Subspace clustering is a problem of exploring the low-dimensional subspaces of high-dimensional data. State-of-the-art 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, in this paper, we 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 an upper bound that 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 data sets reveal that our proposed method outperforms several representative clustering methods.
Subspace clustering is a problem of finding a multi-subspace representation that best fits sample points drawn from a high-dimensional space. The existing clustering models generally adopt different norms to describe noise, which is equivalent to assuming that the data are corrupted by specific types of noise. In practice, however, noise is much more complex. So it is inappropriate to simply use a certain norm to model noise. Therefore, we propose Mixture of Gaussian Regression (MoG Regression) for subspace clustering by modeling noise as a Mixture of Gaussians (MoG). The MoG Regression provides an effective way to model a much broader range of noise distributions. As a result, the obtained affinity matrix is better at characterizing the structure of data in real applications. Experimental results on multiple datasets demonstrate that MoG Regression significantly outperforms state-of-the-art subspace clustering methods.