Apr 24, 2026 · cs.LGJ/K move · Enter open · S save
Junjun Huang, Xiliang Lu, Xuelin Xie, Jerry Zhijian Yang
China Electric Power Research Institute, Wuhan 430074, China, and also with the Key Laboratory of Measurement and Test of High Voltage and Heavy Current, State Administration for Market Regulation, Wuhan 430074, China · School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China, the National Center for Applied Mathematics in Hubei, Wuhan University, Wuhan 430072, China, and also with the Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan 430072, China · National Center for Applied Mathematics in Hubei, Wuhan University, Wuhan 430072, China, the Wuhan Institute for Math and AI, Wuhan University, Wuhan 430072, China, the School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China, and the Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan 430072, China
K-plane clustering (KPC), hyperplane clustering, and mixture regression all essentially fall within the same class of problems. This problem can be conceptualized as clustering in relatively high-dimensional K subspaces or K linear manifolds. Traditional KPC or fuzzy KPC models demonstrate a pronounced susceptibility to outliers, as they presuppose that the projection distance between data points and the plane normal vector adheres to the L2 distance. Meanwhile, the assumption of infinitely extending clusters adversely affects clustering performance. To solve these problems, this paper proposed a new robust fuzzy local k-plane clustering (RFLkPC) method that combines the mixture distance of hinge loss and L1 norm. The RFLkPC model assumes that each plane cluster is bounded to a finite area, which can flexibly and robustly handle plane clustering tasks with outliers or not. The corresponding model and optimization algorithms of RFLkPC were provided. Compared to other related models on this topic, a large number of experiments verify the efficiency of RFLkPC on simulated data and real data. The source code for the proposed RFLkPC method is publicly available at https://github.com/xuelin-xie/RFLkPC.