Solving the small sample size problem in face recognition using generalized discriminant analysis

Authors:
Peg Howland;Jianlin Wang;Haesun Park
Affiliations:
Department of Mathematics and Statistics, Utah State University, 3900 Old Main Hill, Logan, UT 84322, USA;Department of Civil and Coastal Engineering, University of Florida, 365 Weil Hall, Gainesville, FL 32611, USA;Department of Computer Science and Engineering, University of Minnesota, 4-192 EE/CS Building, Minneapolis, MN 55455, USA
Venue:
Pattern Recognition
Year:
2006

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Abstract

The goal of face recognition is to distinguish persons via their facial images. Each person's images form a cluster, and a new image is recognized by assigning it to the correct cluster. Since the images are very high-dimensional, it is necessary to reduce their dimension. Linear discriminant analysis (LDA) has been shown to be effective at dimension reduction while preserving the cluster structure of the data. It is classically defined as an optimization problem involving covariance matrices that represent the scatter within and between clusters. The requirement that one of these matrices be nonsingular restricts its application to datasets in which the dimension of the data does not exceed the sample size. For face recognition, however, the dimension typically exceeds the number of images in the database, resulting in what is referred to as the small sample size problem. Recently, the applicability of LDA has been extended by using the generalized singular value decomposition (GSVD) to circumvent the nonsingularity requirement, thus making LDA directly applicable to face recognition data. Our experiments confirm that LDA/GSVD solves the small sample size problem very effectively as compared with other current methods.