Multi-linear neighborhood preserving projection for face recognition

•A new method for supervised and unsupervised dimensionality reduction problem.•Work in embedded manifold to allow representation of multi-dimensional images.•Natural extension to 2-D, 3-D or higher-order tensors.•Combine intrinsic geometry and discriminative information for face recognition.•Avoid the small sample size and the curse of dimensionality problems.

This paper proposes a novel method of supervised and unsupervised multi-linear neighborhood preserving projection (MNPP) for face recognition. Unlike conventional neighborhood preserving projections, the MNPP method operates directly on tensorial data rather than vectors or matrices, and solves problems of tensorial representation for multi-dimensional feature extraction, classification and recognition. As opposed to traditional approaches such as NPP and 2DNPP, which derive only one subspace, multiple interrelated subspaces are obtained in the MNPP method by unfolding the tensor over different tensorial directions. The number of subspaces derived by MNPP is determined by the order of the tensor space. This approach is used for face recognition and biometrical security classification problems involving higher order tensors. The performance of our proposed and existing techniques is analyzed using three benchmark facial datasets ORL, AR, and FERET. The obtained results show that the MNPP outperforms the standard approaches in terms of the error rate.