sitc/ml1/2_5_1_kNN_Model.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](files/images/EscUpmPolit_p.gif \"UPM\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Course Notes for Learning Intelligent Systems"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Department of Telematic Engineering Systems, Universidad Politécnica de Madrid, © 2016 Carlos A. Iglesias"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## [Introduction to Machine Learning](2_0_0_Intro_ML.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Table of Contents\n",
    "* [kNN Model](#kNN-Model)\n",
    "* [Load data and preprocessing](#Load-data-and-preprocessing)\n",
    "* [Train classifier](#Train-classifier)\n",
    "* [Evaluating the algorithm](#Evaluating-the-algorithm)\n",
    "    * [Precision, recall and f-score](#Precision,-recall-and-f-score)\n",
    "\t* [Confusion matrix](#Confusion-matrix)\n",
    "\t* [K-Fold validation](#K-Fold-validation)\n",
    "* [Tuning the algorithm](#Tuning-the-algorithm)\n",
    "* [References](#References)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# kNN Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The goal of this notebook is to learn how to train a model, make predictions with that model and evaluate these predictions.\n",
    "\n",
    "The notebook uses the [kNN (k nearest neighbors) algorithm](https://en.wikipedia.org/wiki/K-nearest_neighbors_algorithm)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loading data and preprocessing\n",
    "\n",
    "The first step is loading and preprocessing the data as explained in the previous notebooks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# library for displaying plots\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# display plots in the notebook \n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "## First, we repeat the load and preprocessing steps\n",
    "\n",
    "# Load data\n",
    "from sklearn import datasets\n",
    "iris = datasets.load_iris()\n",
    "\n",
    "# Training and test spliting\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "x_iris, y_iris = iris.data, iris.target\n",
    "\n",
    "# Test set will be the 25% taken randomly\n",
    "x_train, x_test, y_train, y_test = train_test_split(x_iris, y_iris, test_size=0.25, random_state=33)\n",
    "\n",
    "# Preprocess: normalize\n",
    "from sklearn import preprocessing\n",
    "scaler = preprocessing.StandardScaler().fit(x_train)\n",
    "x_train = scaler.transform(x_train)\n",
    "x_test = scaler.transform(x_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Train classifier"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The usual steps for creating a classifier are:\n",
    "1. Create classifier object\n",
    "2. Call *fit* to train the classifier\n",
    "3. Call *predict* to obtain predictions\n",
    "\n",
    "Once the model is created, the most relevant methods are:\n",
    "* model.fit(x_train, y_train): train the model\n",
    "* model.predict(x): predict\n",
    "* model.score(x, y): evaluate the prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KNeighborsClassifier(algorithm='auto', leaf_size=30, metric='minkowski',\n",
       "           metric_params=None, n_jobs=1, n_neighbors=15, p=2,\n",
       "           weights='uniform')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "import numpy as np\n",
    "\n",
    "# Create kNN model\n",
    "model = KNeighborsClassifier(n_neighbors=15)\n",
    "\n",
    "# Train the model using the training sets\n",
    "model.fit(x_train, y_train) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction  [1 0 1 1 1 0 0 1 0 2 0 0 1 2 0 1 2 2 1 1 0 0 1 0 0 2 1 1 2 2 2 2 0 0 1 1 0\n",
      " 1 2 1 2 0 2 0 1 0 2 1 0 2 2 0 0 2 0 0 0 2 2 0 1 0 1 0 1 1 1 1 1 0 1 0 1 2\n",
      " 0 0 0 0 2 2 0 1 1 2 1 0 0 2 1 1 0 1 1 0 2 1 2 1 2 0 2 0 0 0 2 1 2 1 2 1 2\n",
      " 0]\n",
      "Expected  [1 0 1 1 1 0 0 1 0 2 0 0 1 2 0 1 2 2 1 1 0 0 2 0 0 2 1 1 2 2 2 2 0 0 1 1 0\n",
      " 1 2 1 2 0 2 0 1 0 2 1 0 2 2 0 0 2 0 0 0 2 2 0 1 0 1 0 1 1 1 1 1 0 1 0 1 2\n",
      " 0 0 0 0 2 2 0 1 1 2 1 0 0 1 1 1 0 1 1 0 2 2 2 1 2 0 1 0 0 0 2 1 2 1 2 1 2\n",
      " 0]\n"
     ]
    }
   ],
   "source": [
    "print(\"Prediction \", model.predict(x_train))\n",
    "print(\"Expected \", y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy in training 0.964285714286\n"
     ]
    }
   ],
   "source": [
    "# Evaluate Accuracy in training\n",
    "\n",
    "from sklearn import metrics\n",
    "y_train_pred = model.predict(x_train)\n",
    "print(\"Accuracy in training\", metrics.accuracy_score(y_train, y_train_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy in testing  0.921052631579\n"
     ]
    }
   ],
   "source": [
    "# Now we evaluate error in testing\n",
    "y_test_pred = model.predict(x_test)\n",
    "print(\"Accuracy in testing \", metrics.accuracy_score(y_test, y_test_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we are going to visualize the Nearest Neighbors classification. It will plot the decision boundaries for each class.\n",
    "\n",
    "We are going to import a function defined in the file [util_knn.py](files/util_knn.py) using the *magic command* **%run**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
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MvogMAaYCZwdqb+ysWcWPe6Sl0SMtrSxxK1XpaQJXZZWZuZDMzIUh1RVjTOkVRMYD1wBe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\nuJlZxVziZmYVc4mbmVXsG46Y2BK+GKQNAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc7cb622908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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N4kopFcdCvbOPUiqCdCxcRYr2xJVSKo5pEldKqTgWchIXkQQRWSUiHwd4bYCI/GW/vkpE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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc7cb632518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%run util_knn.py\n",
    "plot_classification_iris()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluating the algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Precision, recall and f-score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For evaluating classification algorithms, we usually calculate three metrics: precision, recall and F1-score\n",
    "\n",
    "* **Precision**: This computes the proportion of instances predicted as positives that were correctly evaluated (it measures how right our classifier is when it says that an instance is positive).\n",
    "* **Recall**: This counts the proportion of positive instances that were correctly evaluated (measuring how right our classifier is when faced with a positive instance).\n",
    "* **F1-score**: This is the harmonic mean of precision and recall, and tries to combine both in a single number."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "             precision    recall  f1-score   support\n",
      "\n",
      "     setosa       1.00      1.00      1.00         8\n",
      " versicolor       0.79      1.00      0.88        11\n",
      "  virginica       1.00      0.84      0.91        19\n",
      "\n",
      "avg / total       0.94      0.92      0.92        38\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(metrics.classification_report(y_test, y_test_pred, target_names=iris.target_names))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Confusion matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another useful metric is the confusion matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 8  0  0]\n",
      " [ 0 11  0]\n",
      " [ 0  3 16]]\n"
     ]
    }
   ],
   "source": [
    "print(metrics.confusion_matrix(y_test, y_test_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see we classify well all the 'setosa' and 'versicolor' samples. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### K-Fold validation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to avoid bias in the training and testing dataset partition, it is recommended to use **k-fold validation**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.93333333  0.8         1.          0.93333333  0.93333333  0.93333333\n",
      "  1.          1.          0.86666667  1.        ]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import cross_val_score, KFold\n",
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "# create a composite estimator made by a pipeline of preprocessing and the KNN model\n",
    "model = Pipeline([\n",
    "        ('scaler', StandardScaler()),\n",
    "        ('kNN', KNeighborsClassifier())\n",
    "])\n",
    "\n",
    "# create a k-fold cross validation iterator of k=10 folds\n",
    "cv = KFold(10, shuffle=True, random_state=33)\n",
    "\n",
    "# by default the score used is the one returned by score method of the estimator (accuracy)\n",
    "scores = cross_val_score(model, x_iris, y_iris, cv=cv)\n",
    "print(scores)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "We get an array of k scores. We can calculate the mean and the standard error to obtain a final figure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean score: 0.940 (+/- 0.021)\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import sem\n",
    "def mean_score(scores):\n",
    "    return (\"Mean score: {0:.3f} (+/- {1:.3f})\").format(np.mean(scores), sem(scores))\n",
    "print(mean_score(scores))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, we get an average accuracy of 0.940."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tuning the algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are going to tune the algorithm, and calculate which is the best value for the k parameter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7fc7cb526160>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc7cb726ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k_range = range(1, 21)\n",
    "accuracy = []\n",
    "for k in k_range:\n",
    "    m = KNeighborsClassifier(k)\n",
    "    m.fit(x_train, y_train)\n",
    "    y_test_pred = m.predict(x_test)\n",
    "    accuracy.append(metrics.accuracy_score(y_test, y_test_pred))\n",
    "plt.plot(k_range, accuracy)\n",
    "plt.xlabel('k value')\n",
    "plt.ylabel('Accuracy')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result is very dependent of the input data. Execute again the train_test_split and test again how the result changes with k."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* [KNeighborsClassifier API scikit-learn](http://scikit-learn.org/stable/modules/generated/sklearn.neighbors.KNeighborsClassifier.html)\n",
    "* [Learning scikit-learn: Machine Learning in Python](http://proquest.safaribooksonline.com/book/programming/python/9781783281930/1dot-machine-learning-a-gentle-introduction/ch01s02_html), Raúl Garreta; Guillermo Moncecchi, Packt Publishing, 2013.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Licence\n",
    "The notebook is freely licensed under under the [Creative Commons Attribution Share-Alike license](https://creativecommons.org/licenses/by/2.0/).  \n",
    "\n",
    "© 2016 Carlos A. Iglesias, Universidad Politécnica de Madrid."
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}