Selecting Principal Components in a Two-Stage LDA Algorithm

Linear Discriminant Analysis (LDA) is a well-known and important tool in pattern recognition with potential applications in many areas of research. The most famous and used formulation of LDA is that given by the Fisher-Rao criterion, where the problem reduces to a simple simultaneous diagonalization of two symmetric, positive-definite matrices, A and B; i.e. B-1 AV = V. Here, A defines the metric to be maximized, while B defines the metric to be minimized. However, when B has near-zero eigenvalues, the Fisher-Rao criterion gets dominated by these. While this works well when such small variances describe vectors where most of the discriminant information is, the results will be incorrect when these small variances are caused by noise. Knowing which of these near-zero values are to be used and which need to be eliminated is a challenging yet fundamental task in LDA. This paper presents a criterion for the selection of those vectors of B that are best for classification. The proposed so...

• Type: Conference
• Year: 2006
• Where: CVPR
• Authors: Aleix M. Martínez, Manli Zhu
• Keywords: Computer Vision, CVPR 2006, Discriminant Ones, Fisher-rao Criterion, Linear Discriminant Analysis, Simple Simultaneous Diagonalization, Small Variances