεί με περίγραμμα σε αυτή). Αντίστοιχα, στο κέντρο του μηδενικού και στις γωνίες η διασπορά είναι πάρα πολύ μικρή, γιατί δεν υπήρχαν σχέδια σε αυτές γεγονός που προσδίδει περισσότερη ομοιομορφία. Παρατηρούμε ότι παρουσιάζονται αρκετές διαφορές στη συμπεριφορά της διασποράς και της μέσης τιμής, όπως αναλύθηκε παραπάνω."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 386
    },
    "colab_type": "code",
    "id": "5gNR4tGS_wiO",
    "outputId": "5dd2deb7-f362-4406-dc09-721473d0c4bf"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Wivvy5N+Wjlm5pdr3P/9+ZbWLI48aOb90zFcP+l2lXOctenXpmJePqvZU+egbbqgUd+m8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\nzNvNsbsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa0229e358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# draw digit 0 using the variance of each pixel\n",
    "\n",
    "fig = plt.figure(4)\n",
    "plt.imshow(var_pixels_d0)\n",
    "fig.suptitle('Digit \"0\" of train data based on its variances')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "tsCtzbPU_0An"
   },
   "source": [
    "# STEP 9\n",
    "Για τον υπολογισμό της μέσης τιμής και διασποράς των χαρακτηριστικών για όλα τα ψηφία (0-9) με βάση τα train δεδομένα θα γενικεύσουμε τη διαδικασία που υλοποιήσαμε στο Βήμα 6 για τον υπολογισμό της μέσης τιμής και διασποράς των χαρακτηριστικών κάθε pixel για τις θέσεις εμφάνισης ενός συγκεκριμένου ψηφίου μέσω της συνάρτησης  mv_var_digit (indices_d). Για το σκοπό αυτό υλοποιούμε της συνάρτηση mv_var_all_digits (y_train) η οποία για κάθε είδος ψηφίου (0-9) που εμφανίζεται στον y_train υπολογίζει με τη συνάρτηση enumerate() τις θέσεις των δειγμάτων με αντίστοιχο label και τις αποθηκεύει στη λίστα indices_d. Για κάθε ψηφίο και τη λίστα με τις θέσεις του καλείται η mv_var_digit (indices_d) και  επιστρέφονται οι μέσες τιμές για κάθε ψηφίο σε numpy array (16,16) και οι διασπορές για κάθε ψηφίο σε numpy array (16,16). Για την αποθήκευση των παραπάνω έχουν δημιουργηθεί δύο λίστες 10 στοιχείων τύπου numpy array (16,16), μια για τις μέσες τιμές και μια για τις διασπορές.\n",
    "\n",
    "Στον main κώδικα καλείται η mv_var_all_digits(y_train) και μέσω της subplt_samples_all(rsample), η οποία εξηγήθηκε στο Βήμα 3 (κάνει subplot στοιχεία numpy πινάκων χαρακτηριστικών σε διαστάσεις (16,16) μιας λίστας με τη χρήση της imshow()), με όρισμα τις μέσες τιμές που επιστράφηκαν από την κλήση της συνάρτησης. Έτσι σχεδιάζουμε όλα τα ψηφία χρησιμοποιώντας τις τιμές της μέσης τιμής των χαρακτηριστικών τους.\n",
    "\n",
    "Το αποτέλεσμα εμφανίζεται στην παρακάτω εικόνα.\n",
    "\n",
    "Παρατηρούμε ότι αναγνωρίζουμε ξεκάθαρα τα ψηφία 0-9 αν και σε ορισμένες περιπτώσεις παρουσιάζουν blurring σε περιοχές που υπήρχαν μεγαλύτερες ενδεχομένως μεταβολές στις τιμές των χαρακτηριστικών μεταξύ των δειγμάτων, όπως αναλύθηκε και στο Βήμα 7."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 256
    },
    "colab_type": "code",
    "id": "8c5MyaJ8_1MJ",
    "outputId": "c9813f3a-4fe5-4178-df86-90a64c30b693"
   },
   "outputs": [
    {
     "data": {
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1MbJ+KmO+Q72kJT422j+m6VQGeKOpAlQGy90sXrEIxKKECe2elWqEYoOeX9+g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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa02dd65c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#function that takes y_train and returns the mean value and variance of all pixels for all digits in train set - calls function mv_var_digit\n",
    "def mv_var_all_digits (y_train):\n",
    "    mean_pixels_d = [None] * 10\n",
    "    var_pixels_d = [None] * 10\n",
    "    for label in range(0,10):\n",
    "        indices_d = [i for i, x in enumerate(y_train) if x == label]\n",
    "        (mean_pixels_d[label],var_pixels_d[label]) = mv_var_digit(indices_d)\n",
    "    return (mean_pixels_d,var_pixels_d)\n",
    "\n",
    "#function that takes the indices of appareance of a digit and returns the mean value and variance of all pixels for the digit in train set\n",
    "def mv_var_digit (indices_d):\n",
    "    pixels_d = []\n",
    "    for i in indices_d:\n",
    "        pixels_d.append(np.reshape(X_train[i,:], (16,16)))\n",
    "    mean_pixels_d = np.mean(pixels_d,axis=0)\n",
    "    var_pixels_d = np.var(pixels_d,axis=0)\n",
    "    return (mean_pixels_d,var_pixels_d)\n",
    "\n",
    "#function that takes the arrays of features for each digit and subplots them\n",
    "def subplt_samples_all (rsample):\n",
    "    for i in range(0,10):\n",
    "        fig.add_subplot(1,10,i+1)\n",
    "        plt.imshow(rsample[i])\n",
    "    return\n",
    "  \n",
    "# mean value and variance of all pixels for all digits in train set\n",
    "(mean_pixels_d,var_pixels_d) = mv_var_all_digits(y_train)\n",
    "\n",
    "fig = plt.figure(5)\n",
    "subplt_samples_all (mean_pixels_d)\n",
    "fig.suptitle('All digits of train data based on their mean values')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "nVPJa_kp_22w"
   },
   "source": [
    "# STEP 10\n",
    "Για την ταξινόμηση του υπ΄αριθμόν 101 ψηφίου των test δεδομένων σε μία από τις 10 κατηγορίες (0-9) βάσει της Ευκλείδιας απόστασης υλοποιήθηκε η συνάρτηση classify_digit(features_d,mean_pixels_d) η οποία λαμβάνει τα χαρακτηριστικά ενός συγκεκριμένου δείγματος (διαστάσεων (1,256) - στην προκειμένη λαμβάνει τα X_test[101,:]) και τις μέσες τιμές όλων των ψηφίων (0,9) σε μορφή numpy πίνακα (10,256). Οι τιμές αυτές υπολογίστηκαν με την mv_var_all_digits(y_train) στο Βήμα 9α και για τη χρήση τους ως όρισμα στην συνάρτηση μετασχηματίζονται σε διαστάσεις (10,256) με την np.reshape() στο εσωτερικό του main κώδικα πριν την κλήση της συνάρτησης. Στο εσωτερικό της classify_digit(features_d,mean_pixels_d) για κάθε είδος ψηφίου (0-10) υπολογίζεται η ευκλείδια απόσταση μεταξύ των μέσων τιμών των χαρακτηριστικών του και των δοθέντων χαρακτηριστικών του δείγματος προς ταξινόμηση με τη συνάρτηση scipy.spatial.euclidean() και το αποτέλεσμα (1 τιμή) αποθηκεύεται σε μια λίστα. Από τη λίστα αυτή, που περιέχει 10 στοιχεία, υπολογίζεται με τη συνάρτηση np.argmin() η θέση του μικρότερου. Η τιμή αυτή επιστρέφεται από την classify_digit(features_d,mean_pixels_d) και αποτελεί το label του ψηφίου στο οποίο ταξινομήθηκε το δοθέν δείγμα. \n",
    "\n",
    "Παρατηρούμε ότι η ταξινόμηση για το συγκεκριμένο δείγμα δεν ήταν επιτυχής. Είναι λογικό ο ταξινομητής μας να έχει αστοχίες συνεπώς η αξιολόγηση θα γίνει πιο αντικειμενικά όταν υπολογιστεί το score για όλα τα δείγματα.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "fzKyHPb-_4hS",
    "outputId": "93802a6a-b84a-4277-cf44-1f4af9729756"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Digit 101 is classified to 0.0 and its true value is 6.0\n"
     ]
    }
   ],
   "source": [
    "#function that classifies a given digit of test set based on the euclidean distance with mean value of each digit and return the label matched\n",
    "def classify_digit (features_d,mean_pixels_d):\n",
    "    eudist_d_all = []\n",
    "    for i in range(0,10):\n",
    "        eudist_d = distance.euclidean(features_d, mean_pixels_d[i])\n",
    "        eudist_d_all.append(eudist_d)\n",
    "    return (np.argmin(eudist_d_all))\n",
    "\n",
    "# classification of the digit at index 101 of test set based on the euclidean distance with mean value of each digit (0-9) of train set\n",
    "features_101 = X_test[101,:]\n",
    "mean_pixels_d = np.reshape(mean_pixels_d, (10,X_train.shape[1]))\n",
    "digit_matched = classify_digit(features_101,mean_pixels_d)\n",
    "print(\"Digit 101 is classified to\",float(digit_matched),\"and its true value is\",y_test[101])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "n9zrhd1u_7Jx"
   },
   "source": [
    "# STEP 11\n",
    "Για την ταξινόμηση όλων των ψηφίων των test δεδομένων σε μία από τις 10 κατηγορίες με βάση την Ευκλείδια απόσταση υλοποιήθηκε η συνάρτηση classify_all(mean_pixels_d,X_test,y_test) η οποία γενικεύει τη διαδικασία που ακολουθήσαμε στο Βήμα 10 για όλα τα δείγματα του X_test. Συγκεκριμένα, η συνάρτηση αυτή παίρνει ως είσοδο τις μέσες τιμές όλων των ψηφίων (0,9), που υπολογίστηκαν με την mv_var_all_digits(y_train) στο Βήμα 9α, σε μορφή numpy πίνακα (10,256), το σύνολο των δειγμάτων του X_test και τα αντίστοιχα label τους στον y_test. Για κάθε δείγμα του X_test καλείται η συνάρτηση classify_digit(features_d,mean_pixels_d) που εξηγήθηκε στο Βήμα 10 και επιστρέφεται το label που αντιστοιχήθηκε στο συγκεκριμένο δείγμα. Το αποτέλεσμα κάθε ταξινόμησης αποθηκεύεται σε μια λίστα που περιέχει τις αντιστοιχίσεις για το σύνολο των δειγμάτων και επιστρέφεται από την classify_all(mean_pixels_d,X_test,y_test). Παράλληλα, υπολογίζεται το success rate της ταξινόμησης για το σύνολο το δειγμάτων του Χ_test ελέγχοντας απλά αν το label που αντιστοιχίθηκε είναι το ίδιο με το πραγματικό label του δείγματος στο y_test και επίσης επιστρέφεται από την classify_all(mean_pixels_d,X_test,y_test). \n",
    "\n",
    "Εμφανίζεται το success rate της ταξινόμησης όλων των δειγμάτων του X_test με βάσει την ευκλείδια απόσταση."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "RraWvVQc_8zR",
    "outputId": "cfc860f0-d25f-4c53-97ec-c1ce55e76a11"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success rate of euclidean distance classification is 81.4150473343 %\n"
     ]
    }
   ],
   "source": [
    "#function that classifies a given digit of test set based on the euclidean distance with mean value of each digit and return the label matched\n",
    "def classify_digit (features_d,mean_pixels_d):\n",
    "    eudist_d_all = []\n",
    "    for i in range(0,10):\n",
    "        eudist_d = distance.euclidean(features_d, mean_pixels_d[i])\n",
    "        eudist_d_all.append(eudist_d)\n",
    "    return (np.argmin(eudist_d_all))\n",
    "  \n",
    "#function that classifies all digit of test set based on the euclidean distance with mean value of each digit and return the labels matched and the success rate of classification\n",
    "def classify_all (mean_pixels_d,X_test,y_test):\n",
    "    len_samples = X_test.shape[0]\n",
    "    digit_matched = [None] * len_samples\n",
    "    hits_clas = 0\n",
    "    for i in range(0,len_samples):\n",
    "        features_d = X_test[i,:]\n",
    "        digit_matched[i] = float(classify_digit(features_d,mean_pixels_d))\n",
    "        hits_clas = hits_clas + (digit_matched[i] == y_test[i])\n",
    "    srate_eudist = hits_clas / len_samples\n",
    "    return (digit_matched,srate_eudist)\n",
    "\n",
    "  \n",
    "# classification of each digit of test set based on the euclidean distance with mean values of each digit (0-9) of train set\n",
    "mean_pixels_d = np.reshape(mean_pixels_d, (10,X_train.shape[1]))\n",
    "(digit_matched,srate_eudist) = classify_all(mean_pixels_d,X_test,y_test)\n",
    "#print(\"Digits in test are classified as\",digit_matched)\n",
    "print(\"Success rate of euclidean distance classification is\",srate_eudist*100,\"%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "xdwCUcsS__Hw"
   },
   "source": [
    "# STEP 12\n",
    "Για την υλοποίηση του ταξινομητή ευκλείδιας απόστασης σαν ένα scikit-learn estimator χρησιμοποιήθηκε ως σαν βάση ο κώδικας που δόθηκε και δημιουργήθηκε μια κλάση class EuclideanClassifier(BaseEstimator, ClassifierMixin) με τις μεθόδους _init_,fit, predict και score (βρισκεται στις Παρατηρήσεις). Στο εσωτερικό των μεθόδων αυτών χρησιμοποιήσαμε τον κώδικα που γράψαμε στα προηγούμενα ερωτήματα, με εξαίρεση της _init_(self) η οποία υλοποιήθηκε όπως ακριβώς στο δοθέν παράδειγμα. \n",
    "\n",
    "*   Στην fit(self, X, y) υπολογίζονται οι μέσες τιμές για κάθε ψηφίο (0-9) και αποθηκεύονται στο self.X_mean_  στη μορφή numpy array (10,256).\n",
    "*   Στην predict(self, X) υπολογίζονται σε μια λίστα οι προβλέψεις των labels (0-9) για κάθε δείγμα του Χ με βάση την Ευκλείδια απόσταση των χαρακτηριστικών κάθε δείγματος και του self.X_mean_ που έχει υπολογιστεί για τα 10 ψηφία.\n",
    "*  Τέλος, στην score(self, X, y) καλείται η predict(self, X) και για τις προβλέψεις που επιστρέφονται γίνεται ο έλεγχος με τα πραγματικά labels y και επιστρέφεται το ποσοστό επιτυχίας. \n",
    "\n",
    "Στο εσωτερικό του main κώδικα δοκιμάζουμε τον scikit-learn classifier που φτιάξαμε. Συγκεκριμένα, καλούμε αρχικά τη μέθοδο fit με εισόδους τα X_train, y_train και στη συνέχεια καλούμε τη μέθοδο score με εισόδους τα X_test, y_test. \n",
    "\n",
    "Το ποσοστό επιτυχίας που παίρνουμε είναι ίδιο με πριν γεγονός που επιβεβαιώνει την ορθότητα του μοντέλου που υλοποιήσαμε."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "ZH30y8dqABjM",
    "outputId": "f964e150-5924-4750-b3ba-383761252d62"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success rate of scikit-learn Euclidean Classifier is 81.4150473343 %\n"
     ]
    }
   ],
   "source": [
    "# classifier of euclidean distance as a scikit learn learn estimator - class EuclideanClassifier\n",
    "# as in STEP 11 we try to classify each digit of test set with mean values of each digit (0-9) of train set\n",
    "clf = EuclideanClassifier()\n",
    "clf.fit(X_train,y_train)\n",
    "score = clf.score(X_test,y_test)\n",
    "print(\"Success rate of scikit-learn Euclidean Classifier is\",score*100,\"%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "4k7Y6Hg_AEOz"
   },
   "source": [
    "# STEP 13 A\n",
    "Για τον υπολογισμό του score του ευκλείδιου ταξινομητή με χρήση 5-fold cross-validation χρησιμοποιούμε τη συνάρτηση sklearn.model_selection.cross_val_score() με παραμέτρους το μοντέλο που υλοποιήσαμε EuclideanClassifier(), τα X_train, y_train, cv=KFold(n_splits=5, shuffle = True, random_state=100) και scoring=\"accuracy\". Για να υπολογίσουμε το score παίρνουμε την μέση τιμή των 5 folds με την np.mean(). Επιλέγουμε να γίνεται shuffle (δηλαδή ανάμειξη του set) των δεδομένων πριν τον διαχωρισμό τους και έπειτα από κάποιες δοκιμές για το random_state επιλέγουμε αυτό που δίνει καλύτερο score.\n",
    "\n",
    "Με τον τρόπο αυτό αποφεύγουμε το overfitting στο train set και καταλήγουμε όπως αναμέναμε σε καλύτερο score για την ταξινόμηση και με μικρές αποκλίσεις."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "opX1kKOJAJbF",
    "outputId": "fb815147-1bcb-4b0c-d859-f429d1ecaaf0"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success rate of scikit-learn Euclidean Classifier with 5-fold cross-validation is 85.036465 +-0.469976 %\n"
     ]
    }
   ],
   "source": [
    "# A - calculate the score of the scikit-learn Euclidean Classifier with 5-fold cross-validation\n",
    "score_crossval = cross_val_score(EuclideanClassifier(), X_train, y_train, cv=KFold(n_splits=5, shuffle = True, random_state=100), scoring=\"accuracy\")\n",
    "print(\"Success rate of scikit-learn Euclidean Classifier with 5-fold cross-validation is %f +-%f\"%(np.mean(score_crossval)*100,np.std(score_crossval)*100),\"%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "2X11HGXqAHAu"
   },
   "source": [
    "# STEP 13 B\n",
    "Για το σχεδιασμό της  περιοχής απόφασης (decision surface) του Ευκλείδιου ταξινομητή υλοποιήσαμε τη συνάρτηση plot_clf(clf, X_new, y_train,labels) η οποία παρουσιάστηκε στο notebook Lab 0.3 Scikit-learn.ipynb στο εργαστήριο. Για το σχεδιασμό της περιοχής απόφασης αρκεί να διαλέξουμε δύο τυχαία features. Για το λόγο αυτό, στο εσωτερικό του main κώδικα και πριν από την κλήση της συνάρτησης για το plot δημιουργούμε τον πίνακα X_new με δύο χαρακτηριστικά από το σύνολο του Χ_train (επιλέξαμε τα χαρακτηριστικά στις θέσεις 10,104). Καλούμε τη μέθοδο fit του EuclideanClassifier() που υλοποιήσαμε με εισόδους τον νέο πίνακα χαρακτηριστικών X_new και το y_train, ώστε να υπολογιστεί ο πίνακας μέσων τιμών για τα ψηφία βάσει των χαρακτηριστικών στα οποία θα γίνει η σχεδίαση. Επίσης, δημιουργούμε τη λίστα labels με τιμές από 0-9 για να αποδοθούν στην αναπαράσταση των 10 ψηφίων στη γραφική. Στο εσωτερικό της συνάρτησης plot_clf(clf, X_new, y_train,labels) σχεδιάζουμε την περιοχή απόφασης χρησιμοποιώντας το αποτέλεσμα της μεθόδου predict του EuclideanClassifier() για τα δύο χαρακτηριστικά που επιλέχθηκαν και το σύνολο των δειγμάτων. Επιπλέον αναπαριστούμε με διαφορετικά χρώματα κάθε ψηφίο στην περιοχή που βρίσκεται.\n",
    "\n",
    "Με τα δύο τυχαία χαρακτηριστικά προκύπτει η πρώτη επιφάνεια απόφασης. Για το σχεδιασμό της επιφάνειας απόφασης κανονικά χρειαζόμαστε και τα 256 χαρακτηριστικά για να μπορέσουμε να σχολιάσουμε τις θέσεις των ψηφίων ως προς τις περιοχές που αυτά ορίζουν στην επιφάνεια. Αυτό οφείλεται στο γεγονός ότι οι τιμές των δειγμάτων κάποιου ψηφίου πιθανόν να διαφέρουν σε μεγάλο βαθμό ως προς τα δύο τυχαία χαρακτηριστικά που επιλέχθηκαν και να τοποθετούνται σε αρκετά διαφορετικά σημεία στις 2 περιοχές.\n",
    "\n",
    "Δοκιμάζουμε, επίσης, να σχεδιάσουμε την περιοχή απόφασης χρησιμοποιώντας την τεχνική PCA για το χωρισμό των χαρακτηριστικών σε δύο συνιστώσες, για να πετύχουμε καλύτερα αποτελέσματα. Με την τεχνική αυτή μειώνουμε τις διαστάσεις, βρίσκοντας ένα νέο σύνολο χαρακτηριστικών - συνιστωσών, οι οποίες είναι σύνθετες από τα αρχικά χαρακτηριστικά, αλλά δεν συνδέονται μεταξύ τους. Η πρώτη συνιστώσα αντιπροσωπεύει τη μεγαλύτερη δυνατή διασπορά στα δεδομένα, η δεύτερη αντιπροσωπεύειτη δεύτερη μεγαλύτερη διασπορά κλπ. Προκύπτει η δεύτερη επιφάνεια απόφασης στην οποία πλέον διακρίνουμε ευκρινώς τις περιοχές ταξινόμησης όλων των ψηφίων. Ταυτόχρονα, παρατηρούμε ότι ψηφία που μοιάζουν σε χαρακτηριστικά (όπως το 4,9,8 και 5,6) καταλαμβάνουν κοντινές περιοχές."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 673
    },
    "colab_type": "code",
    "id": "ZzQ0G9MeAKA5",
    "outputId": "f75283b1-5b4b-493a-8abc-0d1446c1b3e1"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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f/Z95jEq7nWHp/WhaL5WMwnymLZnH8q1foUnJtJFjMRmNuL1ealxO9uZkYTIa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Rc225vMmilj8jGDp4nX7PJ4PXCnafz1xWzm9OzK2/klBIWFUXLpErExMbgdTh4ZPAyjbPA+dTTt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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa026291d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Uf829/XPx/5A/8oElisp0lOr1yBRKNBoN+QWFFOv0vLhoxV9mOlgsFiYvXcP6I6coKC3n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\nOOzfYGoCz6EI+jrE0R5AhbYHUUWlPSL6PsJ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lSQGRcak0v2gU+duXE7HzQx4ydDI1G99U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\ncN3lLmKioolwR6Fjp31jBQWTm3uokn1xNwy+QEbUe2TBgjs0PMd30vPakWR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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa02d90cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#function that plots the decision surface of the Euclidean Classifier\n",
    "def plot_clf(clf, X, y, labels):\n",
    "    fig,ax = plt.subplots()\n",
    "    # title for the plots\n",
    "    title = ('Decision surface of Classifier')\n",
    "    # Set-up grid for plotting.\n",
    "    X0, X1 = X[:, 0], X[:, 1]\n",
    "    x_min, x_max = X0.min() - 1, X0.max() + 1\n",
    "    y_min, y_max = X1.min() - 1, X1.max() + 1\n",
    "    xx, yy = np.meshgrid(np.arange(x_min, x_max, .05),np.arange(y_min, y_max, .05))\n",
    "    Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])\n",
    "    Z = Z.reshape(xx.shape)\n",
    "    out = ax.contourf(xx, yy, Z, cmap=plt.cm.coolwarm, alpha=0.8)\n",
    "\n",
    "    colour_label = ['blue','red','green','white','black','yellow','orange','grey','purple','pink']\n",
    "    for i in range(0, 10):\n",
    "        ax.scatter(X0[y==i], X1[y==i],c=colour_label[i],label = labels[i],s=60, alpha=0.9, edgecolors='k')\n",
    "\n",
    "    ax.set_xticks(())\n",
    "    ax.set_yticks(())\n",
    "    ax.set_title(title)\n",
    "    ax.legend()\n",
    "    plt.show()\n",
    "    \n",
    "# B - draw the decision surface of the scikit-learn Euclidean Classifier using 2 random features\n",
    "X_new = X_train[:,[10, 104]]\n",
    "labels = [0,1,2,3,4,5,6,7,8,9]\n",
    "clf = EuclideanClassifier()\n",
    "clf.fit(X_new,y_train)\n",
    "plot_clf(clf, X_new, y_train,labels)\n",
    "plt.show()\n",
    "\n",
    "# draw the decision surface using PCA for better results\n",
    "pca = PCA(n_components=2)\n",
    "pca.fit(X_train)\n",
    "X_new = pca.transform(X_train)\n",
    "labels = [0,1,2,3,4,5,6,7,8,9]\n",
    "clf = EuclideanClassifier()\n",
    "clf.fit(X_new,y_train)\n",
    "plot_clf(clf, X_new, y_train,labels)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "4QBC6fGXAIIY"
   },
   "source": [
    "# STEP 13 C\n",
    "Για το σχεδιασμό της καμπύλης εκμάθησης (learning curve) του Ευκλείδιου ταξινομητή χρησιμοποιήθηκε η συνάρτηση sklearn.model_selection.learning_curve() με παραμέτρους το μοντέλο μας EuclideanClassifier(), τα X_train, y_train, cv=5, n_jobs=-1 και train_sizes=np.linspace(.2, 1.0, 5) η οποία επιστρέφει τα train_sizes, train_scores, test_scores που θα χρησιμοποιηθούν για το σχεδιασμό. Επίσης, υλοποιήσαμε την συνάρτηση plot_learning_curve(train_scores, test_scores, train_sizes, ylim=None) η οποία παρουσιάστηκε στο notebook Lab 0.3 Scikit-learn.ipynb στο εργαστήριο και η οποία με τα παραπάνω δεδομένα δημιουργεί την καμπύλη εκμάθησης και συγκεκριμένα αναπαριστά το training score και το cross validation score συναρτήσει των training examples.\n",
    "\n",
    "Παρατηρούμε ότι με την αύξηση των training examples το Training score μειώνεται ελάχιστα ενώ το Cross - validation score αυξάνεται ελάχιστα και τείνουν να λάβουν πολύ κοντινή τιμή. Οι αποκλίσεις μεταξύ των score με την αύξηση των δειγμάτων είναι της τάξης του 1-2%.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 376
    },
    "colab_type": "code",
    "id": "555brdVzAKmZ",
    "outputId": "8e8b6a72-2b27-4ae0-dcd2-41f7c103227b"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6cH3mGbjtNhP+u7ft1Rv4fEaEnQ7/4cOtKFss3YgVl7aYPx/OPRc2bDBvuulE\nxAhCXp4Jf+4MjY2pLaKWorRtmwlCqKhoNnJ9evKxPJ4mAWrLSmq5Pnnq4WeeMdF0Tmd5X4muc7nM\nx5krZsQII7QWi2WfSau4iMg84JeAG/itqt7WYvtY4FEgP15moaouj2+bAjwADAJiwExVDYvIocAj\nQABYDvyH6gAciu31wtCh5tMZVKGmJiFE//f++0zJyWneZ+SI0rp15u+ePW0fLyenSXzWrTNupmTq\n6owlk8ni4hAIGPfY1q1G4IcMMYJrsVi6TNruIBFxA/cBxwOlwLsi8ryqrksqdgPwlKreLyITMGJR\nLCIe4A/A+ar6gYgUAc4ct/cDC4C34uXnAS+k6zr6DU5fQ04OjB1LhdcLEye2v08kYtxvqfqLkj8t\nhcVh27buv4500XKumBEjjNvQYrF0iXS+ns0CNqjqRgARWQacBiSLi2IsE4A8wHkanQD8n6p+AKCq\nu+LHGAEMUtWV8eXfA6djxSU9eDzGMikqar/crFnmrb8lInDXXfC97xkrpy/gDLzcvLnp2m3IssWy\n16TzrhkFbElaLo2vS+Zm4LsiUoqxQi6Lrz8QUBF5SUTeE5Frko5Z2sExLT3NwoXmoZyMzwfjx8Md\nd8Bhh8FNN6UWoEzEzhVjsewz6bRcUoUftewbORd4RFV/ISKHA4+JyKR4veYAM4Fa4FURWQ1UdeKY\n5uQiCzDuM4YNG0ZJSUliW3V1dbPldqmv75dvrtXhMCVr13bPwQ46iKE/+Qn7L1mCr6yM+iFD2Pj9\n77PzuOPI/uILxvzxjwx7+GF0yRJ2HnMMm//1X6ktLu6ec+8jHbaDKnz6qenj6qcDYPfqfuin2Dbo\n/jaQdPWFx8XiZlU9Mb78nwCq+vOkMmuBeaq6Jb68EZgNHBtff2F8/X8BYUw/zGuqenB8/bnAXFX9\nt/bqMmPGDF21alViuaSkhLlz53Z8EbFYz0SL9QIla9cyt6M+l+6ktBQefBAef9x09h9/PFxyCcyc\n2XN1SEGn2kHVDLp0Qsyzsnqmcj1Ep++Hfoxtg9RtICKrVXVGV46Xzlfyd4EDRGSciGQB5wDPtyiz\nGTgOQETGA36gDHgJmCIiwXjn/tHAOlXdDoREZLaICHAB8Oc0XoOluxg9GhYtgnfegauuglWr4PTT\n4Ywz4JVXjJBnKnauGItlr0mbuKhqBLgUIxTrMVFha0VkkYicGi92FfAjEfkAeAK4UA27gTsxArUG\neE9V/xaqnS9kAAAgAElEQVTf58fAb4ENwOfYzvy+RWEhXHmlEZlFi0w/zIUXwje/CX/8oxm/k6nY\nuWIslk6T1mD++JiV5S3W3Zj0fR1wRBv7/gHjBmu5fhUwqXtraulxgkH44Q/hggvg+efh17+Gyy+H\n//kfk3rnvPMyMxTYmSumrq5p4GU/dJtaLPtK/+uptvQtvF749rdhxQp49FHjPrvpJtMX84tfmHE0\nmUggYCLiSkthxw7jMrNYLAmsuFgyAxHjGnvmGXjuOTN25s47jcj813+Zh3im4cwVEwrZuWIslhZY\ncbFkHjNnwpIl8NprcOqp8Pvfwze+AZddBuvX93btWhMMmjDlTZvMnD+ZHJxgsfQQVlwsmcuBB5oR\n/v/8J/zgB/Dii8a6Of98ePvtzIrY8npNX0xFhRnd31ZKHItlgGDFxZL5jBoFN99sIsyuvho++MAk\nxDztNHjppcyxFJz8bapmZP/u3ZklgBZLD2LFxdJ3KCgwEWVvv20mdNu501g0xx4LTz7ZbEqBXsXn\nMyHLO3eavqJMDq+2WNKEFZcOqIuEiWmGvBlbDIGAGRvzj3/AffcZl9SVV5p+mQceaHua6Z7ECVl2\n5ooJhXq7RhZLj2LFpR1iGmNL7XY+r/qS8rpd1EetHz2j8HjMKP+XX4Y//AGKi83AzFmz4PbbTed6\nbxMImM/WrbB9ux14aRkwWHHpBAG3nz0NVXwZ2sKXoS2EGqqJxuy4hoxBBI45Bv70J/jLX4wF86tf\nmWzM111norh6k5ZzxdTW9m59LJYewIpLJ3CJi6AnQK43BwG21e5gY2gTO+vKrTWTaUyfDr/9LZSU\nmLxljz8Oc+aYJJndlQW6qwQCxoW3eTOUlWVOIILFkgasuOwlXpeXXG82QXeAUEMoYc1U1YesNZNJ\nfP3rZi6ZlStNOplXXoETToD58+HNN3svisvOFWMZIFhx6SIiQiDJmvmqbmfCmglH7AMjYxgxwozw\nf/ddM6nZRx/Bv/4r/Mu/wPLlvWM9OCHLLpdxk23YAFu2mCmkq6vNGBlr1Vj6OGlNXDlQ8Lq8eF1e\nVJVQQ4jd9ZX43FkUZuWT7Q3idvXPSab6FHl5ZoT/RReZ7Mu/+Q386EfMGj3ahDefeaYJIe5JsrLM\nR9WEK+/ZY3KUqRoB8niaAgKysoxLzeMx2yyWDMdaLt1IkzWTnbBmPg99aa2ZTCIQMJmY33gD7r+f\nqN8PP/2pCQK4//7eCRkWMeIRCBiLJjfX/PV6jdusrMxYNl98YaycTZvMGJpQyGy3EWiWDMRaLmki\nlTWT5c6iyFozmYHbDaeeyur992duRYUZL3PLLSbK7IILjIUzZEjv19Htbm5RqRrrJhQylo6Dy2XE\nye83H4/HiFM/nKLb0jew4pJmHGsGoDHWyFd1OyEMg7y55GcNwuf2IdbN0XuIwFFHmc8HHxiRue8+\neOgh+M534OKLYdy43q5lE467zNPi1o3FjGutrq6pv0bVWER+v0mu6fVa15qlx7Di0oMkWzM1jbVU\nNoTwurwU+fLJ8WZba6a3mToVHnwQNm40fTJPPWVCmU8+2YQyT57cLadpjDUSjtQTaqymprEWEcHr\n8pIV/3hdXtwuN25xxf+6cUkHFojL1dSHk0w0agSnutqIjaop6/M1WTqONeS2vz9L92HFpRcw1owf\ngEgsws5wOTvCZQzy5pKXlYvf7bfWTG+y//5mhP9VV8HvfmdS/v/lL3DkkUZk5szZqzf/aCxKfayB\nmsZaQg3VNMYaEZfgFS9BTwBFiWmMcLSe2kgtUY2hgCCAgoALFx6XB6/LQ5YriyyXF4/Lg1tcuMSF\nW9ypX04c11oyqqafpqrKhEQ3NMDnn5tyjpWTHEBgXWuWLmDFpZfxuDx4XJ6ENbOnvsr0zfhM34zH\nZf+Jeo1hw8wI/0svNellHnoIzjkHpkyBf/93OOmklG/7qkp9tJ66aJhQQzV10TCo4HG5yHJl4fc0\nj0oTBJe42r0ZVZWoRmmIGqsnpjE0LkFKDIn/53F7yXJ54lay+euOi48jQiLS5CIDIx45OU2utV27\njCXjCKjXawTH7zei47jl7AuQpR3skytDcKyZAMaa2REuQ+uUvKxB1prpbQYNMmLygx/A00+bqLKL\nLza5zH78YzjrLBqz3NRHGwg1VFPdWIMKiEKW20uuN2efqyAieMTToQDFNEZjNEI4Um8sImKgxgJS\n1AiQePC6PWS5s/CKh5jGqI3UGRHyuHF7A81/a9Eo1NRAZWVyhYzYOK41J4DAutYscdIqLiIyD/gl\n4AZ+q6q3tdg+FngUyI+XWaiqy0WkGFgPfBIv+paqXhzfpwQYAThzyp6gqjvTeR09jcflISfJmqls\nCOEVD0X+AmvN9CZ+vxnhf845RF9YDvfdh/vaa4nc/t/sOf8sKs85HVdePkFPoFdeBETEuMdwA942\ny8U0RlSj1DTWGjGKNVJavc0IRjxzgUtcrfuBfEn9QLhwRWNGcCoqzIFVjcA4ouO41rxea+UMQDr9\nlBKROcABqrpERIYAOar6RTvl3cB9wPFAKfCuiDyvquuSit0APKWq94vIBGA5UBzf9rmqTmvj8PNV\ndVVn695Xadk341gzud4cCnx51prpQVSVhlgD4Ug9lQ1VhI+cAEfcR84771Pwu8cZcveDFP12KTXn\nnkXN984lNrSXw5jbwRXvp/EmlivJ8WY3KxPTWNf6gYjgqqnEHdqDWwW3uJqP43Hyqzn9OZZuRdVY\nqBp/SVC0115GO3VWEbkJmAEcBCzBvBb9ATiind1mARtUdWP8GMuA04BkcVFgUPx7HrBtbyo/kEi2\nZuoiYUKNNXjFQ6HfRJpZa6b7aYw1NnN1xVAE8LmzyPHEH8Zz5rB7zhxC6z4m98FHyfndY+Q88ji1\np59M9UUXEB23X69eQ1dxBKgz/UCOG87pBzIiZEj0A9WBpwayYi684sbt8uB2e3D5A7izcxG/v0lw\n+rBrLfnhblqic+scMXBEPaaxxLb21qnGXZ9ALBbD0X4AxLT/2Lyx+Dw9nH0CEOei2i0ksgY4BHhP\nVQ+Jr/s/VZ3Szj5nAfNU9aL48vnAYap6aVKZEcDLQAGQDXxTVVfH3WJrgU+BKuAGVX0jvk8JUARE\ngaeBWzTFRYjIAmABwLBhww5dtmxZYlt1dTU5OZ3zg9fXVuFyZ+6D25nIzCUuPOJGOgpZjVMdDpPj\n96ezan2Clu2gGiPq3Ljxu1SQTluIgW3b2e+ZZxj50iu4IhF2HvENvvzOWVQddGBa6t8dhOsj+H3p\n/Y2bh2JiKXmDYwghIom2FpcbXC7E5TJt38nfdavzkuL5pq3X11TXEMwJtlkm8T3FvmpWGpyHe4uH\nfKfXpUDa2CBGPdolpjGy3FltHiOZVM/FY445ZrWqzuhw5xR09hfVoKoqIgogItkd7UDqy275L30u\n8Iiq/kJEDgceE5FJwHZgrKruEpFDgedEZKKqVmFcYltFJBcjLucDv291ItUHgQcBZsyYoXPnzk1s\nKykpIXm5LWLRCBvef5WcvMx1cUA8OinWQGMsglc8FPjzyPXmtGvNlKxdy9yJE3uwlpmHqlKybi2H\nfH0MVY0h6qJhVMEjJqqrS+OO9h8Ocw6hrPxysn+/jCGP/5Fh/3iT+tkzqF5wIfVHzM64/oe1G79i\n4v7De7UOTj9QVGPEohG0sRGNRICm1DYunx9vMAd8PmJuN+p2gdtDTDTx1q6qTQ/ddh7oLct98cEX\njJ0y1hSLi5zz3ewqzcSvrXWZRnVDNfvl7dcpy6Wzz8XO0llxeUpEHgDyReRHwA+AhzrYpxQYk7Q8\nmtZurx8C8wBUdaWI+IHB8Q76+vj61SLyOXAgsEpVt8bXh0TkcYz7rZW4DCREBL/bh9/tIxqLUh6u\noKxuFznebPJ9eQRs30yCSCxCOFpPdWMN1Y01NEQb2BkuxyveJldXNxAbXEToykuoXnAhwSefIWfJ\nUop+cCkNEw6i+qLvIZFGcu++H/f2HURHDCN05aXUnfqtbjt/X6NZP5DbB1mty2gkQrS6Biqr8Ej8\n8S8uJMtn3Go+X5NrbS9DpV3iIjur+/79LZ0UF1W9Q0SOx7ioDgJuVNVXOtjtXeAAERkHbAXOAc5r\nUWYzcBzwiIiMB/xAWTxgoEJVoyKyP3AAsFFEPEC+qpaLiBc4BVjRqSsdILhdbrJdxrwPR+vZUr0t\nYc3keLPxutqOItonolEzRiIWawpLzQBBi2mM+mg9tY11VEVqaIjWm34Alwe/22ceKp5gxwfqIpqT\nTc0Pz6fm/LMJPP8COQ89SuGV16EiSNyb69n2FXk33AIwoAWmI8TjweNp4c5WNb+5mhozKNSsNG60\nrCwjOPsgOpau06G4xKO+XlLVbwIdCUoCVY2IyKXAS5gw44dVda2ILMJYIM8DVwEPicgVGIP1wrj7\n7ShgkYhEMH0rF6tqRdwd91JcWNwYYenIghqwtLRmdtaVk+vNId+X1/WDOiLipIZ30sN7vU3hp3V1\n5mZPTh2fldUjI72To7pCjdXURutQBbe4yHJ1z5iTLpGVRd1Zp1F35r8w7PDjce/e02yzKxwm/z9/\nRuCvLxIrLCBWWEC0sIBYYT6xgnyzrsCs1+ygfUA6iLSdhSAWM1NKJ0QnjpNvLVl0LN1Oh60atx5q\nRSRPVSs7Kt9i3+WY8OLkdTcmfV9HiogzVX0a05/Scn0NcOje1MGS2pqpjzawu35P29ZMJGI+0ai5\nSVuO1nZCSp23wZbCoWrSitTXG6GpqWlKqOh2mxu8m6KCIrEI9dEGqiM1hBqqiWnM5OsSL9nuYGa5\nBF0uXHvauI0aG3HtLMP78We4KnYjDQ0pi2lWVkJwosni43yaiVE+sbxBfToCq0ski07LeXqi0dai\nU19vpjXYR/eapYnOSnYY+FBEXgFqnJWq+pO01MqSNhxrxiUhY82EdpItXgo9uQQkC3FEIpWI7I2r\nS6TJJTFoUNOEWA0N5saurjZ/oenYnXyDdFxddZEwlY3VNETrAcEj7oSrK5OJjhiGZ9tXrdePHE75\nc4+bBVWkphZXxW5cu/fE/+7GVbEH1+49uCt2m3UVu/Fs2Wq+V9e0OiaAulzE8ga1Fp9C83d4o+Db\nXky0oCCxvlUCzP5EKtFxhcwLUm2tmc5AYyRikpyBoU64tNudMW7fTKaz4vK3+MfSV4lGm6wRgFiM\n7HqFrAD1XhdbPA14slwU5A4hN1iA19PNDxdnIF1WlsljNXSoqUuy2DiZe12uZiO7VTWRSbiqMURt\npA4QXCK96+rqIqErLyXvhltwhZsmkIv5/YSuvLSpkAiak000J5vo2NGdO3BDQ0J8XBW7ce/e3Vyc\nKsxfz8Yvca16H9eeSiQWI1Wu51h2dkJ8ki2jaGK5uXWk2dl9/2Gbyr0GLTJLO9NPx13BTnZpR3Rs\nos8Ene3Qf1REsjARWwCfqGpj+qpl6RKOn9npEzErgfiDPRhsMvl31ZnsvyL4AB8me29FY4iyPXvI\n9mZTECgg4A2kzxJw3A7BIAwebOrc0ADhMJGqPdRXllHdWEsoUkPU5UJ8XrJcPrI9Gebq2kucTvvc\nO+/t3mixrCxiw4cSGz60c+WjUVyVVXz+4QYOCnqarKOEGJmPe8feuepiBfnGXdfKUuq6qy7w/Avd\n316dpS3RiUXNTKBO/6Jzrzmi4yT6HKCi09kR+nMxOcC+xNiKY0Tke6r69/RVzdImbYmIEyGTnd2x\n31ik1Tq3y00wy/TN1EfqKa0qxePyUBAoICcrhyx3+lwlMY3RoI3UUkcVVTTkNELAjzvmwx/Jx1UX\nNhaO1gP14O65IIF0UHfqt3o/MsztJlZYQO2YMTR0ZpzLXrjqskr3zVWX6FMqKCBr9fsM+p97EpZe\nxkTXudzg64zoACh4k6LXkrNL99HfcEd01i32C0yCyE8ARORA4Als53p6cSZxikSMmDh+YMfFlJPT\nfN6Nbux89Hl8+Dw+YhqjoraCspqybrdmGqINhBvDhBpC1DTWoKq4XW6y3FnktAw5zaOp36ax0QhN\nbW2Tm8/xgw+0juuepAdddR3hCofJ+3+3E8vPI7LfGKIjhzdNIdDbtCc6ToBLsuh4vE2BBP1IdDor\nLl5HWABU9dN4OLClO+iMiPh8TT+6HoxgcYmrlTXjFjcFgQJyfbl7Zc1EY1HCkTA1jTVU11cT0Yh5\noXN7yfZmd+zqSu63yY4PeHPEJhw2PvFwPFm2y23DTDOBLrrqjPgY4Sm47OqU6T5clVUUXXQZAOp2\nEx01gsh+Y43Y7De66fuokZCVAY8rlxuy3K2DJRzRqa01352r9Xhau9e83j4jOp2981aJyO+Ax+LL\n84HV6alSPyZZRBLuLJoiq3JyzA8p+S08g/oWmlkzdRWU15YT8AYoChSltGYSk2Y11lFVX0U4EkYQ\n3C43Po8Pv3RDbjOn4z8YhMLCpn6b5BDolmUzqE0tLYi76mKFBfA1syo6cnjK6LrIsKHsuetW3Ju3\n4PlyC55NW3Bv3kLwvQ9wJf27q8tFdOQIIsVjiI4dQ2S/MXEBGkNkzKjej4xzRKclsfhvua6uteg4\nWaYzWHQ6Ky4/Bi4BfoK5wr8Dv05Xpfo8HYlIbq75m6Ei0hHJqTKSrZl8fz45vhwaIg1UN1ZT01BD\nTGO4xEWWO4tcX276K+d2N6V2z883lmBDg/nU1Jgb1XFJWKumT9BmdN3VP6FhxiEw45DmO6gaF9wm\nIziezVtwx8Un64MXcIWqm4qKEB05HN+QofjHf53I2Ljo7DeGyNjRrcfI9CRtik6syVqPxUgEEjii\n47jY3O64KPUOnb27PMAvVfVOSIza78VWzxBSiojGfa5ZTSLiuLL6mIh0hmRrZnd4NxXhioSrK+jN\ngKgul6tpjEKq8TaxCqiJP2zcHuM+6UrCSkva2OvoOhFiRYXEigppnD61+TZVZE+lEZ34x71pM55P\nNxJ4YUWzAa4qQnT40LjYxF1sY0cn/mogkK5Lbh+XK7W1lUp0ovWQMxp6IeV+Z8XlVeCbgCP5AUyq\n/G+ko1IZh2qTgHRGRAbgG3GfSfzXcrzNpjIYu5+5KZ2xDJH4G7Iz3mYA/ntmGt0WXSeCFuTTWJBP\n47SmET5OZuiE8GzeYiyfL813/8v/2yplT3TY0ISFEy0eG/8eF57s9OWra5NUolOZZKn3MJ29a/yq\nmrAlVbVaRHqh9XoBl9u8CfiSQnyduHX70OkfJPfbFBU1G2/T1G+TNF7IpgTpt2h+Ho35eTROndRq\nm1SF4paOERzH8vG/9gbuXRXNykaHDm7uYnP6ecaOQXP6wEtYN9DZp2ONiExX1fcARGQGTXPY919c\nLhg9GgKDOi5r6T8k99sUFDTvt6mubt1vk4GdqZbuRwfl0jh5Ao2TJ7TaJtXVTcKzqTTez7MZ39/f\nJFi2q1nZ6OAiY+0kRGds/PtoNLcH+iV7iM6Ky+XAH0VkG+YVbiRwdtpqlUnYh4YlVb+NIzbOeBsn\nmsfttv02AxDNyaFx4ngaJ45vtU1qanFvLsWzaXOS5VOK7823CT7712ZlowX5xsU21ohNcn+P5vWt\nl9x2xUVEZgJbVPVdETkY+DfgTOBF4IseqJ/FknkkJ+XMzW3qk3PCRmtqIJI03qYbM0Bb+h6aHSQy\n/kAi41tPdS21dbi3lCb6dhyXm+/tVQT/3DydYyw/j8jY0USKxzaFVBebfh7Nz2vmqnXS5YzYvsN4\nX37+c5g/P+3XmkxHlssDmI58gMOB64DLgGmYKYTPSl/VLJY+gjOfjddr+uUGDzZi4wQJ1NY2jbdx\nymZqv01y52/yKHJafE1VrqN17Z1jbzudXS7zcbubvvdBNBggctABRA46oPXGcBjPlq1NEW2bSk04\n9ar3cf/lxcRkcwCxQbnG2ikeg9TX4y95E2mMp3/csgUWLDDfe1BgOhIXt6o6PVVnAw86c62IyJr0\nVs1i6cM4AR+BQOvBnbU18ekGnEne2yN5InhpsS5VuS6sc2ZyhOYPaed7sggmr3NWi7v9fZ39Ux2n\no/Ol2tcJuW1shMYG89dJA5R8jU7CSbfL5N3LRDFvD7+fyAFfI3LA11pvq6/Hs2VbfADp5oTVk7Xm\nI9ylW1v/qmpr4frrM0tcRMSjqhHMdMQL9mJfi8Xi0HJwp9Nv05iUXDzVQ7Xl986US/VAbq9cxTr4\nWooHWF8iFjMfJ4WSYzk6bRypb20dJVs/fQ2fj8jXxxH5+jjqW2wacdCM1Jbg5s09UjWHjgTiCeB1\nESnHRIe9ASAiXwf2alZKi8WSRHK/jWXfcYSiveEBzjg1Z3ZVx/ppaICYJoWcQyK3nyM+fcj6aWsy\nOsaO7dF6tCsuqrpYRF4FRgAvqybk0IXpe7FYLJa+QVvzsgBs2wPjxjUXn721fjKk7ydVuhyCQVi8\nuEfr0aFrS1XfSrHu0/RUx2KxWHoJRxzaSt3vzKPU0vpxxKe+PimXV5LrMdn66YEQ9Zbpchg9GsnA\naLF9QkTmAb8E3MBvVfW2FtvHYiYhy4+XWaiqy0WkGFgPOGn+31LVi+P7HAo8gklBsxz4jySLymKx\nWNKDSPvWD7QWn16yfpx0OdWVZew3/nB82T0/RiZt4hJPbnkfcDxQCrwrIs+r6rqkYjcAT6nq/SIy\nASMWxfFtn6vqtBSHvh8TWPBWvPw84IX0XIXFYrHsBV2xfpwBuQnrp8Vkab1g/XQH6bRcZgEbVHUj\ngIgsA04DksVFAUdS84Bt7R1QREYAg1R1ZXz598DpWHGxWCx9gVTWT3aLXGN7Zf3Ew66TAxpcmRF4\nkE5xGQVsSVouBQ5rUeZm4GURuQzIpmnAJsA4EXkfqAJuUNU34scsbXHMUalOLiILiIdODxs2jJKS\nksS26urqZsvtUR+px5UBnXTdTbgmzNp31/Z2NXod2w62DaAPtoHG/6dqvqs2/8Sj3mIaY2vVKqQT\nz7C9eS52hnSKSyrpbNk3ci7wiKr+QkQOBx4TkUnAdmCsqu6K97E8JyITO3lMs1L1QUwWAWbMmKFz\n585NbCspKSF5uS1iGmPDrg3k+HI6LNvXWPvuWibOnNjb1eh1bDvYNoB+2AZx66e6ror9hh6Az9vx\nrK+dfS52lnSKSykwJml5NK3dXj/E9JmgqitFxA8MVtWdYMYGqepqEfkcODB+zNEdHNNisVgGNo6b\nTH295iJLp7/nXeAAERknIlnAOcDzLcpsxoz8R0TGA36gTESGxAMCEJH9gQOAjaq6HQiJyGwxUxxe\nAPw5jddgsVgsli6QNstFVSMicinwEibM+GFVXSsii4BVqvo8cBXwkIhcgXFvXaiqKiJHAYtEJAJE\ngYuTcpz9mKZQ5BewnfkWi8WScaR1nIuqLseECyevuzHp+zrgiBT7PQ083cYxVwGtp4mzWCwWS8bQ\n/8KgLBaLZYDzzPpnmPXQLA6+92AOvOdAln64tMfrYMXFYukFnJt/9J2jmfXQLJ5Z/0xvV8nST3hm\n/TNc88o1bA1tRVE2V21mwV8W9LjA2LT5FksP49z8dfHZKreGtnLNK9cAcOb4M3uzapY+QkO0gbLa\nMspqythZs5OymrLE8rK1ywhHws3K1zbWcv2r1zN/cubM52KxWDqJqhJqCLV50++sNctry9YS0+Yp\nPuoidVz+4uU8+sGjFAWKKAoUURgsZHBwcGK5KFhEYaCQokARPo9N1d/fiMaiVNRVJH4nLX9Hyev3\nhPekPEa+P7+VsDhsrsys+VwslgFPXWMdZbVti4WzXFZTRjja+sb2uDwMDgxmSPYQhmQPIbYzluIs\nENUoPrePzZWbef+r96moqyASi6Qsm5OVw+DAYAqDha3FJ1jE4MBgioJxkQoUEvAGurVNLJ1DVams\nr0z5u2n2e6oto7y2vNVLB0C2N5shQfPbOaDoAI4YcwRDsocwNHsog4ODGZo9lCHZQxgcGIzP42PW\nQ7PYGtra6jhj8zJoPheLpb/SEG2gvLacT0Ofsn3j9pRisbNmJ2W1ZVQ3VLfaXxAKA4WJG7s4v5ih\nwaGtbvqh2UPJ9+fjkqbuzbZu/lG5o3jqO08llmMaozJcya66XVTUVbCrdhe76uKf2l2J5a2hrXy4\n40N21e2iMdbY6rgAQW+QokARg4ODEwLkiFJ4R5jtG7c3WUnBIoLeYDe0cv+ltrG2XaFI/v00RBta\n7e91ec1vJTiUkbkjmTZ8WpNQBIckfldDgkPIzspOUYO2WThnYTO3K5h//8XHZdh8LhZLXyEai7I7\nvLuZG6G8prz5AyB+4+8O727acU3T1zxfXuImnzxscuKNsaVwFAWK8LrbyHzbAalu/oAnwMI5C5uV\nc4mLgkABBYGCTh3XccuV15YbQaqtaC5G8b87anawrmwdFXUV1Efjk+S2mKHJ7/EnhKbZ3xbuucFB\nYyFle7ORDEiWuC84LxwtRaO8tjzx23F+WzWNNa32F4TBwcGJ38vXCr/W7HfjiMbg4GDy/flpay+n\n3+62f9zGttA2xgwaw63fvLVH+1vAioslw0l2KyRu9DZu/LbcCgFPIPEm+PWCrzN79OzETR/eFmb6\n1OmJm97v6TgH077S8uYfmTuShXMW7nNnvogwyDeIQb5B7F+wf4flVZWaxhreeustCg8opLy2vJWF\nVFFbQXldOZ/u+pRddbva9Of73L5WFlFRsLkoJbvwBvkG7dXD9Zn1z3SpvWIaM/0Ybbg0nd/OV5Vf\nUfVGVcpj5PvyGZw9mCHBIUwdNjXly8bQ7KEUBgrxuDLjkXrm+DM5c/yZVDdUs1/efr3SR5cZLZGB\nLP1wKde9eh1bKrd0283fn9nbm7+moSblW2Fi2bE8ass7dCuMyB3RdNMn+6Hjb4rtuRXW1q9l4oie\nT1jo3Py9iYiQk5XDiMCITrdBbWNtMyuovK68lYVUUVfBF3u+oLy2nNrG2pTH8bq8rQSnpRg5FtLK\nLSv52es/axZdd/UrV7OjegfThk9rcmemcG2W15YT1Wir87d84Tgo6yAOGndQk0sq/rcoWNQjLxz9\nEScRMCkAABXrSURBVCsuKVj64VIW/GVB4sZwQkUjsQinH3w6bU18qakTNJttXZgss63jdcf5ayI1\nhOpDXapzy33++ulfuankpsRb7dbQVq56+Sre3Pwmo/NGJ2785LfGVA8dl7gYHBxsxCE4lAOKDkgp\nFul2K1jaJugNEswLMiZvTMeFMcEQFXUVzVxzqSykLZVb2FW3i1BDqFPHDUfC3PLGLc3WeVyexG9k\neM5wJg+d3MrKcNycLd14/S4rcgZgxSUF1796fauHX12kjiteuoIrXrqil2qVBlam79AN0QaWrV0G\nmPBI58aeNnxa040e77B0HgCFgULcfWSWPUvnCHgDjPKOYtSglNMutaI+Ut8qgOGyFy5rs/yTZz2Z\n+A21DJyw9C5WXFLQXjz4tUdcC9DmW7OknHKm/W3tvYF3ZZ82j5W0z1ebv2L42OHtnqO98yTvc1PJ\nTW2W2fgfG8lyZ+11XS0DE5/Hx8jckYzMHZlYd9s/bmszum7O2Dk9WT3LXmDFJQVj88ayqXJTq/Wj\nckfxk8N+0gs16n7WxtYy8dDucQM8uPrBlDf/yNyRVlgs+0xno+ssmYW1IVOw+LjFreL87Y+5bRbO\nWUjA03yQnm0vS3dx5vgzuf342xmVOwpBGJU7ituPv73XAyIs7WMtlxQ48eA2WqxzpCu01mJxyITo\nOsveYcWlDeZPns+5k85lw64N5Phyers6GY+9+S0WSzLWLWaxWCyWbseKi8VisVi6HSsuFovFYul2\n0iouIjJPRD4RkQ0i0ip0SETGishrIvK+iPyfiJyUYnu1iPw0ad2XIvKhiKwRkVXprL/FYrFYukba\nOvRFxA3cBxwPlALvisjzqrouqdgNwFOqer+ITACWA8VJ2+8CXkhx+GNUtTw9NbdYLBbLvpJOy2UW\nsEFVN6pqA7AMOK1FGQUGxb/nAducDSJyOrARWJvGOlosFoslDaRTXEYBW5KWS+PrkrkZ+K6IlGKs\nlssARCQbuBb4WYrjKvCyiKwWkQXdXWmLxWKx7DvpHOeSKilVyzS75wKPqOovRORw4DERmYQRlbtU\ntTpFbqsjVHWbiAwFXhGRj1X1761OboRnAcCwYcMoKSlJbKuurm623B71kXpcrv4X9xCuCbP2XWsU\n2nawbQD9tw1iGmOre2u7+QMd9ua52BnSKS6lQHJe7tEkub3i/BCYB6CqK0XEDwwGDgPOEpHbgXwg\nJiJhVb1XVbfFy+8UkWcx7rdW4qKqDwIPAsyYMUPnzp2b2FZSUkLyclvENNZvB1HaFOMG2w62DaD/\ntsHeTBbW2ediZ0nnK/m7wAEiMk5EsoBzgOdblNkMHAcgIuMBP1CmqkeqarGqFgN3A7eq6r0iki0i\nufHy2cAJwEdpvAaLxWKxdIG0WS6qGhGRS4GXADfwsKquFZFFwCpVfR64CnhIRK7AuMwu1PZn1RoG\nPBt3lXmAx1X1xXRdg8VisVi6Rlpzi6nqckxHffK6G5O+rwOO6OAYNyd93whM7d5aWiwWi6W76X89\n1RaLxWLpday4WCwWi6XbseJisVgslm7HiovFYrFYuh0rLhaLxWLpdqy4WCwWi6XbseJisVgslm7H\niovFYrH8//buPkiuqszj+PfX3TM9yXQmAWPGLCCEMmURQN5CkFdBXhaorXUt2V2QYtHFxVWxENgX\nWC0KWKsWXZVFpYDwIiysAougWQoEF4kLKwtJEEISCERACcjbuqgDTGa6+9k/zrmdO52emcykOzPd\n9/lUdfW9556+c++Z7vv0c+7tc13TeXBxzjnXdB5cnHPONZ0HF+ecc03nwcU551zTeXBxzjnXdB5c\nnHOuA41995LWa+mQ+y5bKtUKQ5UhAHLKkVOOfC5PTv4dxrlWqVqVcrVMpVqhUq3UyiVRzBfJ5/JT\nsl0eXNw221TexFBliEKuwOzibAyjXC0zXB1mqDxEuVoGwDDijd4ws1oAkkRe+RHzzrmRKtUK5WqZ\ncrVM1aq18nwuT0++h1KxRLFQpJAr0JXvIq/8lH6WPLi4SalUKwyWB6lald6uXvpL/cwozBj1zVy1\nKpVqhapVw7RVah+W4coww9Xh8O0rlosYhFIBKQk+9Q/nOoWZjQggxuaura5cFz2FHnoKPXTnuynk\nChRyhSnLTMbjwcVNSDpLmTtzLqXuEl35rnFfl1OOXH7rAkESgOoDUrlaZqgyVPvwDVYGR3yDS30O\nkTQiAHn3nJtOki9WFauMeA/nlKOYL9JX7KOn0FMLIIVcoe0yeg8ublwTzVK21YiMZJwvZWZWy4TS\nQWm4MlwLQmN1z1WrVd4aesu751zTpbOQilVGLCvkCswozGibLGQyPLi4UQ2WBxmuDE84S9mekoCQ\nHy8KRfXZ0Mb8Rub1zmvYPVetbv5GOVb33FT3bbuplWTVyUn1RE45ioUis4qzKOaLdOW7akEkC1l0\nS4OLpOOBywnfP681s0vrlr8XuBGYE+ucb2Z31y1fB1xkZl/bmnW6bZPOUkrdJd5Tek9Ls5Ttrb57\nLqccs3tmN6w7WvfccHW4lhkNV4YZsqFa14aZ1c4XAeRyOYRGdM1l4cDSacyMilVqASR9mW8hVwhB\npHtW7YR68siylu29pDxwBXAssBFYIWmZma1LVfsScJuZXSlpEXA3sFtq+WXAPRNcp5uEdshStrdt\n7Z5LX92TnC9KzhkBkI7XybFK1IKRJIRq54/S5a41xrqstzvfTW9XLz2FnsxlIZPRytC6BNhgZs8B\nSLoF+AghE0kY0BenZwMvJwsk/QnwHPDWBNfptlI6S5lVnNVxWcr2NJHuuSQQpR9GKEv66dNX1FWq\nldq35irVzd11yb8pFZiSeUljBqesHxDT3VhmRrVaZWDTQList9CzRRbiXZ8T18rgshPwYmp+I3BQ\nXZ2LgPskfR7oBY4BkNQL/D0hQ/mbCa6TuI4zgTMB+vv7Wb58eW3ZwMDAiPmxbCpvIpfrrA+imTH4\n9iDrVq6rffMS2fzgTOS9MB2lL1XFNs/Xni01b3Xl8V++6e1NPPnIk6MHK9ji/dEuB1ozq+17TYPs\ncGhwiJfXvDzqerKg2Z+FVgaXRu+++vEITgFuMLOvSzoYuEnSXsDFwGVmNlD3Jt6adYZCs6XAUoDF\nixfbkUceWVu2fPly0vOjqVqVDf+7gVKxNG7d6a4+S3l65dMcdeRRbXOQaJWtfS90oiSDevC/HuSQ\nww+pzTfKouqfK9XKiCyqdsHDFGRR413Wm/w2ZKzLerP8Pkg0uw1aGVw2Aruk5ncm1e0VnQEcD2Bm\nD0vqAeYSspGTJH2VcLK/KmkQWLUV63QpybmUrlzXiHMpz+iZzAeWrEu68gC6892TWkeSGSTBKAlO\njbr+0gEq6eZLAthYXXzJfBKU6i/rbbcfF2ZFK4PLCmChpAXAS8DJwMfr6vwKOBq4QdIeQA/wupkd\nnlSQdBEwYGbfllTYinVmnp9LcdtLkpFsa/bRKGsaLYvqynWNOKHu7+vpqWXBxczKks4C7iVca3O9\nma2VdAmw0syWAecB10g6h/Ad5RM2xlCeo62zVfvQbgbLgwxVhujOdTN35lxmFWdl/nJI1x7SWZTr\nDC098sTfrNxdV3ZhanodcOg467hovHVmWZKlGNaRv0txzrUn/1rbhsyMTZVNnqU456YtPxq1kUq1\nwjvD74Cg1F1ifmk+PYUez1Kcc9OOB5dpLslSkiu+5pXmUeoueZbinJvW/Ag1TSVZimHMKs7yLMU5\n11Y8uEwjZsZgeZBytUxXrov+Uj+93b2epTjn2o4ftaaBcrXM4HC44quv2MecnjmepTjn2poHlyni\nWYpzrpP5kWw7S2cps4uzmd0z27MU51zH8eCyHXiW4pzLGj+6tZBnKc65rPLg0mQjspS8ZynOuWzy\nI16TJFkKQF+xz7MU51ymeXDZBp6lOOdcY34UnATPUpxzbmweXLZSoyyl1F3yu90551wDHlzGYRgD\nmwaAkKXMmTGHYr7oWYpzzo3Bg8sYhOgr9jGza6ZnKc45NwEeXMYgifmz5k/1ZjjnXNvJTfUGOOec\n6zweXJxzzjVdS4OLpOMlrZe0QdL5DZa/V9IDkn4uabWkE2P5EkmPx8cTkj6aes0Lkp6My1a2cvud\nc85NTsvOuUjKA1cAxwIbgRWSlpnZulS1LwG3mdmVkhYBdwO7AWuAxWZWljQfeELSf5hZOb7uKDN7\no1Xb7pxzbtu0MnNZAmwws+fMbAi4BfhIXR0D+uL0bOBlADN7OxVIemI955xzbUJmrTluSzoJON7M\nPhXnTwMOMrOzUnXmA/cBOwC9wDFmtiouOwi4HtgVOM3M7ozlzwP/Rwg4V5vZ0lH+/pnAmQD9/f0H\n3HLLLbVlAwMDlEql5u5wm/E2CLwdvA3A2wAat8FRRx21yswWT2qFZtaSB/CnwLWp+dOAb9XVORc4\nL04fDKwDcnV19gAeBXri/B/E53nAE8AR423LAQccYGkPPPCAZZ23QeDt4G1g5m1g1rgNgJU2yRjQ\nym6xjcAuqfmdid1eKWcAtwGY2cOELrC56Qpm9hTwFrBXnE+6zl4D7iR0vznnnJtGWvkjyhXAQkkL\ngJeAk4GP19X5FXA0cIOkPQjB5fX4mhctnNDfFXg/8IKkXkJm8/s4fRxwyXgbsmrVqjck/TJVNBfI\n+gUB3gaBt4O3AXgbQOM22HWyK2tZcImB4SzgXiAPXG9mayVdQki1lgHnAddIOodwDuUTZmaSDgPO\nlzQMVIHPmtkbknYH7ozjehWA75rZj7ZiW96dnpe00ibbj9ghvA0CbwdvA/A2gOa3QUuHfzGzuwmX\nF6fLLkxNrwMObfC6m4CbGpQ/B+zT/C11zjnXTP4Lfeecc02X1eDS8PLljPE2CLwdvA3A2wCa3AYt\n+52Lc8657Mpq5uKcc66FPLg455xruo4JLpKul/SapDWpsh0l/VjSs/F5h1guSd+MozWvlrR/6jWn\nx/rPSjp9KvZlsiTtEkeZfkrSWklnx/LMtIOkHkmPxtG010q6OJYvkPRI3J9bJXXH8mKc3xCX75Za\n1wWxfL2kP5yaPZo8Sfk44vhdcT5TbdBoBPUsfRYSkuZIul3S0/HYcPB2aYfJ/rR/uj2AI4D9gTWp\nsq8C58fp84GvxOkTgXsAAR8EHonlOwLPxecd4vQOU71vE2iD+cD+cXoW8AywKEvtEPelFKe7gEfi\nvt0GnBzLrwI+E6c/C1wVp08Gbo3TiwjDCxWBBcAvgPxU798E2+Jc4LvAXXE+U20AvADMrSvLzGch\ntc83Ap+K093AnO3RDlO+401uxN0YGVzWA/Pj9HxgfZy+Gjilvh5wCmEwTBrVa7cH8EPCLQ8y2Q7A\nTOAx4CDCL48Lsfxg4N44fS9wcJwuxHoCLgAuSK2rVq8dHoThlu4HPgzcFfcpa23wAlsGl0x9Fgij\nzj9PvHhre7ZDx3SLjaLfzH4NEJ/nxfKdgBdT9TbGstHK207s2tiP8M09U+0Qu4MeB14Dfkz4xv2m\nbb6NQ3p/avsal/8WeBdt3gbAvwB/RxjhAsI+Za0NDLhP0iqFUdIhY58FYHfgdeA7sYv0WoWhs1re\nDp0eXEajBmU2RnlbkVQCvg98wcx+N1bVBmVt3w5mVjGzfQnf3pcQRtbeolp87rg2kPRHwGsWb1+R\nFDeo2rFtEB1qZvsDJwCfk3TEGHU7tQ0KhNMFV5rZfoRBgLe4K3BK09qh04PLqwr3jEnuHfNaLB9t\nxOatGcl5WpPURQgs/2Zmd8TizLUDgJm9CSwn9B3PkZQMd5Ten9q+xuWzgd/Q3m1wKPDHkl4g3KTv\nw4RMJkttgDUeQT1rn4WNwEYzeyTO304INi1vh04PLsuA5KqG0wnnIJLyv4hXRnwQ+G1MDe8FjpO0\nQ7x64rhY1hYkCbgOeMrMvpFalJl2kPRuSXPi9AzgGOAp4AHgpFitvg2StjkJ+ImFTuVlwMnxSqoF\nwELCfYWmPTO7wMx2NrPdCCfof2Jmp5KhNpDUK2lWMk14D68hQ58FADN7BXhR0vtj0dGE+2a1vh2m\n+oRTE09cfQ/4NTBMiLJnEPqN7weejc87xroCriD0xT8JLE6t5y+BDfHxyanerwm2wWGEVHU18Hh8\nnJildgA+APw8tsEa4MJYvjvhwLgB+HegGMt74vyGuHz31Lq+GNtmPXDCVO/bJNvjSDZfLZaZNoj7\n+kR8rAW+GMsz81lIbf++wMr4mfgB4WqvlreDD//inHOu6Tq9W8w559wU8ODinHOu6Ty4OOecazoP\nLs4555rOg4tzzrmm8+DiOoKkd8XRbx+X9Iqkl1Lz3Vu5ju+kfg8wWp3PSTq1OVs9PUh6SNK+U70d\nrrP4pciu40i6CBgws6/VlYvwnq82fGFGSXoIOMvMHp/qbXGdwzMX19EkvU/SGklXEUZIni9pqaSV\nCvd7uTBV9yFJ+0oqSHpT0qUK94V5WNK8WOfLkr6Qqn+pwv1j1ks6JJb3Svp+fO334t/aIjOQdKCk\nn8aBFe+R1C+pK84fFuv8szbfk+ZiSSuS/YnBMtmOb0h6UNI6SYsl3alw342LUu2wVtJNCvc4uS2O\nYFC/TSfE/X1M4R4vvantWKdwj4+vNPWf5DqSBxeXBYuA68xsPzN7iXAfi8XAPsCxkhY1eM1s4Kdm\ntg/wMOHXyY3IzJYAfwskgerzwCvxtZcSRqce+SKpCFwOfMzMDgBuBv7RzIaBTwJLJR1HGBfsy/Fl\nl5vZgcDecfuOT63yHTM7nDD8zw+Av471zkyGw4ntcIWZ7Q0MAp+u26Z5hEENj7Yw4ONq4GxJ/YSR\nHvY0sw8A/zRKWzhX48HFZcEvzGxFav4USY8RMpk9CAfdeu+Y2T1xehXhXkGN3NGgzmGEASMxs2T4\nkXp7AHsC/6lwe4DziQMDmtnq+PofEobZGI6vOVrSo4QhTT4UX59YFp+fBJ40s1fNbJBwT5Od47Ln\nzex/4vTNcTvTDiG0xc/iNp0a9+k3hKH7r5H0UcLIus6NqTB+FefaXu1gKGkhcDawxMzelHQzYWyt\nekOp6Qqjf1Y2NajTaHjyegJWx2yjkb0I91VJuuNmAt8m3Gn0JUlfrtvuZDuqqelkPtmu+hOs9fMC\nfmRmp22xsdJiwo3nTgY+Qxi40LlReebisqYP+D3wO4WhxltxX/iHgD8DkLQ3jTOjdcBOkpbEet2S\n9ozTfw6UCINOXiGpD5hBCBRvxNF+PzaJ7Vog6cA4fUrczrSfAR+StHvcjl5JC+Pf6zOzu4BzaNDN\n51w9z1xc1jxGOLCvIdwH/L9b8De+BfyrpNXx760hZCE1ZrZJ0knAN+PBuwB8XdLrhHMsR8YM5Wrg\nMjM7Q9KNcV2/JNxhdKLWAn8l6TrgaWBp3Ta9KukM4NbU5dv/ALwD3BHPE+WAcyfxt13G+KXIzjWZ\nwg23CmY2GLvh7gMW2uZbDE/FNr0PuN3CHTqdaznPXJxrvhJwfwwyAj49lYHFuangmYtzzrmm8xP6\nzjnnms6Di3POuabz4OKcc67pPLg455xrOg8uzjnnmu7/AQzqw+frnIkVAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa02af3278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#function that plots the learning curve of the Euclidean Classifier\n",
    "\n",
    "def plot_learning_curve(train_scores, test_scores, train_sizes, ylim=None):\n",
    "    plt.figure()\n",
    "    plt.title(\"Learning Curve\")\n",
    "    if ylim is not None:\n",
    "        plt.ylim(*ylim)\n",
    "    plt.xlabel(\"Training examples\")\n",
    "    plt.ylabel(\"Score\")\n",
    "\n",
    "    train_scores_mean = np.mean(train_scores, axis=1)\n",
    "    train_scores_std = np.std(train_scores, axis=1)\n",
    "    test_scores_mean = np.mean(test_scores, axis=1)\n",
    "    test_scores_std = np.std(test_scores, axis=1)\n",
    "    plt.grid()\n",
    "    plt.fill_between(train_sizes, train_scores_mean - train_scores_std,train_scores_mean + train_scores_std, alpha=0.1,color=\"r\")\n",
    "    plt.fill_between(train_sizes, test_scores_mean - test_scores_std,test_scores_mean + test_scores_std, alpha=0.1, color=\"g\")\n",
    "    plt.plot(train_sizes, train_scores_mean, 'o-', color=\"r\",label=\"Training score\")\n",
    "    plt.plot(train_sizes, test_scores_mean, 'o-', color=\"g\",label=\"Cross-validation score\")\n",
    "\n",
    "    plt.legend(loc=\"best\")\n",
    "    return plt\n",
    "\n",
    "# C - draw the learning curve of the scikit-learn Euclidean Classifier\n",
    "train_sizes, train_scores, test_scores = learning_curve(EuclideanClassifier(), X_train, y_train, cv=5, n_jobs=-1, train_sizes=np.linspace(.2, 1.0, 5))\n",
    "plot_learning_curve(train_scores, test_scores, train_sizes)\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "zhhfQ5HU4kty"
   },
   "source": [
    "# STEP 14\n",
    "\n",
    "Για τον υπολογισμό των a-priori πιθανοτήτων για κάθε κατηγορία 0-9 χρησιμοποιούμε τη συνάρτηση np.bincount() στο σύνολο των labels των δειγμάτων, η οποία μετρά των αριθμό των εμφανίσεων κάθε ετικέτας σε αυτό. Το πλήθος δειγμάτων κάθε ετικέτας διαιρείται στη συνέχεια με τον συνολικό αριθμό των δειγμάτων και το αποτέλεσμα αποτελεί την a-priori πιθανότητα για το ψηφίο. \n",
    "\n",
    "Εμφανίζουμε τις a-priori πιθανότητες για όλα τα ψηφία 0-9 όπως φαίνεται στη συνέχεια. Παρατηρούμε ότι δεν υπάρχουν μεγάλες αποκλίσεις στις πιθανότητες αυτές (η μεγαλύτερη απόκλιση είναι 0.1) και όλες κινούνται γύρω στην τιμή 0.1. Επιπλέον παρατηρούμε ότι το άθροισμα όλων των a-priori πιθανοτήτων είναι 1 γεγονός που επιβεβαιώνει την ορθότητα του υπολογισμών μας."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 185
    },
    "colab_type": "code",
    "id": "Gos7GihZHUhC",
    "outputId": "a633838f-59e1-45db-b83a-a844ffb6aabb"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Apriori of digit 0 is 0.163763544095\n",
      "Apriori of digit 1 is 0.13784117405\n",
      "Apriori of digit 2 is 0.100260595254\n",
      "Apriori of digit 3 is 0.0902482512687\n",
      "Apriori of digit 4 is 0.0894253188863\n",
      "Apriori of digit 5 is 0.0762584007681\n",
      "Apriori of digit 6 is 0.0910711836511\n",
      "Apriori of digit 7 is 0.0884652311068\n",
      "Apriori of digit 8 is 0.0743382252092\n",
      "Apriori of digit 9 is 0.0883280757098\n"
     ]
    }
   ],
   "source": [
    "# calculate the a priori propabilities for each category of digit 0-9\n",
    "frequencies = np.bincount(y_train.astype(int))\n",
    "apriori = np.divide(frequencies,y_train.shape[0])\n",
    "\n",
    "for i in range(0,10):\n",
    "    print('Apriori of digit',i,'is',apriori[i])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "rw0wMSOrHUyL"
   },
   "source": [
    "# STEP 15\n",
    "\n",
    "Για την υλοποίηση ενός Bayesian Classifier πρακτικά θέλουμε να δημιουργήσουμε μια συνάρτηση η οποία αντιστοιχεί μια ετικέτα y = Ck για κάποια k ως εξής: \n",
    "\n",
    "*y = argmax{p(Ck)Πp(xi | Ck)}* για k από 1-Κ κατηγορίες και i από 1-n χαρακτηριστικά για κάθε δείγμα.\n",
    "\n",
    "Για τον υπολογισμό του παραπάνω χρειαζόμαστε τις a-priori πιθανότητες κάθε κατηγορίας p(Ck) καθώς και τις πιθανότητες p(xi | Ck) οι οποίες μπορούν να υπολογισθούν από τη συνάρτηση πυκνότητας πιθανότητας της κανονικής κατανομής με τη βοήθεια των μέσων τιμών και διασπορών των χαρακτηριστικών (όπως υπολογίζονται στο βήμα 9α). \n",
    "\n",
    "Για την υλοποίηση του Bayes ταξινομητή σαν ένα scikit-learn estimator δημιουργήθηκε μια κλάση class BayesClassifier(BaseEstimator, ClassifierMixin) με τις μεθόδους _init_,fit, predict και score (βρισκεται στις Παρατηρήσεις) και μια επιπλέον μέθοδος calcGaussian(self,x,mean,var) η οποία χρησιμοποιείται στους υπολογισμούς από την predict.\n",
    "\n",
    "*   Στο εσωτερικό της _init_(self) γίνονται αρχικοποιήσεις για τις μεταβλητές της κλάσης.\n",
    "*    Στην fit(self, X, y, v) υπολογίζονται οι μέσες τιμές και  οι διασπορές για κάθε ψηφίο (0-9) και αποθηκεύονται στις μεταβλητές self.X_mean_, self.X_var_ στη μορφή numpy array (10,256) και επιπλέον υπολογίζονται οι a-priori πιθανότητες κάθε κατηγορίας οι οποίες αποθηκεύονται στην self.X_apriori_ ως λίστα 10 στοιχείων.\n",
    "*   Στην predict(self, X) υπολογίζεται για κάθε δείγμα η πιθανότητα να ανήκει σε κάθε κλάση 0-9 καλώντας την μέθοδο calcGaussian(self,x,mean,var), η οποία υπολογίζει σε όλα τα χαρακτηριστικά του δείγματος τη συνάρτηση πυκνότητας πιθανότας χρησιμοποιώντας τις τιμές self.X_mean_, self.X_var_ για κάθε χαρακτηριστικό και κάθε ψηφίο 0-9. Οι τιμές επιστρέφονται ως στοιχεία μιας λίστας και πολλαπλασιάζονται μεταξύ τους και με την a-priori πιθανότητας της κλάσης. Η πρόβλεψη για κάθε δείγμα υπολογίζεται παίρνοντας την κλάση με την υψηλότερη πιθανότητα από όσες υπολογίστηκαν και επιστρέφονται σε μια λίστα οι προβλέψεις των labels (0-9) για κάθε δείγμα του Χ. \n",
    "*   Στην score(self, X, y) καλείται η predict(self, X) και για τις προβλέψεις που επιστρέφονται γίνεται ο έλεγχος με τα πραγματικά labels y και επιστρέφεται το ποσοστό επιτυχίας.\n",
    "\n",
    "Στο εσωτερικό του main κώδικα δοκιμάζουμε τον scikit-learn classifier που φτιάξαμε. Συγκεκριμένα, καλούμε αρχικά τη μέθοδο fit με εισόδους τα X_train, y_train και στη συνέχεια καλούμε τη μέθοδο score με εισόδους τα X_test, y_test.\n",
    "\n",
    "Επίσης καλούμε την έτοιμη υλοποίηση GaussianNB() του scikit-learn με τον ίδιο τρόπο.\n",
    "\n",
    "Παρατηρούμε ότι τα ποσοστά που πετυχαίνουν οι δύο μέθοδοι είναι κοντά αλλά η δική μας υλοποίηση πετυχαίνει καλύτερο αποτέλεσμα κατά 6% περίπου. Από την άλλη, ο χρόνος εκτέλεσης του έτοιμου μοντέλου είναι μικρότερος του δικού μας κατά 2 sec περίπου.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 50
    },
    "colab_type": "code",
    "id": "gfp5pbdNJGgs",
    "outputId": "abf8f728-c1aa-45d8-ba83-3331e271e300"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success rate of our scikit-learn Bayes Classifier is 77.4788241156 %\n",
      "Success rate of imported scikit-learn GaussianNB is 71.9481813652 %\n"
     ]
    }
   ],
   "source": [
    "# create a naive Bayesian Classifier as a scikit learn learn estimator - class BayesClassifier\n",
    "clf = BayesClassifier()\n",
    "clf.fit(X_train,y_train,0)      # 0 is used when we normally calculate the variance from X_train\n",
    "score = clf.score(X_test,y_test)\n",
    "print(\"Success rate of our scikit-learn Bayes Classifier is\",score*100,\"%\")\n",
    "\n",
    "# compare our Bayes Classifier with the scikit-learn GaussianNB\n",
    "clf = GaussianNB()\n",
    "clf.fit(X_train, y_train)\n",
    "score = clf.score(X_test,y_test)\n",
    "print(\"Success rate of imported scikit-learn GaussianNB is\",score*100,\"%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ZyAnzwYzHW9c"
   },
   "source": [
    "# STEP 16\n",
    "\n",
    "Για τον υπολογισμό της ταξινόμησης Bayes υποθέτοντας ότι η διασπορά για όλα τα χαρακτηριστικά, για όλες τις κατηγορίες ισούται με 1, χρησιμοποιούμε στο μοντέλο που υλοποιήσαμε στη μέθοδο fit την παράμετρο v. Συγκεκριμένα, αν η παράμετρος v=0 τότε οι διασπορές των χαρακτηριστικών για κάθε ψηφίο υπολογίζονται κανονικά όπως έχουμε αναλύσει προηγουμένως, διαφορετικά όλες οι τιμές τίθενται στο 1. \n",
    "\n",
    "Στο εσωτερικό του main κώδικα καλούμε τη μέθοδο fit του Bayes classifier με εισόδους τα X_train, y_train και v=1 (ώστε να έχουμε διαπορές ίσες με 1). Στη συνέχεια καλούμε τη μέθοδο score με εισόδους τα X_test, y_test.\n",
    "\n",
    "Παρατηρούμε αύξηση του score της μεθόδου κατά 4% περίπου. Θέτοντας τις διασπορές ίσες με 1 πρακτικά είναι σαν να ανεξαρτητοποιούμε τις πιθανότητες p(xi | Ck) (που υπολογίζονται βάσει του Gaussian distribution) από την επίδραση της διασποράς. Αντιθέτως οι μέσες τιμές είναι αυτές που, πλέον, καθορίζουν τις πιθανότητες βάσει της συνάρτησης.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "lzN0wY1rHZJo",
    "outputId": "eb337f72-4f9d-45f6-8a8f-5a89f9f6c02e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success rate of our scikit-learn Bayes Classifier with variances 1 is 81.2655705032 %\n"
     ]
    }
   ],
   "source": [
    "# calculate the score of our naive Bayes classifier when variances of features of all digits are equal to 1\n",
    "clf = BayesClassifier()\n",
    "clf.fit(X_train,y_train,1)      # 0 is used when we normally calculate the variance from X_train\n",
    "score = clf.score(X_test,y_test)\n",
    "print(\"Success rate of our scikit-learn Bayes Classifier with variances 1 is\",score*100,\"%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "9rJiP_qHRE_O"
   },
   "source": [
    "# STEP 17\n",
    "\n",
    "Θα συγκρίνουμε την επίδοση των Naive Bayes ταξινομητών (του δικού μας και του έτοιμου GaussianNB()) των οποίων τις επιδόσεις τυπώσαμε παραπάνω με τους Nearest Neighbors, SVM. Καλούμε τις  μεθόδους fit, score των KNeighborsClassifier() με k=5 και svm.SVC() με kernel = 'rbf', kernel = 'linear' και kernel = 'poly'. Παρατηρούμε ότι και οι δύο αυτοί ταξινομητές εμφανίζουν πολύ μεγαλύτερα ποσοστά επιτυχίας από τους Bayes classifiers που μελετήσαμε προηγουμένως, προσεγγίζοντας το 95%. Το μεγαλύτερο ποσοστό εμφανίζεται στον svm classifier με kernel = 'poly' ενώ ακολουθεί ο KNeighbors.\n",
    "\n",
    "Το μοντέλο των k πλησιέστερων γειτόνων επιτυγχάνει σταθερά υψηλές επιδόσεις, χωρίς a priori υποθέσεις σχετικά με τις κατανομές από τις οποίες χαρακτηρίζονται τα δείγματα του training set. Από την άλλη το μοντέλο είναι υπολογιστικά πολύ εξαντλητικό, καθώς για κάθε δείγμα ο αλγόριθμος διατρέχει όλα τα δεδομένα για να βρει τον κοντινότερο γείτονα. Ένα νέο δείγμα ταξινομείται βάσει του υπολογισμού της απόστασης από τα χαρακτηριστικά τoυ κοντινότερου δείγματος. Η μετρική που χρησιμοποιείται by default για την απόσταση είναι η minkowski με p=2 που ισοδυναμεί με την Euclidean απόσταση. Ο k-NN ταξινομητής επεκτείνει την παραπάνω ιδέα παίρνοντας τα k πλησιέστερα σημεία και αποφασίζοντας βάσει της πλειοψηφίας από την ψήφο των γειτόνων. Συνήθως επιλέγονται 1, 3 ή 5 γείτονες, ενώ υψηλότερες τιμές μπορεί να οδηγήσουν σε overfitting. Επιπλέον, το μοντέλο δεν αποδίδει καλά σε imbalanced data, κάτι που δεν συμβαίνει στην ερίπτωση μας μιας και έχουμε παρόμοιο αριθμό δειγμάτων σε κάθε κατηγορία.\n",
    "\n",
    "Το μοντέλο Support Vector Machine προσπαθεί να βρει το βέλτιστο υπερεπίπεδο για το διαχωρισμό των διάφορων κλάσεων, μεγιστοποιώντας την απόσταση μεταξύ των σημείων που αντιστοιχούν σε κάθε δείγμα στον χώρο των χαρακτηριστικών και του υπερεπιπέδου. Η παράμετρος kernel προσδιορίζει το είδος του υπερεπιπέδου που χρησιμοποιείται για να διαχωρίσει τα δεδομένα. Το συγκεκριμένο μοντέλο είναι αποτελεσματικό σε χώρους με μεγάλες διαστάσεις, ενώ χρησιμοποιεί ένα υποσύνολο των σημείων του training set στη συνάρτηση απόφασης (που ονομάζονται support vectors), επομένως είναι επίσης αποδοτικό στη μνήμη.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 107
    },
    "colab_type": "code",
    "id": "CIr50WuNRMQV",
    "outputId": "32db6e15-3b86-4522-e3ff-b369a43dfc9c"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success rate of scikit-learn GaussianNB is 71.9481813652 %\n",
      "Success rate of scikit-learn KNeighborsClassifier is 94.4693572496 %\n",
      "Success rate of scikit-learn svm with kernel='rbf' is 94.2202291978 %\n",
      "Success rate of scikit-learn svm with kernel='linear' is 92.6258096662 %\n",
      "Success rate of scikit-learn svm with kernel='poly' is 94.6686596911 %\n"
     ]
    }
   ],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings(action='ignore', category=FutureWarning)\n",
    "\n",
    "# compare scores of scikit-learn Naive Bayes, Nearest Neighbors, SVM classifiers\n",
    "clf_gauss = GaussianNB()\n",
    "temp = clf_gauss.fit(X_train, y_train)\n",
    "score1 = clf_gauss.score(X_test, y_test)\n",
    "\n",
    "clf_kneigh = KNeighborsClassifier()\n",
    "clf_kneigh.fit(X_train, y_train)\n",
    "score2 = clf_kneigh.score(X_test,y_test)\n",
    "\n",
    "clf_rbf = svm.SVC(probability = True, random_state=72)\n",
    "clf_rbf.fit(X_train, y_train)\n",
    "score3 = clf_rbf.score(X_test,y_test)\n",
    "\n",
    "clf_linear = svm.SVC(kernel='linear', probability = True, random_state=72)\n",
    "clf_linear.fit(X_train, y_train)\n",
    "score4 = clf_linear.score(X_test,y_test)\n",
    "\n",
    "clf_poly = svm.SVC(kernel='poly', probability = True, random_state=72)\n",
    "clf_poly.fit(X_train, y_train)\n",
    "score5 = clf_poly.score(X_test,y_test)\n",
    "\n",
    "print(\"Success rate of scikit-learn GaussianNB is\",score1*100,\"%\")\n",
    "print(\"Success rate of scikit-learn KNeighborsClassifier is\",score2*100,\"%\")\n",
    "print(\"Success rate of scikit-learn svm with kernel='rbf' is\",score3*100,\"%\")\n",
    "print(\"Success rate of scikit-learn svm with kernel='linear' is\",score4*100,\"%\")\n",
    "print(\"Success rate of scikit-learn svm with kernel='poly' is\",score5*100,\"%\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "DOVTZkppRGjb"
   },
   "source": [
    "# STEP 18 Α\n",
    "\n",
    "Παρατηρώντας τα confusion matrices κάθε classifier από τo προηγούμενo ερώτημα, επιλέγουμε για να εφαρμόσουμε ensembling τους ταξινομητές SVM με kernel linear, SVM με kernel poly και KNeighborsClassifier. Αυτό το κάνουμε γιατί οι ταξινομητές που θα συνδυαστούν θέλουμε να χαρακτηρίζονται από διαφορετικό τύπο λαθών και ταυτόχρονα να παρουσιάζουν καλά ποσοστά στην ταξινόμηση ώστε να πετύχουμε κάτι υψηλότερο μέσω του συνδυασμού τους. Είναι αναγκαίο να επιλεχθεί μονός αριθμός ταξινομητών, ώστε να είναι δυνατή η επίτευξη απόλυτης πλειοψηφίας.\n",
    "\n",
    "Ο VotingClassifier στον συνδυασμό με hard voting προβλέπει το label βάσει της πλειοψηφίας της ψηφοφορίας, ενώ στο soft voting βάσει του argmax των αθροισμάτων των προβλεπόμενων πιθανοτήτων. Καθώς το soft voting προτείνεται κυρίως σε σύνολα καλά βαθμονομημένων ταξινομητών και οι confusion matrices δεν παρουσιάζουν μεγάλες αποκλίσεις, τα ποσοστά επιτυχίας για hard και soft είναι καλύτερα από το ερώτημα 17 και παρόμοια μεταξύ τους. Επίσης, δοκιμάσαμε μεταβολές στα βάρη κάθε ταξινομητή στο ensembling με hard voting δίνοντας λίγο παραπάνω στον svm(kernel='poly') και στον KNeighbors που κάνουν ορθότερα predictions. Οι βελτιώσεις είναι μικρές. Στην περίπτωση του soft παρατηρήσαμε ότι δεν προσφέρουν βελτίωση και δεν τα συμπεριλάβαμε. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 53
    },
    "colab_type": "code",
    "id": "5GjrmgejRNF5",
    "outputId": "74e2a98a-3d08-41cc-c0b9-1042896b9cc3"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success rate of hard VotingClassifier is 95.067264574 %\n",
      "Success rate of soft VotingClassifier is 94.9177877429 %\n"
     ]
    }
   ],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings(action='ignore', category=DeprecationWarning)\n",
    "\n",
    "weights = [1, 2, 2]\n",
    "#voting classifier of SVM poly, SVM linear and KNeighbors with hard voting\n",
    "eclf1 = VotingClassifier(estimators=[('linear', clf_linear), ('KNeighborsClassifier', clf_kneigh), ('poly', clf_poly)], voting='hard', weights=weights)\n",
    "eclf1 = eclf1.fit(X_train, y_train)\n",
    "score_eclf1 = eclf1.score(X_test, y_test)\n",
    "print(\"Success rate of hard VotingClassifier is\", score_eclf1*100,\"%\")\n",
    "\n",
    "#voting classifier of SVM poly, SVM linear and KNeighbors with soft voting\n",
    "eclf2 = VotingClassifier(estimators=[('linear', clf_linear), ('KNeighborsClassifier', clf_kneigh), ('poly', clf_poly)], voting='soft')\n",
    "eclf2 = eclf2.fit(X_train, y_train)\n",
    "score_eclf2 = eclf2.score(X_test, y_test)\n",
    "print(\"Success rate of soft VotingClassifier is\", score_eclf2*100,\"%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "YgIQjbvfPijb"
   },
   "source": [
    "# STEP 18 Β\n",
    "\n",
    "Δοκιμάζοντας τον Bagging Classifier με base estimator κάθε φορά έναν από τους ταξινομητές που δοκιμάσαμε παραπάνω, παρατηρήσαμε ότι στις περισσότερες περιπτώσεις οδηγούμασταν σε ελάχιστα καλύτερο score μετά το ensembling, σε σχέση με τα score των ταξινομητών (ερώτημα 17), ακόμη και έπειτα από tuning στην παράμετρο του πλήθους των estimators και του πλήθους των δειγμάτων.\n",
    "\n",
    "Στην τεχνική του bagging υπάρχει ένα trade-off μεταξύ της ακρίβειας του base estimator και του κέρδους που επιτυγχάνετε μέσω του bagging. Το aggregation που πραγματοποιείται στο bagging μπορεί να βελτιώσει σημαντικά το σύνολο, όταν έχουμε ένα ασταθές μοντέλο, αλλά όταν τα βασικά μας μοντέλα είναι πιο σταθερά - έχουν εκπαιδευτεί σε περισσότερα δείγματα με μεγαλύτερη ακρίβεια - οι βελτιώσεις μειώνονται.\n",
    "\n",
    "Επιλέξαμε λοιπόν ως Base estimator τον svm με kernel='linear' classifier που κάνει αποτελεσματική ταξινόμηση, αλλά δεν εμφανίζει το καλύτερο score από όλους τους παραπάνω, γιατί εμφάνιζε πιο αισθητές βελτιώσεις μέσω της τεχνικής. Κάνοντας tuning στις παραμέτρους επιλέξαμε πλήθος estimators ίσο με 9 και βρήκαμε το παρακάτω βελτιωμένο ποσοστό σε σχέση με το κανονικό ποσοστό του classifier.\n",
    "\n",
    "Τέλος, θέτοντας max_samples=0.6492 χρησιμοποιούμε ουσιαστικά το 64.92% των δειγμάτων για την εκπαίσδευση κάθε estimator. Παρατηρούμε από τους παρακάτω χρόνους εκτέλεσης ότι παρόλο τον περιορισμό τον max_samples, το ποσοστό επιτυχίας είναι σχεδόν ίδιο, ενώ ο χρόνος παρουσιάζει σημαντική μείωση."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 143
    },
    "colab_type": "code",
    "id": "Us_bOHEKRj35",
    "outputId": "075528f3-c3a0-4174-d01d-c3e324fc8dde"
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 4.52 s, sys: 7.99 ms, total: 4.53 s\n",
      "Wall time: 4.53 s\n",
      "Success rate of BaggingClassifier with base estimator svm kernel='linear' with max_samples is 93.6223218734 \n",
      "\n",
      "CPU times: user 6.72 s, sys: 7.93 ms, total: 6.73 s\n",
      "Wall time: 6.73 s\n",
      "Success rate of BaggingClassifier with base estimator svm kernel='linear' is 93.6721474838\n"
     ]
    }
   ],
   "source": [
    "# BaggingClassifier with base estimator svm kernel='linear' with max samples restriction\n",
    "%time clf_bagging = BaggingClassifier(base_estimator=svm.SVC(kernel='linear'), n_estimators=9, random_state=762, max_samples=0.6492).fit(X_train, y_train)\n",
    "print(\"Success rate of BaggingClassifier with base estimator svm kernel='linear' with max_samples is\", clf_bagging.score(X_test, y_test)*100, \"\\n\")\n",
    "\n",
    "# BaggingClassifier with base estimator svm kernel='linear' without max samples restriction\n",
    "%time clf_bagging = BaggingClassifier(base_estimator=svm.SVC(kernel='linear'), n_estimators=9, random_state=762).fit(X_train, y_train)\n",
    "print(\"Success rate of BaggingClassifier with base estimator svm kernel='linear' is\", clf_bagging.score(X_test, y_test)*100)\n"
   ]
  }
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