Probabilistic K-means Clustering via Nonlinear Programming

• URL: http://arxiv.org/abs/2001.03286v2
• Date: Fri, 20 Nov 2020 00:59:26 GMT
• Title: Probabilistic K-means Clustering via Nonlinear Programming
• Authors: Yujian Li, Bowen Liu, Zhaoying Liu, and Ting Zhang
• Abstract summary: Probabilistic K-Means (PKM) is a nonlinear programming model constrained on linear equalities and linear inequalities. In theory, we can solve the model by active gradient projection, while inefficiently. By experiments, we evaluate the performance of PKM and how well the proposed methods solve it in five aspects.
• Score: 13.026121785720395
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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