Embedded conformal deep low-rank auto-encoder network for matrix recovery

摘要

We present a novel embedded conformal deep low-rank auto-encoder (ECLAE) neural network architecture for matrix recovery and it can be utilized for image restoration and clustering. Traditionally, robust principal component analysis based methods attempt to decompose the raw matrix into two components: low-rank part and sparse part. For image data as an example, the primary information of the raw data is gathered in the low-rank component and other information, such as noise, exists in the sparse part. The principal components of a data matrix can be recovered even though a positive fraction of its elements are arbitrarily corrupted. However, these methods neglect the non-linear structure information of the original data. Many recent researches pay more attention to the structure of deep learning to extract the nonlinear relationship of data. The deep auto-encoder as a classical deep structure has performed many splendid results. Hence, we propose ECLAE to integrate the advantage of auto-encoder and low-rank representation. And the conformal local structure of data is perfectly embedded into the novel deep frame. Our key idea includes two folds. The first fold is to adaptively obtain latent layer learning the neighbor structure of data with the conformal constraint. The other is to embed the global information into the network by appending the low-rank constraint over the network outputs. To verify the ability of matrix decompose, our method is used for image restoration. And to evaluate the structure of low-dimensional space, the latent representation is exploited for cluster. Extensive experimental results illustrate the efficiency of the proposed algorithm. (c) 2018 Elsevier B.V. All rights reserved.