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

Junjun Huang; Xiliang Lu; Xuelin Xie; Jerry Zhijian Yang

cs.LGApr 24, 2026

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

Authors: Junjun Huang, Xiliang Lu, Xuelin Xie, Jerry Zhijian Yang

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.

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May 8, 2026 · cs.LGJ/K move · Enter open · S save

Simple KNN-Based Outlier Detection Achieves Robust Clustering

Tianle Jiang, Yufa Zhou

Duke University

Being robust to the presence of outliers is crucial for applying clustering algorithms in practice. In the

\textit{robust

-Means}

problem (i.e.,

k

-Means with outliers), the goal is to remove

z

outliers and minimize the

k

-Means cost on the remaining points. Despite the close connection between robust

k

-Means and outlier detection, both theoretical and empirical understanding of the effectiveness of

\textit{classic outlier detection heuristics}

for robust

k

-Means remains limited. In this paper, we prove that under a practical assumption on the optimal cluster sizes, simply removing points with large

K

-Nearest-Neighbor distances achieves performance comparable to prior work in terms of approximation guarantees: it yields a constant-factor reduction from robust

k

-Means to standard

k

-Means, without introducing additional centers or discarding extra outliers, as is commonly required by existing approaches. Empirically, experiments on real-world datasets show that our method outperforms or matches several more sophisticated algorithms in terms of clustering cost and runtime. These results demonstrate that simple KNN-based heuristics can be surprisingly effective for robust clustering, highlighting new opportunities to bridge techniques from outlier detection and clustering.

K-Means Image Clustering Outliers Approximate Nearest-Neighbor Search

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Abstract

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