Nonconvex clustering via ℓ0 fusion penalized regression. (August 2022)

• Record Type: Journal Article
• Authors: Chen, Huangyue; Kong, Lingchen; Li, Yan
• Is Part Of: Pattern recognition. Volume 128(2022)
• Publication Date: 2022-08
• Subjects: Penalized clustering -- ℓ0 fusion penalty -- Nonconvex discontinuous optimization -- Alternating direction method of multipliers; Pattern perception -- Periodicals; Perception des structures -- Périodiques; Patroonherkenning; 006.4
• DOI: 10.1016/j.patcog.2022.108689
• Languages: English
• ISSNs: 0031-3203

Abstract

Highlights: A novel penalized clustering model is proposed based on the ℓ 0 fusion penalty. We derive some properties and optimality conditions of the proposed model. Efficient optimization algorithm is designed to solve the model. Experimental results show that our method is superior to the state-of-the-art methods. Abstract: Cluster analysis has attracted widespread attention in the past several decades. Generally speaking, clustering is considered as an important unsupervised learning method because its goal is to discover unknown subgroups in data without category label information. In this paper, we propose the ℓ 0 fusion penalized clustering model ( ℓ 0 -PClust), which is a novel clustering framework founded on the penalized regression method. Theoretically, we first analyze the existence of the optimal solutions of our model and deduce an upper bound of the tuning parameter. Then we define the Karush-Kuhn-Tucker point and P-stationary point of the ℓ 0 -PClust model, and establish the relationship between them and local optimal solutions. Moreover, based on the P-stationary point of the ℓ 0 -PClust model, we prove that the distances among different cluster centers are greater than a positive threshold. Computationally, we solve the ℓ 0 -PClust model via the famous alternating direction method of multipliers, whose limit point is a P-stationary point and local optimal solution of the model. Finally, we conduct extensive experiments on both synthetic and real data sets. Experimental results show outstanding performance of our method in comparison with several state-of-the-art clustering methods.