The 2D factor analysis and its application to face recognition with a single sample per person

In this paper, a novel theoretical model of data reduction and multivariate analysis is proposed. The Two-dimensional Factor Analysis is an extension of classical factor analysis in which the images are treated as matrices instead of being converted to unidimensional vectors. By maximally representing the correlation among the pixels, it is able to capture meaningful information about the spatial relationships of the elements in a two-dimensional signal. The method is illustrated in the problem of face recognition with superior results when compared to other approaches based on principal component analysis. Experiments using public databases under different pose and illumination conditions show that the proposed method is significantly more effective than the two-dimensional principal component analysis while dealing with samples composed by a single image per person.