Sparse Convex Clustering Based on ℓ₂-Norm Regularization on Probability Simplex

Convex clustering is a clustering method that does not require the number of clusters in advance. This method is based on the mixture models which have all the samples as the means of clusters and clustering is achieved by finding sparse mixing weights. However, a large number of iterations are needed until convergence because its objective function does not evaluate the sparsity of the mixing weights. This article derives an efficient algorithm for convex clustering with regularization that represents sparsity. Focusing on the fact that sparse solutions on the probability simplex which is the solution space of the convex clustering have a large l₂-norm, we use the l₂-norm to regularize the solution. Experimental results show that the proposed method converges faster ones and the proposed regularization is adequate to represent sparsity.