Face Subspace Learning

The last few decades have witnessed a great success of subspace learning for face recognition. From principal component analysis (PCA) [43] and Fisher’s linear discriminant analysis [1], a dozen of dimension reduction algorithms have been developed to select effective subspaces for the representation and discrimination of face images [17, 21, 45, 46, 51]. It has demonstrated that human faces, although usually represented by thousands of pixels encoded in high-dimensional arrays, they are intrinsically embedded in a vary low dimensional subspace [37]. The using of subspace for face representation helps to reduce “the curse of dimensionality” in subsequent classification, and suppress variations of lighting conditions and facial expressions. In this chapter, we first briefly review conventional dimension reduction algorithms and then present the trend of recent dimension reduction algorithms for face recognition. The earliest subspace method for face recognition is Eigenface [43], which uses PCA [23] to select the most representative subspace for representing a set of face images. It extracts the principal eigenspace associated with a set of training face images. Mathematically, PCA maximizes the variance in the projected subspace for a given dimensionality, decorrelates the training face images in the projected subspace, and maximizes the mutual information between appearance (training face images) and identity (the corresponding labels) by assuming that face images are Gaussian distributed. Thus, it has been successfully applied for face recognition. By projecting face images onto the subspace spanned by Eigenface, classifiers can be used in the subspace for recognition. One main limitation of Eigenface is that the