Local Sparsity Preserving Projection Method For Face Recognition

In the field of signal processing, pattern recognition, image processing, sparsity method has been successfully applied to solve many practical problems. For example, in the field of signal processing, the research of sparsity is largely on signals compression and representation, signals compression potentially use lower sampling rates than the Shannon-Nyquist bound, and the processed signals remain sufficient information to restore the original signals. Based on the wide research of sparsity in various fields, this paper firstly introduces the application of sparse representation in face recognition, including the sparse representation-based classification, sparsity preserving projections, two-dimensional sparse method and so on.At the same time, most of the current linear analysis are starting from the global structure of the samples, ignoring their local characteristics, so several local structure-retained methods are discussed in the article, they all project the high-dimensional original samples to low-dimensional space in the way of maintaining local structure, they can deal with the decentralized inner-class samples while the linear analysis can not.Based on the deep research of sparse representation and local structure-retained algorithms, we explore that whether they can combine. From the total sparse coefficients of the target sample, we found that most of the non-zero coefficients belong to those samples who are close to the target sample, it indicates that the sparse representation itself has local property. Then this article proposes a new local sparsity preserving projection WLSPP based on our previous work. WLSPP can reconstruct target sample from few neighbors, and look for a projection space that maintains the relationship of local sparse reconstruction between all training samples.WLSPP is an unsupervised method, it means a bad ability to identify. To enhance the discriminant ability of WLSPP, label information is hoped to add to the local structure algorithm, this paper further proposes a supervised local sparsity preserving projection WSLSPP, it adds label information which is crucial for classification to the WLSPP, and then seeks the projection vector to minimize the reconstructive error caused by homogeneous neighbors, and simultaneously maximize the reconstructive error caused by inhomogeneous neighbors.