# Robust subspace clustering by Cauchy loss function

## TL;DR

This paper introduces a robust subspace clustering method using the Cauchy loss function to effectively handle noisy data, outperforming existing methods on real datasets.

## Contribution

It proposes a novel subspace clustering approach based on Cauchy loss, addressing noise influence and proving the grouping effect theoretically.

## Key findings

- Outperforms several existing clustering methods on five real datasets.
- Uses Cauchy loss to suppress large noise in data.
- Theoretically proves the grouping effect of the method.

## Abstract

Subspace clustering is a problem of exploring the low-dimensional subspaces of high-dimensional data. State-of-the-arts approaches are designed by following the model of spectral clustering based method. These methods pay much attention to learn the representation matrix to construct a suitable similarity matrix and overlook the influence of the noise term on subspace clustering. However, the real data are always contaminated by the noise and the noise usually has a complicated statistical distribution. To alleviate this problem, we in this paper propose a subspace clustering method based on Cauchy loss function (CLF). Particularly, it uses CLF to penalize the noise term for suppressing the large noise mixed in the real data. This is due to that the CLF's influence function has a upper bound which can alleviate the influence of a single sample, especially the sample with a large noise, on estimating the residuals. Furthermore, we theoretically prove the grouping effect of our proposed method, which means that highly correlated data can be grouped together. Finally, experimental results on five real datasets reveal that our proposed method outperforms several representative clustering methods.