Subspace Clustering by Relaxed Block Diagonal Representation

The deluge of high dimensional data brings great challenges to data analysis, processing and storage. Subspace clustering aims to solve this dilemma by uncovering the latent low-dimensional structure inherent in high dimensional data. The most popular methods are self-representation (SR) based methods, which learn an affinity matrix by using the SR of the dataset and then apply the spectral clustering to obtain the final clustering results. The SR basically determines the clustering performance; therefore, existing methods use various regularity to impose clustering advantageous structure on the SR. In this work, we incorporate an orthogonal matrix in the block diagonal regularity (BDR) and adapt the BDR model as the relaxed BDR(RBDR) model. Our model enforces the block diagonal structure of SR, but allows an orthogonal matrix difference. We also present an alternative minimization algorithm to solve our model. Extended experimental results show that our model can greatly improve the performance of the BDR, especially when the dataset is not arranged cluster by cluster, which is true in practice. Therefore, our method fits better for practical data.