Lab7-Exercises.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# k-Nearest Neighbours"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 1\n",
    "\n",
    "Ternary classification\n",
    "\n",
    "Given three points R=(-1, 0), G=(0, 1), B=(1, 0), colored in red, green and blue, respectively. Using `matplotlib`, create a plot that shows the decision surface of the 1-NN classifier using these three points as a dataset with three different classes, similart to the way `plot_decision_surface_knn` works for two classes (the function is located in `tools/plots.py`)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 2\n",
    "Accuracy comparison with ID3\n",
    "\n",
    "Considering the dataset below:\n",
    "1. plot the points using the `scatter` function from `matplotlib`;\n",
    "1. compare the training accuracy of 1-NN and ID3;\n",
    "1. compare the CVLOO accuracy of 1-NN and ID3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "d = pd.DataFrame({\n",
    "    'X1': [1, 2, 4, 5, 7],\n",
    "    'X2': [2, 1, 5, 4, 3],\n",
    "    'Y': [0, 0, 0, 1, 1]\n",
    "})\n",
    "X, Y = d[['X1', 'X2']], d['Y']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 3\n",
    "1-NN decision boundary\n",
    "\n",
    "Using the code below, change the value of the `boundary` variable such that it correctly represents the decision boundary for 1-NN between the two classes of points. You can specify hard-coded values (you don't have to calculate them in Python)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "from scipy.spatial import Voronoi, voronoi_plot_2d\n",
    "d = pd.DataFrame({\n",
    "    'X1': [2, 2, 3, 6, 8, 10, 10, 13, 14],\n",
    "    'X2': [1, 8, 6, 10, 4, 6, 14, 13, 8],\n",
    "    'Y': [0, 0, 0, 0, 0, 1, 1, 1, 1]\n",
    "})\n",
    "X, Y = d[['X1', 'X2']], d['Y']\n",
    "\n",
    "# Correct this line\n",
    "boundary=pd.DataFrame([(0,16),(16,0)], columns=['x','y'])\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "c= ['white' if l == 0 else 'black' for l in Y]\n",
    "fig, ax = plt.subplots(figsize=(5, 5))\n",
    "ax.set_axisbelow(True)\n",
    "plt.scatter(X['X1'], X['X2'], color=c, edgecolor='k')\n",
    "plt.xlim(0, 16)\n",
    "plt.ylim(0, 16)\n",
    "plt.plot(boundary['x'],boundary['y'])\n",
    "plt.grid(linestyle='dashed')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 4\n",
    "Finding optimum value for $k$\n",
    "\n",
    "For the dataset below:\n",
    "1. plot the points using `pyplot.scatter`;\n",
    "1. plot a line chart using `pyplot.plot` that shows the training error and the CVLOO error of k-NN for all values of $k$ between 1 and 15. \n",
    "1. What is the best value of $k$ in this case?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import norm\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "x_red = norm.rvs(0, 1, 100, random_state=1)\n",
    "y_red = norm.rvs(0, 1, 100, random_state=2)\n",
    "x_green = norm.rvs(1, 1, 100, random_state=3)\n",
    "y_green = norm.rvs(1, 1, 100, random_state=4)\n",
    "d = pd.DataFrame({\n",
    "    'X1': np.concatenate([x_red,x_green]),\n",
    "    'X2': np.concatenate([y_red,y_green]),\n",
    "    'Y': [1]*100+[0]*100\n",
    "})\n",
    "X, Y = d[['X1', 'X2']], d['Y']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 5\n",
    "Large number of attributes\n",
    "\n",
    "Considering the following dataset (attributes in the `X` variable and labels in the `Y` variable):\n",
    "1. Measure the CVLOO accuracy for 5-NN;\n",
    "1. Measure the CVLOO accuracy for ID3;\n",
    "1. What is the reason for the difference?\n",
    "1. What can be done to improve the accuracy of 5-NN? If something can be done, what is the new accuracy?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import norm\n",
    "import pandas as pd\n",
    "from statistics import median\n",
    "\n",
    "def new_var(n):\n",
    "    return norm.rvs(0, 1, 100, random_state=n)\n",
    "\n",
    "d = {f'X{i}':new_var(i) for i in range(10)}\n",
    "m = median(X['X2'])\n",
    "\n",
    "X = pd.DataFrame(d)\n",
    "Y = pd.Series([0 if i < m else 1 for i in X['X2']])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 6\n",
    "Comparison between k-NN and ID3\n",
    "\n",
    "Create a simple two-dimensional dataset on which the CVLOO accuracy is at least 75% for 3-NN, but less than 50% for ID3 (with entropy and no prunning). Plot the dataset using `matplotlib.pyplot` and calculate the CVLOO accuracy for 3-NN and ID3 for confirmation."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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"
  }
 },
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 "nbformat_minor": 4
}