Non-Negative Matrix Factorization Framework for Face Recognition

Abstract

Non-negative Matrix Factorization (NMF) is a part-based image representation method which adds a non-negativity constraint to matrix factorization. NMF is compatible with the intuitive notion of combining parts to form a whole face. In this paper, we propose a framework of face recognition by adding NMF constraint and classifier constraints to matrix factorization to get both intuitive features and good recognition results. Based on the framework, we present two novel subspace methods: Fisher Non-negative Matrix Factorization (FNMF) and PCA Non-negative Matrix Factorization (PNMF). FNMF adds both the non-negative constraint and the Fisher constraint to matrix factorization. The Fisher constraint maximizes the between-class scatter and minimizes the within-class scatter of face samples. Subsequently, FNMF improves the capability of face recognition. PNMF adds the non-negative constraint and characteristics of PCA, such as maximizing the variance of output coordinates, orthogonal bases, etc. to matrix factorization. Therefore, we can get intuitive features and desirable PCA characteristics. Our experiments show that FNMF and PNMF achieve better face recognition performance than NMF and Local NMF.

Discriminative Basis Selection Using Non-negative Matrix Factorization

“…FNMF is shown to work better for classification purposes than LNMF [7]; however, as we can see from Table 1, our method outperforms FNMF for all but one of the chosen numbers of bases. It should be noted that this is a skewed comparison because while FNMF is using all 96 bases our method is using only 82 to obtain the same accuracy.…”

“…We present the performance of our proposed algorithm on the dataset and compare our algorithm against three other methods: FNMF [7], LNMF [4], and CLNMF as explained in Section 3. For classification we use kneareast neighbors where k = 3.…”

“…However, it does not encode discrimination information for a classification problem and this can lead to redundant bases. Another variant which is specifically meant for classification is Fisher NMF (FNMF) [7]. This method incorporates Fisher constraints within the NMF framework in order to boost classification results.…”

Non‐negative Matrix Factorization for the identification of patterns of atmospheric pressure and geopotential for the Northern Hemisphere

“…Additionally, over-fitting and generalization could be interesting topics with regard to the question of best representation of the natural conditions. It seems very useful to apply the NMF method also to other types of meteorological fields, such as boundary layer height and temperature and to test new algorithms, such as LNMF and FNMF (Wang et al, 2005;Kim and Park, 2008;Cichocki et al, 2007;Ho, 2008) that both present additional modifications to obtain more localized patterns in the NMF-factors. Furthermore, it would be interesting to analyse the time series of the obtained NMF-factors in a more detailed way.…”

Projected Gradients for Subclass Discriminant Nonnegative Subspace Learning

“…Focusing on applications operating on facial image data, numerous specialized NMF variants have been proposed for face recognition [7], [13], [14], face verification [15], [16], and facial expression recognition [17], [18]. In these approaches, the entire facial image is considered as a feature vector and NMF aims to find projections that optimize a given criterion.…”