Recipes for sparse LDA of horizontal data

Nickolay T. Trendafilov () and Tsegay Gebrehiwot Gebru ()
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Nickolay T. Trendafilov: The Open University
Tsegay Gebrehiwot Gebru: The Open University

METRON, 2016, vol. 74, issue 2, No 6, 207-221

Abstract: Abstract Many important modern applications require analyzing data with more variables than observations, called for short horizontal. In such situation the classical Fisher’s linear discriminant analysis (LDA) does not possess solution because the within-group scatter matrix is singular. Moreover, the number of the variables is usually huge and the classical type of solutions (discriminant functions) are difficult to interpret as they involve all available variables. Nowadays, the aim is to develop fast and reliable algorithms for sparse LDA of horizontal data. The resulting discriminant functions depend on very few original variables, which facilitates their interpretation. The main theoretical and numerical challenge is how to cope with the singularity of the within-group scatter matrix. This work aims at classifying the existing approaches according to the way they tackle this singularity issue, and suggest new ones.

Keywords: Diagonal within-group scatter; Function constrained LDA; Minimization of classification error; Common and proportional principal components (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s40300-016-0093-8

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