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Erschienen in:
2013 | OriginalPaper | Buchkapitel
4. Linear Discriminant Analysis
verfasst von : Petros Xanthopoulos, Panos M. Pardalos, Theodore B. Trafalis
Erschienen in: Robust Data Mining
Verlag: Springer New York
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Abstract
In this chapter we discuss another popular data mining algorithm that can be used for supervised or unsupervised learning. Linear Discriminant Analysis (LDA) was proposed by R. Fischer in 1936. It consists in finding the projection hyperplane that minimizes the interclass variance and maximizes the distance between the projected means of the classes. Similarly to PCA, these two objectives can be solved by solving an eigenvalue problem with the corresponding eigenvector defining the hyperplane of interest. This hyperplane can be used for classification, dimensionality reduction and for interpretation of the importance of the given features. In the first part of the chapter we discuss the generic formulation of LDA whereas in the second we present the robust counterpart scheme originally proposed by Kim and Boyd. We also discuss the non linear extension of LDA through the kernel transformation.