A Sparse Corruption Non-Negative Matrix Factorization method and application in face image processing & recognition

Abstract

Non-negative Matrix Factorization (NMF) has attracted widely attentions in the areas of data analysis, image processing & measurement and noise separation. NMF can obtain the non-negative low-dimensional representation of the data and low-rank matrix is of great importance to classification and recognition. Classic NMF assumes that noise is subject to Gaussian noise or Poisson noise, while it is inapplicable to some other noise. In addition, corrupted data in the test set cannot be restored by NMF. Many scholars have studied NMF and proposed a variety of improved algorithms so far, such as Robust Non-Negative Matrix Factorization (RNMF), which is designed to deal with sparse corruption. Our paper presents Sparse Corruption Non-Negative Matrix Factorization (SCNMF). SCNMF separates a sparse noise matrix out of the corrupted input matrix, and the rest of the input matrix is represented as the product of two low-dimensional matrices. The product of two low-dimensional matrices approximates the non-corrupted input matrix. The base matrix calculated by the proposed method is tolerant to noise. It can reconstruct new data well regardless of whether the new data is corrupted and non-corrupted. Experiments on specific face databases verifies the validity of SCNMF. Reconstructed faces by the proposed method are clearer and more recognizable and the recognition rate is three percentage points higher by comparison.