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Measuring LDA Performance Affected by Normal and Skew-Normal Distributions Using the Normwise Condition Number

H. Saberi Najafi, A. Zeinal

Abstract


Linear Discriminant Analysis (LDA) provides a mapping to a space of reduced dimensionality in which discrimination is usually easier. For evaluating LDA performance, different measures have been presented. In this paper, we have presented a new measure which evaluates the accuracy of linear transformations in LDA. Noticing that these linear trasformations are eigenvectors of a generalized eigenvalue problem, we have found out that the condition number of these eigenvectors should provide us with some information about LDA performance. Using simulation and regression for normal and skew-normal data, we have shown that normwise condition number along with Apparent Error Rate (APER) can evaluate LDA performance. We have found out that standard coefficient this new measure is more than that of “APER”, the common measure for evaluating LDA, for both normal and skew-normal data. Furthermore, this difference for skew-normal data is more than that for normal data. We have also found the factors affecting this measure for normal and skew-normal data.

Keywords


Apparent Error Rate; Eigenvalue Problem; Factorial Design; Regression; Simulation.

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