Title:
Fast Linear Discriminant Analysis using QR Decomposition and Regularization
Fast Linear Discriminant Analysis using QR Decomposition and Regularization
Author(s)
Park, Haesun
Drake, Barry L.
Lee, Sangmin
Park, Cheong Hee
Drake, Barry L.
Lee, Sangmin
Park, Cheong Hee
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Abstract
Linear Discriminant Analysis (LDA) is among the most optimal dimension reduction methods for
classification, which provides a high degree of class separability for numerous applications from science
and engineering. However, problems arise with this classical method when one or both of the scatter
matrices is singular. Singular scatter matrices are not unusual in many applications, especially for high-dimensional
data. For high-dimensional undersampled and oversampled problems, the classical LDA
requires modification in order to solve a wider range of problems. In recent work the generalized singular
value decomposition (GSVD) has been shown to mitigate the issue of singular scatter matrices, and a new
algorithm, LDA/GSVD, has been shown to be very robust for many applications in machine learning.
However, the GSVD inherently has a considerable computational overhead. In this paper, we propose fast
algorithms based on the QR decomposition and regularization that solve the LDA/GSVD computational
bottleneck. In addition, we present fast algorithms for classical LDA and regularized LDA utilizing
the framework based on LDA/GSVD and preprocessing by the Cholesky decomposition. Experimental
results are presented that demonstrate substantial speedup in all of classical LDA, regularized LDA, and
LDA/GSVD algorithms without any sacrifice in classification performance for a wide range of machine
learning applications.
Sponsor
The work of the first
three authors was supported in part by the National Science Foundation grants ACI-0305543 and CCF-0621889. Any opinions,
findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect
the views of the National Science Foundation.
Date Issued
2007-03-23
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Technical Report