Mechanism and a new algorithm for nonconvex clustering

Abstract

ABSTRACTNonconvex clustering is based on over-parameterization and uses a shrinkage term to achieve sparsity in the differences among individual centroids. In this paper, we elaborate the mechanism of nonconvex clustering from a new perspective by reformulating the basic alternating direction method of multipliers (ADMM) algorithm, and explain for the first time how nonconvex clustering can identify outliers that are far from the nearest cluster centre [Knorr EM, Ng RT. Algorithms for mining distance-based outliers in large datasets. Proceedings of the 24th VLDB Conference; New York, USA: 1998. p. 392–403]. To overcome the computational burden owing to complexity, inspired by the mechanism of nonconvex clustering, we develop another novel and accelerating algorithm called aBlock_ADMM, which combines adaptive block clustering and the ADMM algorithm. We evaluate the clustering performance of the new algorithm on both simulated and real data examples.