Toward Efficient Image Representation: Sparse Concept Discriminant Matrix Factorization

The key ingredients of matrix factorization lie in basic learning and coefficient representation. To enhance the discriminant ability of the learned basis, discriminant graph embedding is usually introduced in the matrix factorization model. However, the existing matrix factorization methods based on graph embedding generally conduct discriminant analysis via a single type of adjacency graph, either similarity-based graphs (e.g., Laplacian eigenmaps graph) or reconstruction-based graphs (e.g., ${L}_{1}$ -graph), while ignoring the cooperation of the different types of adjacency graphs that can better depict the discriminant structure of original data. To address the above issue, we propose a novel Fisher-like criterion, based on graph embedding, to extract sufficient discriminant information via two different types of adjacency graphs. One graph preserves the reconstruction relationships of neighboring samples in the same category, and the other suppresses the similarity relationships of neighboring samples from different categories. Moreover, we also leverage the sparse coding to promote the sparsity of the coefficients. By virtue of the proposed Fisher-like criterion and sparse coding, a new matrix factorization framework called Sparse concept Discriminant Matrix Factorization (SDMF) is proposed for efficient image representation. Furthermore, we extend the Fisher-like criterion to an unsupervised context, thus yielding an unsupervised version of SDMF. Experimental results on seven benchmark datasets demonstrate the effectiveness and efficiency of the proposed SDMFs on both image classification and clustering tasks.