Supervised orthogonal discriminant subspace projects learning for face recognition.

In this paper, a new linear dimension reduction method called supervised orthogonal discriminant subspace projection (SODSP) is proposed, which addresses high-dimensionality of data and the small sample size problem. More specifically, given a set of data points in the ambient space, a novel weight matrix that describes the relationship between the data points is first built. And in order to model the manifold structure, the class information is incorporated into the weight matrix. Based on the novel weight matrix, the local scatter matrix as well as non-local scatter matrix is defined such that the neighborhood structure can be preserved. In order to enhance the recognition ability, we impose an orthogonal constraint into a graph-based maximum margin analysis, seeking to find a projection that maximizes the difference, rather than the ratio between the non-local scatter and the local scatter. In this way, SODSP naturally avoids the singularity problem. Further, we develop an efficient and stable algorithm for implementing SODSP, especially, on high-dimensional data set. Moreover, the theoretical analysis shows that LPP is a special instance of SODSP by imposing some constraints. Experiments on the ORL, Yale, Extended Yale face database B and FERET face database are performed to test and evaluate the proposed algorithm. The results demonstrate the effectiveness of SODSP.