Marginal and Nonlocal Discriminant Embedding for Face Recognition

This paper develops a supervised discriminant technique, called marginal and nonlocal discriminant embedding (MNDE), for dimensionality reduction of high-dimensional data in small sample size problems. MNDE can be seen as a linear approximation of a multimanifold-based learning framework in which nonlocal property is taken into account besides the marginal property and local property. MNDE seeks to find a set of perfect projections that not only can impact the samples of intraclass and maximize the margin of interclass, but also can simultaneously maximize the nonlocal scatter that characterizes the sum scatter of any pair of data out of local K-neighborhood. This characteristic makes MNDE more intuitive and more powerful than LDA and marginal Fisher analysis (MFA). The proposed method is applied to face recognition and is examined on the Yale and AR face image databases.