pca-logreg-mnist.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "9ff39180",
   "metadata": {},
   "source": [
    "In this notebook we will see how using PCA to project our data onto some Principle Components, and consequently reducing the size of our feature matrix, affects the time taken to fit the model and it's accuracy.\n",
    "\n",
    "Here we use a Logistic Regression Model to fit over the [MNIST dataset of handwritten digits.](http://yann.lecun.com/exdb/mnist/)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e36d51a",
   "metadata": {},
   "source": [
    "#### Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "8784b41e",
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import time\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "from sklearn.datasets import fetch_openml\n",
    "\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8fd414a",
   "metadata": {},
   "source": [
    "#### Load Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "10eac7fb",
   "metadata": {},
   "outputs": [],
   "source": [
    "# this may take a while\n",
    "data = fetch_openml('mnist_784', data_home=os.path.join('data', 'MNIST'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c8fee10f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X: (70000, 784)\n",
      "y: (70000,)\n"
     ]
    }
   ],
   "source": [
    "# extract feature and target matrices\n",
    "X = data.data.to_numpy()\n",
    "y = data.target.to_numpy()\n",
    "\n",
    "n_initial = X.shape[1]\n",
    "\n",
    "print(f\"X: {X.shape}\")\n",
    "print(f\"y: {y.shape}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1fb8e44b",
   "metadata": {},
   "source": [
    "#### Useful Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3fd7b826",
   "metadata": {},
   "outputs": [],
   "source": [
    "# display an example with 784 features as image\n",
    "def display_image(X, idx):\n",
    "    plt.imshow(X[idx, :].reshape((28, 28)), cmap='Greys')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "beab5b6e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# example\n",
    "display_image(X, 800)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "adbb7b4e",
   "metadata": {},
   "source": [
    "#### Split Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "57736509",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training Data -> X_train: (46900, 784), y_train: (46900,)\n",
      "Test Data -> X_test: (23100, 784), y_test: (23100,)\n"
     ]
    }
   ],
   "source": [
    "# train-test-split\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33, random_state=0)\n",
    "\n",
    "print(f\"Training Data -> X_train: {X_train.shape}, y_train: {y_train.shape}\")\n",
    "print(f\"Test Data -> X_test: {X_test.shape}, y_test: {y_test.shape}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a87887c",
   "metadata": {},
   "source": [
    "#### Scale Features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d39108a8",
   "metadata": {},
   "outputs": [],
   "source": [
    "# scale features\n",
    "scaler = StandardScaler().fit(X_train)\n",
    "X_train_norm = scaler.transform(X_train)\n",
    "X_test_norm = scaler.transform(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee05a72a",
   "metadata": {},
   "source": [
    "#### PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "bc33d1bf",
   "metadata": {},
   "outputs": [],
   "source": [
    "# run and fit pca on scaled training data\n",
    "pca = PCA()\n",
    "pca.fit(X_train_norm)\n",
    "\n",
    "# project original data on PCs\n",
    "# note that we have not specified the no. of PCs, thus the\n",
    "# data is being projected on n_initial (784) PCs\n",
    "Z_train = pca.transform(X_train_norm)\n",
    "Z_test = pca.transform(X_test_norm)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b569ab3a",
   "metadata": {},
   "source": [
    "#### Train Models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d3e930ad",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 1.0 variance retained, we need 784 principle components.\n",
      "Training model using 784 components...\n",
      "The time taken to train the model using 784 PCs is 138.58s.\n",
      "The accuracy for a model trained with 784 PCs is 90.95.\n",
      "------------------------------------------------------\n",
      "For 0.95 variance retained, we need 322 principle components.\n",
      "Training model using 322 components...\n",
      "The time taken to train the model using 322 PCs is 73.54s.\n",
      "The accuracy for a model trained with 322 PCs is 91.86.\n",
      "------------------------------------------------------\n",
      "For 0.9 variance retained, we need 229 principle components.\n",
      "Training model using 229 components...\n",
      "The time taken to train the model using 229 PCs is 60.56s.\n",
      "The accuracy for a model trained with 229 PCs is 91.85.\n",
      "------------------------------------------------------\n",
      "For 0.85 variance retained, we need 178 principle components.\n",
      "Training model using 178 components...\n",
      "The time taken to train the model using 178 PCs is 56.29s.\n",
      "The accuracy for a model trained with 178 PCs is 91.91.\n",
      "------------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "# the amount of variances we want to retain\n",
    "variances = [1.00, 0.95, 0.90, 0.85]\n",
    "\n",
    "# variables to see how models trained with different variance retained compare\n",
    "n_components = [] # number of principle components used\n",
    "accuracies = [] # the accuracy of each model on test set\n",
    "time_intervals = [] # the time it takes to fit the model\n",
    "\n",
    "for var in variances:\n",
    "    # find the no. of PCs n we need to reach this variance\n",
    "    n = 0\n",
    "    if var == 1.00: # in case var is 1.00, we'd simply use all the PCs\n",
    "        n = n_initial\n",
    "    else:\n",
    "        # increase until we have enough PCs to retain this variance (var)\n",
    "        while np.sum(pca.explained_variance_ratio_[:n]) < var:\n",
    "            n += 1\n",
    "\n",
    "    # record no. of PCs\n",
    "    print(f\"For {var} variance retained, we need {n} principle components.\")\n",
    "    n_components.append(n)\n",
    "    \n",
    "    # Reduce train and test matrices\n",
    "    Z_train_red = Z_train[:, :n]\n",
    "    Z_test_red = Z_test[:, :n]\n",
    "    \n",
    "    # train model on a Z (original data projected on n PCs)\n",
    "    print(f'Training model using {n} components...')\n",
    "    model = LogisticRegression(dual=False, max_iter=1000)\n",
    "    start = time.time()\n",
    "    model.fit(Z_train_red, y_train)\n",
    "    stop = time.time()\n",
    "    \n",
    "    # record time\n",
    "    time_taken = round(stop - start, 2)\n",
    "    print(f\"The time taken to train the model using {n} PCs is {time_taken}s.\")\n",
    "    time_intervals.append(time_taken) \n",
    "        \n",
    "    # predict and calculate accuracy on test set\n",
    "    y_pred = model.predict(Z_test_red)\n",
    "    acc = round(sum(y_pred == y_test) / y_test.size * 100, 2)\n",
    "    \n",
    "    # record accuracy\n",
    "    print(f\"The accuracy for a model trained with {n} PCs is {acc}.\")\n",
    "    accuracies.append(acc)\n",
    "    \n",
    "    print(\"------------------------------------------------------\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8fa625e",
   "metadata": {},
   "source": [
    "#### Plot How the Different Models Compare"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "86a12d69",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x1080 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(3, figsize=(10, 15))\n",
    "\n",
    "# plot variance-retained against no. of PCs\n",
    "axs[0].plot(variances, n_components, '--ro')\n",
    "axs[0].set(ylabel=\"No. of components\")\n",
    "for v, n in zip(variances, n_components):\n",
    "    axs[0].annotate(n, xy=(v, n))\n",
    "\n",
    "# plot variance-retained against model accuracy on test set\n",
    "axs[1].plot(variances, accuracies, '--bo')\n",
    "axs[1].set(ylabel=\"Acc. on test set (%)\", ylim=(70, 100))\n",
    "\n",
    "# plot variance-retained against time taken to train model\n",
    "axs[2].plot(variances, time_intervals, '--go')\n",
    "axs[2].set(ylabel=\"Time taken to fit model (s)\")\n",
    "for v, t in zip(variances, time_intervals):\n",
    "    axs[2].annotate(t, xy=(v, t))\n",
    "\n",
    "# some common settings for each subplot\n",
    "for ax in axs:\n",
    "    ax.set(xlabel='Varaince Retained', xticks=variances)\n",
    "    ax.invert_xaxis()\n",
    "\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3f2bf73",
   "metadata": {},
   "source": [
    "**Observations:**\n",
    "   \n",
    "We see that reducing the variance retained from 1.00 to 0.85, and as a result reducing the number of Principle Components from 784 to 178, to train our model barely affects the accuracy of our model to predict the test set while greatly lowers the time it takes to fit the model."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5cb35c08",
   "metadata": {},
   "source": [
    "#### Bonus: Predict a Random Test Set Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "fae4d1da",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model prediction: 9\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# run this cell to test your model on a random example from the test set\n",
    "# using the last model we trained\n",
    "idx = np.random.choice(y_test.size)\n",
    "\n",
    "display_image(X_test, idx)\n",
    "pred = model.predict(Z_test_red[idx, :].reshape((1, -1)))\n",
    "print(f\"Model prediction: {pred[0]}\")"
   ]
  }
 ],
 "metadata": {
  "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": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}