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{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "20fce00f",
   "metadata": {},
   "source": [
    "# ML, Data Analysis\n",
    "### Machine learning: Entropy\n",
    "\n",
    "The **entropy** measures how much a random variable (or a dataset) has disorder or uncertainty. It is often used in decision tree algorithms to measure how *diverse* or *mixed* a set of items is with respect to their class labels (similar to the **Gini impurity** mentioned earlier).\n",
    "<br>**Definition:** We have a dataset with $K$ different classes (or a random variable with $K$ possible outcomes). Let's denote the probability of selecting an item of class $i$ by $p_i$. Then, the entropy is defined by:\n",
    "<div style=\"margin-top:4px\"></div>\n",
    "$\\large Entropy=-\\sum_{i=1}^K p_i \\cdot log(p_i)$\n",
    "<div style=\"margin-bottom:4px\"></div>\n",
    "\n",
    "where the base of the logarithm is usually used to be 2, $e$, or 10.\n",
    "<br>**Hint 1, Lowest value:** The lowest value of entropy is zero, and it occurs when all items are of the same class.\n",
    "<br>**Hint 2, Highest value:** When the number of items in classes are the same, the $entropy$ gets its maximum value, which is $log(k)$ for a dataset with $K$ classes. This is when the dataset is at its maximum disorder.\n",
    "<br> Some properties of entropy (for random variables $X$ and $Y$):\n",
    "- Nonnegativity: $H(X)\\geq 0$\n",
    "- Subadditivity: $H(X,Y)\\leq H(X)+H(Y)$\n",
    "- Additivity: $H(X,Y)=H(X)+H(Y)$ if $X$ and $Y$ are independent.\n",
    "\n",
    "<hr>\n",
    "\n",
    "In the following, we compute the entropy for a sample of dataset.\n",
    "\n",
    "<hr>\n",
    "https://github.com/ostad-ai/Machine-Learning\n",
    "<br> Explanation: https://www.pinterest.com/HamedShahHosseini/Machine-Learning/background-knowledge"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e4b21289",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import the required module\n",
    "from math import log,log2,log10\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "fcd61029",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate the entropy Impurity for a list of data labels\n",
    "def entropy(data,base='e'):\n",
    "    if len(data) == 0:\n",
    "        return 0\n",
    "    if base=='e': log_p=log\n",
    "    elif base=='10': log_p=log10\n",
    "    elif base=='2': log_p=log2\n",
    "    else:\n",
    "        raise ValueError('The base is not correct')\n",
    "    # Count the occurrences of each class\n",
    "    classes = set(data) # The classes\n",
    "    total = len(data) # number of all items\n",
    "    result = 0.0\n",
    "    for c in classes:\n",
    "        p=data.count(c)/total # p is never zero here\n",
    "        result -= p*log_p(p) \n",
    "        \n",
    "    return result "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "61a4a198",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['apple', 'apple', 'apple', 'apple', 'apple', 'orange', 'orange', 'orange', 'banana', 'banana', 'banana', 'banana']\n",
      "its entropy is: 1.0776\n",
      "--------------------------------------------------\n",
      "['apple', 'apple', 'apple', 'apple', 'apple', 'apple', 'apple', 'apple', 'apple', 'apple', 'apple', 'apple']\n",
      "its entropy is (lowest): 0.0000\n",
      "--------------------------------------------------\n",
      "['apple', 'apple', 'apple', 'apple', 'orange', 'orange', 'orange', 'orange', 'banana', 'banana', 'banana', 'banana']\n",
      "its entropy is (highest): 1.0986\n"
     ]
    }
   ],
   "source": [
    "# Some examples\n",
    "# A sample dataset\n",
    "dataset = ['apple'] * 5 + ['orange'] * 3 + ['banana'] * 4\n",
    "# Calculate entropy\n",
    "print(f'{dataset}')\n",
    "print(f\"its entropy is: {entropy(dataset):.4f}\")\n",
    "\n",
    "# Perfectly pure case (all same class), lowest entropy\n",
    "one_class_case = ['apple'] * 12\n",
    "print('-'*50+f'\\n{one_class_case}')\n",
    "print(f\"its entropy is (lowest): {entropy(one_class_case):.4f}\")\n",
    "\n",
    "# Worst case (equal distribution), highest entropy\n",
    "equal_probs_case = ['apple'] * 4 + ['orange'] * 4+['banana']*4\n",
    "print('-'*50+f'\\n{equal_probs_case}')\n",
    "print(f\"its entropy is (highest): {entropy(equal_probs_case):.4f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d41ebef9",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Draw entropy for a dataset of two classes: A and B\n",
    "# X-axis the proportion of class A\n",
    "# Y-axis the value of entropy\n",
    "ps=[i/100 for i in range(1,100)]\n",
    "entropies=[-p*log(p)-(1-p)*log(1-p) for p in ps] # base=e\n",
    "plt.plot(ps,entropies,'-')\n",
    "plt.xlabel('Prob. of  class A')\n",
    "plt.ylabel('Entropy')\n",
    "plt.title('Entropy for a two-class dataset')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a3aaf290",
   "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": "3.11.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}