When collaborative representation meets subspace projection: A novel supervised framework of graph construction augmented by anti-collaborative representation

摘要

Collaborative representation (CR) offers an appealing way for similarity graph construction in subspace projection (SP) methods. However, the dissimilarities between samples from different classes under the CR framework have been far less investigated. In this paper, we try to integrate the full-length CR with graph embedding based SP, and gradually arrive at the following findings: (1) The methods involving both CR and SP can be formulated as a two-stage framework, where CR servers as a feature extraction step while SP further constructs the similarity graph for feature embedding. This uncovers the essence of this type of methods, as well as their limitations due to the unsupervised property of CR. (2) A novel concept of anti-collaborative representation (Anti-CR), as a counterpart of CR, is introduced to characterize the coding ability of each sample by the samples from different classes. In this way, the label information could be fully exploited to capture the sample-by-sample dissimilarities derived from Anti-CR at the first stage. (3) At the second stage, the above two representations are incorporated into the construction of within-class and between-class graphs, respectively, so that in the projected subspace, the collaborative relationship of the samples in the same class could be strengthened while the collaborative relationship of the samples from different classes would be largely inhibited. Straightforwardly, the above analysis leads to a novel SP method, coined Complete Representation based supervised Feature Extraction and Embedding (CRFEE), as well as its accelerated version (CRFEE-A). Extensive experiments on benchmark image datasets show that the proposed methods outperform several state-of-the-art SP and CR algorithms in terms of discriminant power, indicating the benefits of exploring the anti-collaborative representation for feature description and projection. (C) 2018 Elsevier B.V. All rights reserved.