Abstract: Face recognition is a very important topic in data science and biometric security research areas. It has multiple applications in military, finance, and retail, to name a few. In this paper, the novel hypergraph Laplacian Eigenmaps will be proposed and combine with the k nearest-neighbor method and/or with the kernel ridge regression method to solve the face recognition problem. Experimental results illustrate that the accuracy of the combination of the novel hypergraph Laplacian Eigenmaps and one specific classification system is similar to the accuracy of the combination of the old symmetric normalized hypergraph Laplacian Eigenmaps method and one specific classification system. Keywords: face recognition, hypergraph, Laplacian Eigenmaps, classification I. Introduction Given a relational dataset, the pairwise relationships among objects/entities/samples in this dataset can be represented as the weighted graph.

Face recognition is the important field in machine learning and pattern recognition research area. It has a lot of applications in military, finance, public security, to name a few. In this paper, the combination of the tensor sparse PCA with the nearest-neighbor method (and with the kernel ridge regression method) will be proposed and applied to the face dataset. Experimental results show that the combination of the tensor sparse PCA with any classification system does not always reach the best accuracy performance measures. However, the accuracy of the combination of the sparse PCA method and one specific classification system is always better than the accuracy of the combination of the PCA method and one specific classification system and is always better than the accuracy of the classification system itself.