Feature Extraction Based on Sparsity Embedding with Manifold Information for Face Recognition

In the past few years, manifold learning and sparse representation have been widely used for feature extraction and dimensionality reduction. The sparse representation technique shows that one sample can be linearly recovered by the others in a data set. Based on this, sparsity preserving projections (SPP) has recently been proposed, which simply minimizes the sparse reconstructive errors among training samples in order to preserve the sparse reconstructive relations among data. However, SPP does not investigate the inherent manifold structure of the data set, which may be helpful for the recognition task. Motivated by this, we present in this paper a novel feature extraction approach named sparsity embedding with manifold information (SEMI), which not only preserves the sparse reconstructive relations, but also maintains the manifold structure of the reconstructed data. Specifically, for a sparse reconstructed sample, we minimize both its difference to the corresponding original sample as SPP does, and its distance to the original intra-class samples. Provided that this sample lies on different submanifolds from other samples, we additionally maximize, in the objective function, its distance to the original inter-class samples. Experimental results on two public ORL and AR face databases demonstrate that SEMI outperforms related methods in classification performance.