#k-means

Master clustering algorithms for customer segmentation, data exploration, and pattern discovery in unsupervised settings. K-Means clustering: 1. Algorithm implementation: centroid initialization, iterative assignment, convergence criteria. 2. Hyperparameter tuning: k selection using elbow method, silhouette score, gap statistic. 3. Preprocessing: feature scaling, standardization, handling categorical variables. Hierarchical clustering: 1. Agglomerative clustering: bottom-up approach, linkage criteria (ward, complete, average). 2. Dendrogram analysis: optimal cluster count, distance thresholds, visual interpretation. 3. Divisive clustering: top-down approach, computational complexity considerations. Density-based clustering: 1. DBSCAN: density-based spatial clustering, epsilon and min_samples parameters. 2. Outlier handling: noise point identification, varying density clusters. 3. HDBSCAN: hierarchical DBSCAN, cluster stability, automatic parameter selection. Advanced clustering: 1. Gaussian Mixture Models: probabilistic clustering, soft assignments, EM algorithm. 2. Spectral clustering: graph-based approach, non-convex clusters, similarity matrices. 3. Mean shift: mode-seeking algorithm, bandwidth selection, non-parametric density estimation. Cluster evaluation: 1. Internal measures: silhouette score (>0.5 good), Calinski-Harabasz index, Davies-Bouldin index. 2. External measures: adjusted rand index, normalized mutual information, homogeneity/completeness. 3. Visual validation: t-SNE plots, PCA visualization, cluster interpretation. Applications: customer segmentation (RFM analysis), market research, gene expression analysis, image segmentation, social network analysis, dimensionality reduction for visualization and preprocessing.