What is clustering and how do you choose the optimal number of clusters?

Clustering groups similar data points without predefined labels, requiring methods to determine optimal cluster numbers.\n\n• Algorithms: K-means, hierarchical, DBSCAN, Gaussian mixture models\n• Optimization methods: Elbow method, silhouette analysis, gap statistic\n• Evaluation: Silhouette score, Davies-Bouldin index, business interpretation\n• Considerations: Scalability, cluster shape assumptions, noise handling\n\nExample: Customer segmentation uses K-means with elbow method showing optimal k=4, validated with silhouette analysis. Business interprets clusters as high-value, price-sensitive, occasional, and new customers for targeted marketing strategies.