Collaborative graph embedding: A simple way to generally enhance subspace learning algorithms

Collaborative representation (CR), known as an effective way to address the signal representation (regression) problem, has achieved remarkable success in visual classification. According to our theoretical analysis, the subspace learning issue can also be deemed as a signal representation problem. Therefore, we extend the graph embedding (GE) framework as a CR model to improve the discriminating power of the subspace learning algorithm. The new GE framework, which is named collaborative GE (CGE) framework, enjoys many desirable properties of CR. From theoretical analysis, CGE is robust to the noise and has the same computational complexity as GE. From experimental analysis, CGE can generally enhance the subspace learning algorithms and a reasonable regularization parameter can be inferred from its intrinsic graph. Several state-of-the-art subspace learning algorithms are plugged into our framework to produce their collaborative versions. Meanwhile, by exploring the intrinsic relation among GE methods, we present a new collaborative method named collaborative class-scattering locality preserving projections (CCSLPPs). The results of extensive experiments on ORL, AR, Scene15, Caltech256, LFW-A, and OU-ISIR-A databases demonstrate that the collaborative versions consistently outperform their original algorithms with a remarkable improvement and CCSLPP gets the best performance compared with all used methods.