{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Machine Learing, Clustering\n", "## The k-means algorithm\n", "The **k-means** is an iterative algorithm for **Clustering**. In other words, data points are partitioned into a fixed number of clusters. As a result, the number of clusters must be given in advance. The **means** or **centroids** of each cluster is used to represent the relevant cluster. In fact, the k-means looks for *centroids* $\\boldsymbol{m}_i$ that minimize a **within-cluster sum of squares criterion** to finally get the optimal clustering $C^*$. \n", "
$C^*=argmin_C\\sum_{i=0}^{K-1}\\sum_{x\\in C_i}\\left\\Vert \\boldsymbol{x}-\\boldsymbol{m}_i\\right\\Vert^2$\n", "
The summary of steps in a k-means algorithm is given below:\n", "1. **Initialization:** Initialize the value of means (centroids).\n", "2. **Assignment:** assign data points to clusters by their distance to the centroids.\n", "3. **Updating:** Update the centroids by the assigned data points in step (2).\n", "4. **Repeat:** Go to step (2) until we are satisfied.\n", "\n", "In the following, we provide the k-means algorithm from scratch. We try the implemented k-means with the iris datasets that has been reduced to 2-dimensional points by the **PCA** (Principal Components Analysis).\n", "
**Hint:** The k-means algorithm is related to the **Voronoi Diagram**. In fact, we can divide the space of data points into different *Voronoi cells* based on the distance of each data point of the space to the nearest centroid. In Voronoi diagram, we call the centroids as **seeds**. We already talked about the Voronoi diagram in an earlier post.\n", "
\n", "
The code is at : https://github.com/ostad-ai/Machine-Learning\n", "
Explanation: https://www.pinterest.com/HamedShahHosseini/Machine-Learning" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# importing the required modules\n", "import numpy as np\n", "from matplotlib import pyplot as plt\n", "from sklearn.datasets import load_iris\n", "from sklearn.decomposition import PCA" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The number of data points: 150\n", "The dimension of each data point: 4\n" ] } ], "source": [ "# loading the iris dataset from scikit-learn datasets\n", "iris=load_iris()\n", "X,y=iris.data,iris.target\n", "print(f'The number of data points: {X.shape[0]}')\n", "print(f'The dimension of each data point: {X.shape[1]}')" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# the k-means algorithm from scratch is implemented in this cell\n", "# we could simply use KMeans of scikit-learn instead\n", "\n", "# the function to compute the Euclidean distance\n", "def Euclidean(x1,x2):\n", " return np.sqrt(np.sum((x1-x2)**2,axis=1))\n", "\n", "# the class k-means from scratch\n", "# in the initialization ,the number of clusters and the maximum of iteration are given\n", "class MyKMeans:\n", " \n", " def __init__(self,n_clusters,max_iter=10):\n", " self.n_clusters=n_clusters\n", " self.max_iter=max_iter \n", " \n", " def fit(self,data): #data is a matrix of shape: n_samples*n_features\n", " self.means=data[np.random.choice(data.shape[0],\n", " self.n_clusters,replace=False)].copy()\n", " n_samples=data.shape[0]\n", " for _ in range(self.max_iter):\n", " c=[[] for _ in range(self.n_clusters)]\n", " for i in range(n_samples):\n", " j_x=np.argmin(Euclidean(self.means,data[i]))\n", " c[j_x].append(i)\n", " for j in range(self.n_clusters):\n", " sum=0.\n", " for i in c[j]:\n", " sum+=data[i]\n", " self.means[j]=sum/len(c[j])\n", " return self.means\n", " # when we have unassigned data points, \n", " # we can use function predict to get their assigned clusters\n", " def predict(self,data):\n", " n_samples=data.shape[0]\n", " labels=np.zeros(n_samples,dtype='int')\n", " for i in range(n_samples):\n", " labels[i]=np.argmin(Euclidean(self.means,data[i]))\n", " return labels" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# We use PCA to reduce the dimension (number of features) of data points from 4 to 2\n", "pca=PCA(n_components=2)\n", "X2d=pca.fit_transform(X) # transformed data points with dimension 2\n", "K=3 # the number of clusters\n", "km=MyKMeans(K) #three clusters\n", "centroids=km.fit(X2d)\n", "# we can find the labels (clusters) of data points\n", "# labels are the index of clusters\n", "labels=km.predict(X2d)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The centroids of clusters are :\n", "[[ 0.6545702 -0.34120495]\n", " [-2.64241546 0.19088505]\n", " [ 2.32116403 0.27320112]]\n" ] } ], "source": [ "print(f'The centroids of clusters are :\\n{centroids}')" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# displaying the transformed 2-d data points along with the centroids \n", "plt.scatter(X2d[:,0],X2d[:,1],c=labels,alpha=.5)\n", "plt.scatter(centroids[:,0],centroids[:,1],marker='*',c='red',s=150)\n", "plt.title('The iris dataset reduced to 2D, with different color for each cluster'+\\\n", " '\\nThe centroids are shown with stars')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "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": 4 }