Sparse General Non-Negative Matrix Factorization Based on Left Semi-Tensor Product

Zigang Chen,Lixiang Li,Haipeng Peng,Yixian Yang,Yuhong Liu,Haihua Zhu

doi:10.1109/access.2019.2924140

Abstract

The dimension reduction of large scale high-dimensional data is a challenging task, especially the dimension reduction of face data and the accuracy increment of face recognition in the large scale face recognition system, which may cause large storage space and long recognition time. In order to further reduce the recognition time and the storage space in the large scale face recognition systems, on the basis of the general non-negative matrix factorization based on left semi-tensor (GNMFL) without dimension matching constraints proposed in our previous work, we propose a sparse GNMFL/L (SGNMFL/L) to decompose a large number of face data sets in the large scale face recognition systems, which makes the decomposed base matrix sparser and suppresses the decomposed coefficient matrix. Therefore, the dimension of the basis matrix and the coefficient matrix can be further reduced. Two sets of experiments are conducted to show the effectiveness of the proposed SGNMFL/L on two databases. The experiments are mainly designed to verify the effects of two hyper-parameters on the sparseness of basis matrix factorized by SGNMFL/L, compare the performance of the conventional NMF, sparse NMF (SNMF), GNMFL, and the proposed SGNMFL/L in terms of storage space and time efficiency, and compare their face recognition accuracies with different noises. Both the theoretical derivation and the experimental results show that the proposed SGNMF/L can effectively save the storage space and reduce the computation time while achieving high recognition accuracy and has strong robustness.

Highlights

Face recognition is an important research problem in computer vision, and it is widely used in banking, security, human-computer interaction and smart device apps
Referring to Equation (3), we propose SGNMFL/L, where L denotes that the sparseness is imposed on the left factor, and the sparse negative matrix factorization (NMF) formulation imposes sparseness on a factor of NMF by utilizing L1-norm minimization based on alternating non-negativity constrained least squares
In this paper, the proposed SGNMFL/L is presented in details and applied in face recognition

Summary

Introduction

Face recognition is an important research problem in computer vision, and it is widely used in banking, security, human-computer interaction and smart device apps. A face recognition system is a computer application capable of identifying or verifying a person from a digital image or a video frame. ‘‘The trouble with facial recognition technology (in the real world)’’ on The Conversation on December 14, 2016 between Robin Kramer and Kay Ritchie states that, as of 2016, face recognition is still not effective for most applications even though the accuracy has been substantially improved. The systems are often advertised as having accuracy close to 100%, they usually use much smaller sample sizes than what would be necessary for large scale applications [1]. Large scale face recognition systems are still facing many challenges. One of the challenges is to achieve a certain level of recognition accuracy, the large scale face data often requires very high dimensional face features, causing large storage space and long recognition time.

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