K-Means Clustering Tutorial

K-Means Clustering is a simple and popular algorithm used for cluster analysis in unsupervised learning. This tutorial will guide you through the basics of K-Means Clustering, its applications, and how to implement it.

Introduction to K-Means Clustering

K-Means Clustering is a method of vector quantization, originally from signal processing, that is popular for cluster analysis in data mining. It is an iterative algorithm that tries to partition the dataset into K pre-defined distinct non-overlapping subgroups (clusters) where each data point belongs to only one group.

Key Points of K-Means Clustering

K: The number of clusters you want to form.
Centroids: The center points of each cluster.
Distance: The algorithm uses distance (usually Euclidean) to assign data points to clusters.
Iteration: The algorithm iterates until the centroids do not change significantly.

Implementation Steps

Select the number of clusters (K): This can be done using the Elbow Method or other techniques.
Initialize centroids: Randomly select K data points as initial centroids.
Assign data points to clusters: Calculate the distance between each data point and centroids, and assign it to the nearest centroid.
Update centroids: Recompute the centroids as the mean of the data points assigned to each cluster.
Repeat steps 3-4 until the centroids do not change significantly.

Example

Let's say we have a dataset of 100 points in 2D space. We want to cluster these points into 3 clusters.

from sklearn.cluster import KMeans
import numpy as np

# Generate some synthetic data
X = np.random.rand(100, 2)

# Initialize and fit the model
kmeans = KMeans(n_clusters=3, random_state=0).fit(X)

# Get the cluster labels
labels = kmeans.labels_

# Get the cluster centroids
centroids = kmeans.cluster_centers_

Applications

K-Means Clustering has various applications, including:

Market Segmentation
Image Segmentation
Document Clustering
Social Network Analysis