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

TL;DR

This paper introduces RFLkPC, a robust fuzzy local k-plane clustering method that effectively handles outliers by combining hinge loss and L1 norm, with proven efficiency on various datasets.

Contribution

The paper proposes a novel RFLkPC model that assumes finite bounded clusters, improving robustness against outliers compared to traditional methods.

Findings

RFLkPC outperforms existing models on simulated data.

The method demonstrates high accuracy on real-world datasets.

Source code is publicly available at the provided GitHub link.

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.