Assignment 3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ML Summer School - Assignment 3\n",
    "\n",
    "Welcome to Machine Learning Summer School (2018) - Assignment 3. In this assignment, you will make a model that recognises faces! We will also explore Dimensionality Reduction.\n",
    "\n",
    "In this assignment, we will use `NumPy`, `Matplotlib`, `sklearn`, and `skimage` (an image processing library). Instead of `skimage`, one could instead use other image processing libraries like `OpenCV`, `Pillow`, `scipy.ndimage` etc. But for the sake of uniformity, you have to complete this assignment using `skimage`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Importing libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import os\n",
    "import time\n",
    "\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import classification_report\n",
    "from sklearn.metrics import f1_score\n",
    "from sklearn.metrics import accuracy_score\n",
    "from sklearn.preprocessing import scale, StandardScaler\n",
    "from sklearn.svm import LinearSVC"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Loading data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Task 1\n",
    "\n",
    "The first task is to load the images from data/folder as NumPy array. First manually go through the data, and understand how it is organised.  \n",
    "\n",
    "`X` should be a NumPy array containing images and `y` should contain the corresponding labels. \n",
    "\n",
    "Go through `os.path.join` and `os.listdir` functions. Refer to [`skimage.io.imread`](http://scikit-image.org/docs/dev/api/skimage.io.html#skimage.io.imread) function for loading image."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X.shape: (400, 112, 92), y.shape: (400,)\n"
     ]
    }
   ],
   "source": [
    "from skimage import io\n",
    "\n",
    "X = []\n",
    "y = []\n",
    "\n",
    "for sub_dir in os.listdir('data'):\n",
    "    if not os.path.isdir(os.path.join('data', sub_dir)):\n",
    "        continue\n",
    "        \n",
    "    label = int(sub_dir[1:])\n",
    "    for file in os.listdir(os.path.join('data', sub_dir)):\n",
    "        filename = os.path.join('data', sub_dir, file)\n",
    "        \n",
    "        # YOUR CODE STARTS HERE\n",
    "\n",
    "        # YOUR CODE ENDS HERE\n",
    "\n",
    "        X.append(image)\n",
    "        y.append(label)\n",
    "        \n",
    "X = np.array(X, dtype='float64')\n",
    "y = np.array(y)\n",
    "\n",
    "print(\"X.shape: {}, y.shape: {}\".format(X.shape, y.shape))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Analysing data\n",
    "\n",
    "Let us first visualise the first image of our dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f85bc0bf400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "imgplot = plt.imshow(X[0],cmap=\"gray\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are 40 subjects in our dataset with 10 images for each of them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of images : 400\n",
      "Shape of each image: 112 x 92\n"
     ]
    }
   ],
   "source": [
    "print('Number of images :', X.shape[0])\n",
    "print('Shape of each image:', X.shape[1], 'x', X.shape[2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Feature Extraction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Task 2\n",
    "\n",
    "Currently, `X` is a 3D NumPy array. For each of the 400 images, we have a corresponding 2D matrix storing the pixel values. We will flatten this 2D matrix and use the flattened vector as the feature vector for the image.   \n",
    "\n",
    "Note that the number of features obtained this way are very large. There are a number of better methods to extract features from images that you will study later on.\n",
    "\n",
    "Reshape `X` into 400xN, where N is the number of features (112x92)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(400, 10304)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# YOUR CODE STARTS HERE\n",
    "\n",
    "# YOUR CODE ENDS HERE\n",
    "\n",
    "X.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dimensionality Reduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We expect that you have gone through the Dimensionality Reduction part of the recommended material. Essentially we use Dimensionality Reduction for, \n",
    "1. *Data Visualisation* - We convert the data from a high number of dimensions to two or three, which we can plot. \n",
    "2. *Speeding up training* and *reducing memory* required to store the data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Visualisation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we will demonstrate how Dimensionality Reduction is used for Data Visualisation. We will reduce the dimensionality of the data to 2 and plot it. Before applying PCA (one of the Dimensionality Reduction algorithms), we will [standardise](http://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.StandardScaler.html#sklearn.preprocessing.StandardScaler) the data. For sake of clarity, we will be only using the data corresponding to the first `num_labels` classes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_labels = 5\n",
    "X_sample = X[y <= num_labels]\n",
    "y_sample = y[y <= num_labels]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_sample_scaled = scale(X_sample)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Task 3\n",
    "\n",
    "Reduce the dimensionality of `X_sample_scaled` to 2 using [sklearn.decomposition.PCA](http://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html) and assign it to `X_sample_2d`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(50, 2)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# YOUR CODE STARTS HERE\n",
    "\n",
    "\n",
    "# YOUR CODE ENDS HERE\n",
    "\n",
    "X_sample_2d.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8585bbe7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(8, 5))\n",
    "\n",
    "# Go through documentation of this method\n",
    "plt.scatter(X_sample_2d[:,0], X_sample_2d[:,1], c=y_sample, cmap=plt.cm.get_cmap('nipy_spectral', num_labels)) \n",
    "\n",
    "cb = plt.colorbar()\n",
    "loc = np.arange(1, num_labels+1)\n",
    "cb.set_ticks(loc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can clearly see PCA has projected the highly dimensional dataset into 2 dimensions, which we can see on plotting look clustered. \n",
    "\n",
    "Although this data visualisation is not very useful for supervised learning tasks, they prove useful for unsupervised learning tasks.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Speeding up training and reducing memory "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The other two applications of Dimensionality reduction are, speeding up training and reducing memory required to store the data. We will start by investigating the memory required."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Memory used by X: 31.45MB\n"
     ]
    }
   ],
   "source": [
    "print(\"Memory used by X: {:.2f}MB\".format(X.nbytes / 1024 / 1024))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case, because of low resolution of images and less data, the memory used in storing data is already quite low. It doesn't make sense to use PCA for this purpose."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Splitting the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_temp, y_train, y_temp = train_test_split(X, y, test_size=0.3, random_state=42)\n",
    "X_val, X_test, y_val, y_test = train_test_split(X_temp, y_temp, test_size=0.5, random_state=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Standardising the Dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Standardization of datasets is a common requirement for many machine learning estimators implemented in scikit-learn; they might behave badly if the individual features do not more or less look like standard normally distributed data.\n",
    "\n",
    "Standardising the dataset is not only [helpful for training](http://scikit-learn.org/stable/modules/preprocessing.html) machine learning models but is also a requirement before applying PCA. We will standardise all three `X_train`, `X_val` and `X_test`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "scaler = StandardScaler()\n",
    "scaler = scaler.fit(X_train)\n",
    "\n",
    "X_train_scaled = scaler.transform(X_train)\n",
    "X_val_scaled = scaler.transform(X_val)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training and Hyperparameter Tuning "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Without Dimensionality reduction\n",
    "\n",
    "We will be using [time magic command](https://ipython.readthedocs.io/en/stable/interactive/magics.html#magic-time) in Jupyter Notebook to measure the time taken in fitting the model. Read up about other useful magic commands like `timeit` `prun`, `lprun` on the web page linked before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 25 s, sys: 8 ms, total: 25.1 s\n",
      "Wall time: 25.1 s\n",
      "Training accuracy: 1.0000, Val Accuracy: 0.9000\n"
     ]
    }
   ],
   "source": [
    "clf = LinearSVC(C=.001)\n",
    "%time clf = clf.fit(X_train_scaled, y_train)\n",
    "\n",
    "print(\"Training accuracy: {:.4f}, Val Accuracy: {:.4f}\".format(clf.score(X_train_scaled, y_train), clf.score(X_val_scaled, y_val)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1min 12s, sys: 996 ms, total: 1min 13s\n",
      "Wall time: 18.5 s\n",
      "Training accuracy: 1.0000, Val Accuracy: 0.9167\n"
     ]
    }
   ],
   "source": [
    "clf = LogisticRegression(C=.001)\n",
    "%time clf = clf.fit(X_train_scaled, y_train)\n",
    "\n",
    "print(\"Training accuracy: {:.4f}, Val Accuracy: {:.4f}\".format(clf.score(X_train_scaled, y_train), clf.score(X_val_scaled, y_val)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### With Dimensionality reduction\n",
    "\n",
    "Clearly, the time taken to train the model is considerably high. It is infeasible to perform hyperparameter tuning when training the model takes so much time. In some cases when the dataset is even bigger, we might not be able to even train the model with the computing resources in hand. PCA becomes essential to speed up training.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Task 4\n",
    "\n",
    "Make an object of `PCA` class named `pca` so that 99% of variance is preserved. Refer to the documentation of `PCA` class.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# YOUR CODE STARTS HERE\n",
    "\n",
    "# YOUR CODE ENDS HERE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dimensionality reduced to: 236\n"
     ]
    }
   ],
   "source": [
    "X_train_pca = pca.fit_transform(X_train_scaled)\n",
    "X_val_pca = pca.transform(X_val_scaled)\n",
    "\n",
    "print(\"Dimensionality reduced to:\", pca.n_components_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.21 s, sys: 8 ms, total: 1.22 s\n",
      "Wall time: 641 ms\n",
      "Training accuracy: 1.0000, Val Accuracy: 0.8833\n"
     ]
    }
   ],
   "source": [
    "clf = LogisticRegression(C=.01)\n",
    "%time clf = clf.fit(X_train_pca, y_train)\n",
    "\n",
    "print(\"Training accuracy: {:.4f}, Val Accuracy: {:.4f}\".format(clf.score(X_train_pca, y_train), clf.score(X_val_pca, y_val)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.59 s, sys: 20 ms, total: 1.61 s\n",
      "Wall time: 1.03 s\n",
      "Training accuracy: 1.0000, Val Accuracy: 0.8833\n"
     ]
    }
   ],
   "source": [
    "clf = LinearSVC(C=.001)\n",
    "%time clf = clf.fit(X_train_pca, y_train)\n",
    "\n",
    "print(\"Training accuracy: {:.4f}, Val Accuracy: {:.4f}\".format(clf.score(X_train_pca, y_train), clf.score(X_val_pca, y_val)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PCA reduced the training time considerably with negligible loss in accuracy. Though the loss in accuracy might not justified in this case (if training the model didn't take much time for you), it might be necessary in some cases. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Testing \n",
    "\n",
    "We now test our model on the testing data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Couple of utilities functions\n",
    "def plot_gallery(images, titles, rows=3, cols=4):\n",
    "    plt.figure()\n",
    "    for i in range(rows * cols):\n",
    "        fig = plt.subplot(rows, cols, i + 1)\n",
    "        plt.imshow(images[i], cmap=plt.cm.gray)\n",
    "        plt.title(titles[i])\n",
    "        plt.xticks(())\n",
    "        plt.yticks(())\n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "        \n",
    "def titles(y_pred, y_test):\n",
    "    for i in range(y_pred.shape[0]):\n",
    "        yield 'predicted: {0}\\ntrue: {1}'.format(y_pred[i], y_test[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_test_scaled = scaler.transform(X_test)\n",
    "X_test_pca = pca.transform(X_test_scaled)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy score: 0.8667\n"
     ]
    }
   ],
   "source": [
    "y_pred = clf.predict(X_test_pca)\n",
    "print('Accuracy score: {:.4f}'.format(accuracy_score(y_test, y_pred)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f85bc0bf748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "prediction_titles = list(titles(y_pred, y_test))\n",
    "plot_gallery(X_test.reshape(-1, 112, 92), prediction_titles)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Congratulations you have built a face recogniser! You also explored the application of dimensionality reduction in this assignment.   \n",
    "\n",
    "If you have sincerely completed the material and the assignments of last two sections, you have gained sufficient knowledge to solve real life supervised Machine Learning problems. You can now go explore the world of competitive machine learning on [Kaggle.com](www.kaggle.com)."
   ]
  }
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