Classification.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "bdd853bb",
   "metadata": {},
   "source": [
    "# Classification\n",
    "\n",
    "In this notebook, we will contrast regression and classification."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1789ae76",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "%matplotlib widget\n",
    "import matplotlib.pyplot as plt\n",
    "from lab_utils_week3 import dlc, plot_data\n",
    "from plt_one_addpt_onclick import plt_one_addpt_onclick\n",
    "plt.style.use('./deeplearning.mplstyle')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1cda52ad",
   "metadata": {},
   "source": [
    "## Classification Problems\n",
    "<img align=\"left\" src=\"./images/C1_W3_Classification.png\"     style=\" width:380px; padding: 10px; \" > Examples of classification problems are things like: identifying email as Spam or Not Spam or determining if a tumor is malignant or benign. In particular, these are examples of *binary* classification where there are two possible outcomes.  Outcomes can be  described in pairs of 'positive'/'negative' such as 'yes'/'no, 'true'/'false' or '1'/'0'. \n",
    "\n",
    "Plots of classification data sets often use symbols to indicate the outcome of an example. In the plots below, 'X' is used to represent the positive values while 'O' represents negative outcomes. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "6defe1be",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train = np.array([0., 1, 2, 3, 4, 5])\n",
    "y_train = np.array([0,  0, 0, 1, 1, 1])\n",
    "X_train2 = np.array([[0.5, 1.5], [1,1], [1.5, 0.5], [3, 0.5], [2, 2], [1, 2.5]])\n",
    "y_train2 = np.array([0, 0, 0, 1, 1, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "8941f644",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "9129652ac4bf4a90bfcf12ce590465c1",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=800.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(footer_visible=False, header_visible=False, toolbar=Toolbar(toolitems=[('Home', 'Reset original view', …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pos = y_train == 1\n",
    "neg = y_train == 0\n",
    "\n",
    "fig,ax = plt.subplots(1,2,figsize=(8,3))\n",
    "#plot 1, single variable\n",
    "ax[0].scatter(x_train[pos], y_train[pos], marker='x', s=80, c = 'red', label=\"y=1\")\n",
    "ax[0].scatter(x_train[neg], y_train[neg], marker='o', s=100, label=\"y=0\", facecolors='none', \n",
    "              edgecolors=dlc[\"dlblue\"],lw=3)\n",
    "\n",
    "ax[0].set_ylim(-0.08,1.1)\n",
    "ax[0].set_ylabel('y', fontsize=12)\n",
    "ax[0].set_xlabel('x', fontsize=12)\n",
    "ax[0].set_title('one variable plot')\n",
    "ax[0].legend()\n",
    "\n",
    "#plot 2, two variables\n",
    "plot_data(X_train2, y_train2, ax[1])\n",
    "ax[1].axis([0, 4, 0, 4])\n",
    "ax[1].set_ylabel('$x_1$', fontsize=12)\n",
    "ax[1].set_xlabel('$x_0$', fontsize=12)\n",
    "ax[1].set_title('two variable plot')\n",
    "ax[1].legend()\n",
    "plt.tight_layout()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f5a1b82",
   "metadata": {},
   "source": [
    "Note in the plots above:\n",
    "- In the single variable plot, positive results are shown both a red 'X's and as y=1. Negative results are blue 'O's and are located at y=0.\n",
    "   - Recall in the case of linear regression, y would not have been limited to two values but could have been any value.\n",
    "- In the two-variable plot, the y axis is not available.  Positive results are shown as red 'X's, while negative results use the blue 'O' symbol.\n",
    "    - Recall in the case of linear regression with multiple variables, y would not have been limited to two values and a similar plot would have been three-dimensional."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40d3f9e1",
   "metadata": {},
   "source": [
    "## Linear Regression approach\n",
    "In the previous week, we applied linear regression to build a prediction model. Let's try that approach here using the simple example. The model will predict if a tumor is benign or malignant based on tumor size.  Try the following:\n",
    "- Click on 'Run Linear Regression' to find the best linear regression model for the given data.\n",
    "    - Note the resulting linear model does **not** match the data well. \n",
    "One option to improve the results is to apply a *threshold*. \n",
    "- Tick the box on the 'Toggle 0.5 threshold' to show the predictions if a threshold is applied.\n",
    "    - These predictions look good, the predictions match the data\n",
    "- *Important*: Now, add further 'malignant' data points on the far right, in the large tumor size range (near 10), and re-run linear regression.\n",
    "    - Now, the model predicts the larger tumor, but data point at x=3 is being incorrectly predicted!\n",
    "- to clear/renew the plot, rerun the cell containing the plot command."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ec3627e5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2cb4557f41004b24842bf49e3db80285",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=800.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(footer_visible=False, header_visible=False, toolbar=Toolbar(toolitems=[('Home', 'Reset original view', …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "w_in = np.zeros((1))\n",
    "b_in = 0\n",
    "plt.close('all') \n",
    "addpt = plt_one_addpt_onclick( x_train,y_train, w_in, b_in, logistic=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62f22633",
   "metadata": {},
   "source": [
    "The example above demonstrates that the linear model is insufficient to model categorical data. The model can be extended"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab461db5",
   "metadata": {},
   "source": [
    "## Lessons Learnt\n",
    "In this notebook we:\n",
    "- explored categorical data sets and plotting\n",
    "- determined that linear regression was insufficient for a classification problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3b8ad59c",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.11.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}