Multilayer Collaborative Low-Rank Coding Network for Robust Deep Subspace Discovery

For subspace recovery, most existing low-rank representation (LRR) models performs in the original space in single-layer mode. As such, the deep hierarchical information cannot be learned, which may result in inaccurate recoveries for complex real data. In this paper, we explore the deep multi-subspace recovery problem by designing a multilayer architecture for latent LRR. Technically, we propose a new Multilayer Collabora-tive Low-Rank Representation Network model termed DeepLRR to discover deep features and deep subspaces. In each layer (>2), DeepLRR bilinearly reconstructs the data matrix by the collabo-rative representation with low-rank coefficients and projection matrices in the previous layer. The bilinear low-rank reconstruc-tion of previous layer is directly fed into the next layer as the input and low-rank dictionary for representation learning, and is further decomposed into a deep principal feature part, a deep salient feature part and a deep sparse error. As such, the coher-ence issue can be also resolved due to the low-rank dictionary, and the robustness against noise can also be enhanced in the feature subspace. To recover the sparse errors in layers accurately, a dynamic growing strategy is used, as the noise level will be-come smaller for the increase of layers. Besides, a neighborhood reconstruction error is also included to encode the locality of deep salient features by deep coefficients adaptively in each layer. Extensive results on public databases show that our DeepLRR outperforms other related models for subspace discovery and clustering.