zbMATH — the first resource for mathematics

A direct LDA algorithm for high-dimensional data – with application to face recognition. (English) Zbl 0993.68091
Summary: We proposed a direct LDA algorithm for high-dimensional data classification, with application to face recognition in particular. Since the number of samples is typically smaller than the dimensionality of the samples, both \(S_b\) and \(S_w\) are singular. By modifying the simultaneous diagonalization procedure, we are able to discard the null space of \(S_b\) – which carries no discriminative information – and to keep the null space of \(S_w\), which is very important for classification. In addition, computational techniques are introduced to handle large scatter matrices efficiently. The result is a unified LDA algorithm that gives an exact solution to Fisher’s criterion whether or not \(S_w\) is singular.

68T10 Pattern recognition, speech recognition
68W05 Nonnumerical algorithms
Full Text: DOI
[1] Chen, L; Liao, H; Ko, M; Lin, J; Yu, G, A new LDA-based face recognition system which can solve the small sample size problem, Pattern recognition, 33, 10, 1713-1726, (2000)
[2] Swets, D; Weng, J, Using discriminant eigenfeatures for image retrieval, Pattern anal. Mach. intell., 18, 8, 831-836, (1996)
[3] Belhumeur, P.N; Hespanha, J.P; Kriegman, D.J, Eigenfaces vs. fisherfacerecognition using class specific linear projection, Pattern anal. Mach. intell., 19, 7, 711-720, (1997)
[4] Fukunaga, K, Introduction to statistical pattern recogniton, (1990), Academic Press New York
[5] Turk, M; Pentland, A, Eigenfaces for recognition, J. cognitive neurosci., 3, 1, 72-86, (1991)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.