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{
"cells": [
{
"cell_type": "markdown",
"id": "20fce00f",
"metadata": {},
"source": [
"# ML, Data Analysis\n",
"### Machine learning: Gini impurity\n",
"\n",
"The **gini impurity** is a fundamental concept used in decision tree algorithms to measure how *impure* or *mixed* a set of items is with respect to their class labels.\n",
"<br>Imagine you have a basket containing different fruits. Gini Impurity measures the probability that you would be wrong if you randomly picked a fruit and guessed its type based on the distribution of fruits in the basket.\n",
"<br>**Definition:** Consider we have a dataset of $n$ items having $K$ different types (classes). Let's denote the probability of selecting an item of class $i$ by $p_i$. Then, the Gini impurity is:\n",
"<div style=\"margin-top:4px\"></div>\n",
"$\\large Gini_{impurity}=1-\\sum_{i=1}^K p_i^2$\n",
"<div style=\"margin-bottom:4px\"></div>\n",
"\n",
"**Hint 1, Lowest value:** When all the items are of the same class, then $Gini_{impurity}=0$, which is the lowest value. As the diversity increases, the Gini impurity also increases.\n",
"<br>**Hint 2, Highest value:** For a dataset of $K$ classes, the maximum Gini impurity occurs when all the classea have equal items in the dataset. Thus, $gini_{impurity}=1-\\frac {1}{K}$\n",
"\n",
"<hr>\n",
"\n",
"In the following, we compute the Gini impurity 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 matplotlib import pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "fcd61029",
"metadata": {},
"outputs": [],
"source": [
"# Calculate the Gini Impurity for a list of data labels\n",
"def gini_impurity(data):\n",
" if len(data) == 0:\n",
" return 0\n",
" \n",
" # Count the occurrences of each class\n",
" classes = set(data) # The classes\n",
" total = len(data) # number of all items\n",
" gini = 1.0\n",
" for c in classes:\n",
" p=data.count(c)/total\n",
" gini -= p ** 2\n",
" \n",
" return gini "
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "61a4a198",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"['apple', 'apple', 'apple', 'apple', 'apple', 'orange', 'orange', 'orange', 'banana', 'banana', 'banana', 'banana']\n",
"its Gini Impurity is: 0.6528\n",
"--------------------------------------------------\n",
"['apple', 'apple', 'apple', 'apple', 'apple', 'apple', 'apple', 'apple', 'apple', 'apple', 'apple', 'apple']\n",
"its Gini impurity is: 0.0000\n",
"--------------------------------------------------\n",
"['apple', 'apple', 'apple', 'apple', 'orange', 'orange', 'orange', 'orange', 'banana', 'banana', 'banana', 'banana']\n",
"its Gini impurity is: 0.6667\n"
]
}
],
"source": [
"# Some examples\n",
"# A sample dataset\n",
"dataset = ['apple'] * 5 + ['orange'] * 3 + ['banana'] * 4\n",
"# Calculate Gini Impurity\n",
"impurity = gini_impurity(dataset)\n",
"print(f'{dataset}')\n",
"print(f\"its Gini Impurity is: {impurity:.4f}\")\n",
"\n",
"# Perfectly pure case (all same class)\n",
"one_class_case = ['apple'] * 12\n",
"print('-'*50+f'\\n{one_class_case}')\n",
"print(f\"its Gini impurity is: {gini_impurity(one_class_case):.4f}\")\n",
"\n",
"# Worst case (equal distribution)\n",
"equal_probs_case = ['apple'] * 4 + ['orange'] * 4+['banana']*4\n",
"print('-'*50+f'\\n{equal_probs_case}')\n",
"print(f\"its Gini impurity is: {gini_impurity(equal_probs_case):.4f}\")"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "d41ebef9",
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Draw Gini impurity for a dataset of two classes: A and B\n",
"# X-axis the proportion of class A\n",
"# Y-axis the value of Gini impurity\n",
"ps=[i/100 for i in range(0,100)]\n",
"ginis=[1-p**2-(1-p)**2 for p in ps]\n",
"plt.plot(ps,ginis,'-')\n",
"plt.xlabel('Prob. of class A')\n",
"plt.ylabel('Gini impurity')\n",
"plt.title('Gini impurity 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
}
|