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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.

MSC:
68T10 Pattern recognition, speech recognition
68W05 Nonnumerical algorithms
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