A Review of Convex Clustering From Multiple Perspectives: Models, Optimizations, Statistical Properties, Applications, and Connections

Traditional partition-based clustering is very sensitive to the initialized centroids, which are easily stuck in the local minimum due to their nonconvex objectives. To this end, convex clustering is proposed by relaxing K -means clustering or hierarchical clustering. As an emerging and excellent clustering technology, convex clustering can solve the instability problems of partition-based clustering methods. Generally, convex clustering objective consists of the fidelity and the shrinkage terms. The fidelity term encourages the cluster centroids to estimate the observations and the shrinkage term shrinks the cluster centroids matrix so that their observations share the same cluster centroid in the same category. Regularized by the l