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Fundamentals of Machine Learning: A Pythonic Introduction

K-Means Clustering

Explore the k-means clustering algorithm which partitions data into clusters by minimizing variance. Learn its iterative approach through Lloyd's algorithm and improvements with k-means++ initialization. Understand variants such as k-medoids, which uses actual data points as centers, and k-center clustering aimed at minimizing cluster diameter. Gain skills to apply and differentiate clustering methods effectively in real datasets.

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Traditionally, in machine learning, we start with the popular partitional clustering algorithm called kk-means clustering. This algorithm divides the data into kk clusters based on a similarity score. The objective is to minimize the total variance of the kk clusters. The number of clusters, kk, must be specified.

Note: The choice of similarity metric is a hyperparameter.

Objective

K-means clustering aims to partition a dataset into kk clusters such that the total variance of the clusters is minimized. This means we want the data points within each cluster to be as close to each other as possible.

Given a set of nn data points D={x1,x2,…,xn}D=\{\mathbf{x}_1, \mathbf{x}_2, \dots, \mathbf{x}_n\} ...