LAUSR

Manifold learning is a hot topic in feature extraction, wherein high-dimensional data is represented in a potential low-dimensional manifold. In this paper, a novel manifold-learning method called tensor locality preserving sparse projection (TLPSP) is proposed, which extends the locality preserving criterion to include constraints for the tensor and concise sparse case. In order to retain the structural information of images and avoid the “curse of dimensionality” caused by vectorization, the images are treated as second-order tensors. Furthermore, the sparse extension allows the transform matrix to ably perform feature selection. Although there are sparse subspace learning methods that combine the sparse constraint and the equivalent regression version of the generalized eigenvalue problem, the objects are vectors. Direct utilization of that regression version leads to a high-dimensional dictionary in the matrix-based case. Hence, we substitute the regression form for a concise term and prove their equivalence in detail. By introducing the L1 norm penalty to the modified regression problem under the locality preserving criterion, the sparse projection matrices are obtained for feature extraction. Comparison experiments on supervised and unsupervised tasks demonstrate that TLPSP improves the recognition results and clustering performance.