Block diagonal representation learning for robust subspace clustering

Subspace clustering groups a set of data into their underlying subspaces according to the low-dimensional subspace structure of data. The performance of spectral clustering-based approaches heavily depends on the learned block diagonal structure of the affinity matrix. However, this structure is fragile in the presence of noise within data. As such, the clustering performance is degraded significantly. On the other hand, in practice, we often do not have a prior knowledge of error distribution at all, which results in that we cannot model the error with suitable norms. To this end, in this paper, we propose a robust block diagonal representation learning for subspace clustering. Specifically, a non-convex regularizer is directly utilized to constrain the affinity matrix for exploiting the block diagonal structure. Furthermore, we use a penalty matrix to adaptively weight the reconstruction error so that we can handle noise without prior knowledge. We also devise an effective method to compute the parameters related to this matrix, reducing the complexity of the parameter trains. Experimental results show that our method outperformed the state-of-the-art methods on both synthetic data and real-world datasets.