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Elbow curve and Silhouette plots both are very useful techniques for finding the optimal K for K-means clustering
Comparing Clustering Algorithms
Following table will give a comparison (based on parameters, scalability and metric) of the clustering algorithms in scikit-learn.
Sr.No Algorithm Name Parameters Scalability Metric Used
1 K-Means No. of clusters Very large n_samples The distance between points.
2 Affinity Propagation Damping It’s not scalable with n_samples Graph Distance
3 Mean-Shift Bandwidth It’s not scalable with n_samples. The distance between points.
4 Spectral Clustering No.of clusters Medium level of scalability with n_samples. Small level of scalability with n_clusters. Graph Distance
5 Hierarchical Clustering Distance threshold or No.of clusters Large n_samples Large n_clusters The distance between points.
6 DBSCAN Size of neighborhood Very large n_samples and medium n_clusters. Nearest point distance
7 OPTICS Minimum cluster membership Very large n_samples and large n_clusters. The distance between points.
8 BIRCH Threshold, Branching factor Large n_samples Large n_clusters The Euclidean distance between points.