Robust Fuzzy local k-plane clustering with mixture distance of hinge loss and L1 norm

arXiv cs.LG / 4/27/2026

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Key Points

The paper presents a new robust fuzzy local k-plane clustering (RFLkPC) approach that unifies ideas from k-plane clustering, hyperplane clustering, and mixture regression under a common clustering-in-linear-manifolds perspective.
It targets key weaknesses of existing fuzzy/KPC methods, specifically their sensitivity to outliers caused by relying on L2-style projection distances and the performance loss when clusters are assumed to extend infinitely.
RFLkPC improves robustness by using a mixture distance combining hinge loss and the L1 norm, and by constraining each plane cluster to a finite bounded region.
The authors provide the full model formulation and optimization algorithms for RFLkPC, and report extensive experiments showing improved performance on both simulated and real datasets.
The method’s implementation is released publicly on GitHub, enabling other researchers to reproduce and build upon the work.

Abstract

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.