提出新方法，让平面聚类更抗噪、更稳健。
Robust Fuzzy local k-plane clustering with mixture distance of hinge loss and L1 norm
- 用铰链损失与L1范数混合距离增强鲁棒性
- 在模拟和真实数据上表现优于现有模型
- 适合含异常点的平面聚类任务
K平面聚类（KPC）、超平面聚类和混合回归本质上属于同一类问题，可视为在高维空间中对K个子空间或线性流形进行聚类。传统KPC或模糊KPC模型对异常点敏感，因其假设数据点到平面的投影距离服从L2范数。同时，无限延伸簇的假设也影响聚类效果。为此，本文提出一种新的鲁棒模糊局部K平面聚类（RFLkPC）方法，结合铰链损失与L1范数的混合距离。该模型假设每个平面簇限定于有限区域，能灵活且稳健地处理含异常点的平面聚类任务。本文给出了RFLkPC的模型及其优化算法。大量实验验证了其在模拟数据和真实数据上的高效性。相关源代码已公开：https://github.com/xuelin-xie/RFLkPC。
原文摘要 · Abstract (English)
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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