DLRF-Net: A Progressive Deep Latent Low-Rank Fusion Network for Hierarchical Subspace Discovery

Low-rank coding-based representation learning is powerful for discovering and recovering the subspace structures in data, which has obtained an impressive performance; however, it still cannot obtain deep hidden information due to the essence of single-layer structures. In this article, we investigate the deep low-rank representation of images in a progressive way by presenting a novel strategy that can extend existing single-layer latent low-rank models into multiple layers. Technically, we propose a new progressive Deep Latent Low-Rank Fusion Network (DLRF-Net) to uncover deep features and the clustering structures embedded in latent subspaces. The basic idea of DLRF-Net is to progressively refine the principal and salient features in each layer from previous layers by fusing the clustering and projective subspaces, respectively, which can potentially learn more accurate features and subspaces. To obtain deep hidden information, DLRF-Net inputs shallow features from the last layer into subsequent layers. Then, it aims at recovering the hierarchical information and deeper features by respectively congregating the subspaces in each layer of the network. As such, one can also ensure the representation learning of deeper layers to remove the noise and discover the underlying clean subspaces, which will be verified by simulations. It is noteworthy that the framework of our DLRF-Net is general and is applicable to most existing latent low-rank representation models, i.e., existing latent low-rank models can be easily extended to the multilayer scenario using DLRF-Net. Extensive results on real databases show that our framework can deliver enhanced performance over other related techniques.

Deep Latent Low-Rank Fusion Network for Progressive Subspace Discovery

Low-rank representation is powerful for recover-ing and clustering the subspace structures, but it cannot obtain deep hierarchical information due to the single-layer mode. In this paper, we present a new and effective strategy to extend the sin-gle-layer latent low-rank models into multi-ple-layers, and propose a new and progressive Deep Latent Low-Rank Fusion Network (DLRF-Net) to uncover deep features and struc-tures embedded in input data. The basic idea of DLRF-Net is to refine features progressively from the previous layers by fusing the subspaces in each layer, which can potentially obtain accurate fea-tures and subspaces for representation. To learn deep information, DLRF-Net inputs shallow fea-tures of the last layers into subsequent layers. Then, it recovers the deeper features and hierar-chical information by congregating the projective subspaces and clustering subspaces respectively in each layer. Thus, one can learn hierarchical sub-spaces, remove noise and discover the underlying clean subspaces. Note that most existing latent low-rank coding models can be extended to multi-layers using DLRF-Net. Extensive results show that our network can deliver enhanced perfor-mance over other related frameworks.

Pursuit of Low-Rank Models of Time-Varying Matrices Robust to Sparse and Measurement Noise

In tracking of time-varying low-rank models of time-varying matrices, we present a method robust to both uniformly-distributed measurement noise and arbitrarily-distributed “sparse” noise. In theory, we bound the tracking error. In practice, our use of randomised coordinate descent is scalable and allows for encouraging results on changedetection.net, a benchmark.