clustering2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt \n",
    "from scipy.cluster.hierarchy import dendrogram, linkage\n",
    "from sklearn.cluster import AgglomerativeClustering"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##scikit-learn is a popular library for machine learning.\n",
    "\n",
    "#Create arrays that resemble two variables in a dataset.\n",
    " Note that while we only use two variables here, \n",
    "this method will work with any number of variables:#"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = [4,5,10,6,12,7,3,15,9,8]\n",
    "y = [21,19,18,17,16,15,14,13,12,11] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(4, 21), (5, 19), (10, 18), (6, 17), (12, 16), (7, 15), (3, 14), (15, 13), (9, 12), (8, 11)]\n"
     ]
    }
   ],
   "source": [
    "data = list(zip(x, y))\n",
    "print(data)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute the linkage between all of the different points.\n",
    " Here we use a simple euclidean distance measure and Ward's linkage, \n",
    "which seeks to minimize the variance between clusters.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "linkage_data = linkage(data, method='ward', metric='euclidean')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, plot the results in a dendrogram. \n",
    "This plot will show us the hierarchy of clusters \n",
    "from the bottom (individual points)\n",
    " to the top (a single cluster consisting of all data points)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dendrogram(linkage_data)\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The scikit-learn library allows us to use hierarchichal\n",
    " clustering in a different manner. First, we initialize the AgglomerativeClustering\n",
    " class with 2 clusters, using the same euclidean distance and Ward linkage."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "hierarchical_cluster = AgglomerativeClustering(n_clusters=2, affinity='euclidean', linkage='ward')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The .fit_predict method can be called on our data to \n",
    "compute the clusters using the \n",
    "defined parameters across our chosen number of clusters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 1 0 1 0 1 1 0 0 0]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\Ihsan\\AppData\\Local\\Programs\\Python\\Python311\\Lib\\site-packages\\sklearn\\cluster\\_agglomerative.py:983: FutureWarning: Attribute `affinity` was deprecated in version 1.2 and will be removed in 1.4. Use `metric` instead\n",
      "  warnings.warn(\n"
     ]
    }
   ],
   "source": [
    "labels = hierarchical_cluster.fit_predict(data)\n",
    "print(labels)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, if we plot the same data and color \n",
    "the points using the labels assigned to each index by the \n",
    "hierarchical clustering method, we can see the cluster each point was assigned to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y, c=labels)\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.11.1 (tags/v3.11.1:a7a450f, Dec  6 2022, 19:58:39) [MSC v.1934 64 bit (AMD64)]"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "449c8e2da2d50645573d3a78189e38345b85096978a1b2c8f05bd0dfae3df97c"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}