Journal of Applied Mathematics and Decision Sciences
Volume 2005 (2005), Issue 3, Pages 165-175

A new approach to multiple class pattern classification with random matrices

Dong Q. Wang and Mengjie Zhang

School of Mathematics, Statistics, and Computer Science, Victoria University of Wellington, Wellington 6001, New Zealand

Received 8 April 2003; Revised 2 December 2003

Copyright © 2005 Dong Q. Wang and Mengjie Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We describe a new approach to multiple class pattern classification problems with noise and high dimensional feature space. The approach uses a random matrix X which has a specified distribution with mean M and covariance matrix rij(Σs+Σε) between any two columns of X. When Σε is known, the maximum likelihood estimators of the expectation M, correlation Γ, and covariance Σs can be obtained. The patterns with high dimensional features and noise are then classified by a modified discriminant function according to the maximum likelihood estimation results. This new method is compared with a multilayer feed forward neural network approach on nine digit recognition tasks of increasing difficulty. Both methods achieved good results for those classification tasks, but the new approach was more effective and more efficient than the neural network method for difficult problems.