Multimodal sparse and low-rank subspace clustering

In this paper, we propose multimodal extensions of the recently introduced sparse subspace clustering (SSC) and low-rank representation (LRR) based subspace clustering algorithms for clustering data lying in a union of subspaces. Given multimodal data, our method simultaneously clusters data in the individual modalities according to their subspaces. In our formulation, we exploit the self expressiveness property of each sample in its respective modality and enforce the common representation across the modalities. We modify our model so that it is robust to noise. Furthermore, we kernelize the proposed algorithms to handle nonlinearities in data. The optimization problems are solved efficiently using the alternative direction method of multiplier (ADMM). Experiments on face clustering indicate the proposed method performs favorably compared to state-of-the-art subspace clustering methods.