Local Learning Joint with the Adaptive Graph for Subspace Representation

The technique of local learning that recognizes each sample by its predefined neighbors has been successfully applied in unsupervised learning fields. However, how to determine the proper neighbors of a sample is a challenging problem. Inappropriate selection of neighbors will drastically degrade the performance of local learning methods. In this study, a novel subspace representation method based on local learning joint with the adaptive graph (LLAG) is presented. On the one hand, by exploiting the notion of the adaptive graph and the technique of low-rank constraint, the affinity graph can be constructed iteratively, which prompts the produced subspace to well preserve the local and global structures of the data. On the other hand, the neighbors of samples involved in the local learning are produced adaptively during the optimization process. In this way, more accurate local information that is used to guide the generation of the optimal subspace can be revealed. Extensive experimental results on some benchmark data sets demonstrate the superiority of the proposed method LLAG in comparison with some existing unsupervised learning methods.