Clustering Explained

Clustering groups similar data points without predefined labels, uncovering patterns in data science. It’s an unsupervised learning technique. This article covers k-means, metrics, an example, and applications.

K-Means Clustering

Partitions data into \( k \) clusters:

1. Initialize \( k \) centroids.
2. Assign points to nearest centroid.
3. Update centroids as cluster means.
4. Repeat until convergence.

Minimizes \( \sum_{i=1}^k \sum_{x \in C_i} ||x - \mu_i||^2 \).

Evaluation Metrics

• Silhouette Score: Measures cohesion vs. separation (–1 to 1).
• Inertia: Sum of squared distances to centroids.

Assesses cluster quality.

Example Clustering

Data: Points {(1, 2), (2, 3), (5, 8), (6, 7)}, \( k = 2 \):

• Centroids: (1.5, 2.5), (5.5, 7.5).
• Clusters: {(1, 2), (2, 3)}, {(5, 8), (6, 7)}.
• Silhouette: ~0.8 (good separation).

Groups similar points.

Applications

Used in:

• Marketing: Customer segmentation.
• Biology: Gene expression analysis.
• Image Processing: Color quantization.

Reveals hidden structures.