A novel framework called 2D Fisher Discriminant Analysis
(2D-FDA) is proposed to deal with the Small Sample
Size (SSS) problem in conventional One-Dimensional Linear
Discriminant Analysis (1D-LDA). Different from the
1D-LDA based approaches, 2D-FDA is based on 2D image
matrices rather than column vectors so the image matrix
does not need to be transformed into a long vector before
feature extraction. The advantage arising in this way
is that the SSS problem does not exist anymore because
the between-class and within-class scatter matrices constructed
in 2D-FDA are both of full-rank. This framework
contains unilateral and bilateral 2D-FDA. It is applied to
face recognition where only few training images exist for
each subject. Both the unilateral and bilateral 2D-FDA
achieve excellent performance on two public databases:
ORL database and Yale face database B.