2020/01/10 by Yujian Li, Li, Yujian, Bowen Liu +5
Computer Science · #Advanced Clustering Algorithms Research #FOS: Computer and information sciences #Face and Expression Recognition #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Video Surveillance and Tracking Methods
paper · pdf · doi:10.48550/arxiv.2001.03286
openalex publication_date 2020/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
K-means is a classical clustering algorithm with wide applications. However, soft K-means, or fuzzy c-means at m=1, remains unsolved since 1981. To address this challenging open problem, we propose a novel clustering model, i.e. Probabilistic K-Means (PKM), which is also a nonlinear programming model constrained on linear equalities and linear inequalities. In theory, we can solve the model by active gradient projection, while inefficiently. Thus, we further propose maximum-step active gradient projection and fast maximum-step active gradient projection to solve it more efficiently. By experiments, we evaluate the performance of PKM and how well the proposed methods solve it in five aspects: initialization robustness, clustering performance, descending stability, iteration number, and convergence speed.