Orthogonal Sparsity Preserving Projections Based Image Feature Extraction And Recognition

For a given data set, global sparse reconstruction relations among data have been shown to contain useful information for classification. Based on this, a feature extraction method named sparsity preserving projections (SPP) has been proposed, which tends to seek a linear transformed subspace where the sparse reconstruction relations among training data could be preserved.Nevertheless, the SPP transform does not satisfy the orthogonal property that is favorable in many scenarios. In this paper, we extend SPP to an orthogonal SPP (OSPP), and design two implemental algorithms to derive orthogonal transform vectors, namely, holistic OSPP (HOSPP) and iterative OSPP (IOSPP). HOSPP extracts all transform vectors at one time by using orthogonal constrains instead of the original one in SPP. IOSPP extracts transform vectors in an iterative manner by adding the orthogonal constrains, and meanwhile the original constrain can be preserved.In HOSPP and IOSPP, we mainly concern about the global sparse reconstruction relations among data. However, in real world, image samples possibly reside on a nonlinear submanifold, which is the inherent structure among the samples. Thus, we revise the objective function in OSPP by introducing a similarity matrix. As a result, the proposed method can not only preserve the global sparse reconstruction relations, but also preserve the manifold structure among data. Similar to HOSPP and IOSPP, we name the two realizations as Manifold Learning based Holistic Orthogonal Sparsity Preserving Projections (MLHOSPP) and Manifold Learning based Iterative Orthogonal Preserving projections (MLIOSPP).The above approaches are unsupervised so that the discriminant information is limited. Supervised subspace methods are shown to have more effective discriminant features and have better recognition performance. Further, we proposed Manifold Learning based Holistic Orthogonal Sparsity preserving Discriminant analysis (MLHOSDA) and Manifold Learning based Iterative Orthogonal Preserving Discriminant analysis (MLIOSDA). We use samples with labels to reconstruct the sparse reconstruction graph and the similarity graph, so that the projective space has more discriminant information. Further, we simultaneously consider distances and angles between image data vectors to measure data, and name the approaches as Complex Locality Preserving based Holistic Orthogonal Sparsity Preserving Projections (CLPHOSPP) and Complex Locality Preserving based Iterative Orthogonal Preserving projections (CLPIOSPP).Experimental results on the public Yale, CAS-PEAL face databases and PolyU palmprint database show the effectiveness of our proposed approaches.