<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The Linear Discriminant Analysis (LDA) technique is an important and well-developed area of classification, and to date many linear (and also nonlinear) discrimination methods have been put forward. A complication in applying LDA to real data occurs when the number of features exceeds that of observations. In this case, the covariance estimates do not have full rank, and thus cannot be inverted. There are a number of ways to deal with this problem. In this paper, we propose improving LDA in this area, and we present a new approach which uses a generalization of the Moore-Penrose pseudoinverse to remove this weakness. Our new approach, in addition to managing the problem of inverting the covariance matrix, significantly improves the quality of classification, also on data sets where we can invert the covariance matrix. Experimental results on various data sets demonstrate that our improvements to LDA are efficient and our approach outperforms LDA.</p></abstract>

The Linear Discriminant Analysis (LDA) technique is an important and well-developed area of classification, and to date many linear (and also nonlinear) discrimination methods have been put forward. A complication in applying LDA to real data occurs when the number of features exceeds that of observations. In this case, the covariance estimates do not have full rank, and thus cannot be inverted. There are a number of ways to deal with this problem. In this paper, we propose improving LDA in this area, and we present a new approach which uses a generalization of the Moore-Penrose pseudoinverse to remove this weakness. Our new approach, in addition to managing the problem of inverting the covariance matrix, significantly improves the quality of classification, also on data sets where we can invert the covariance matrix. Experimental results on various data sets demonstrate that our improvements to LDA are efficient and our approach outperforms LDA.

Linear discriminant analysis with a generalization of the Moore–Penrose pseudoinverse

Faculty of Mathematics and Computer Science Adam Mickiewicz University, Umultowska 87, 61-614 Pozna´n, Poland

Faculty of Civil Engineering, Environmental and Geodetic Sciences Koszalin University of Technology, ´Sniadeckich 2, 75-453 Koszalin, Poland

International Journal of Applied Mathematics and Computer Science

The Linear Discriminant Analysis (LDA) technique is an important and well-developed area of classification, and to date many linear (and also nonlinear)...

Linear discriminant analysis with a generalization of the Moore–Penrose pseudoinverse

Published Online: Jun 28, 2013

Page range: 463 - 471

DOI: https://doi.org/10.2478/amcs-2013-0035

This content is open access.