Thresholding Method for Reduction of Dimensionality

Often recognition systems must be designed with a relatively small amount of training data. Plug-in test statistics suuer from large estimation errors, often causing the performance to degrade with increasing size of the measurement vector. Choosing a better test statistic or applying a method of dimensionality reduction are two possible solutions to the problem above. In this paper we consider a recognition problem where the data for each population are assumed to have the same parametric distribution but diier in their unknown parameters. The collected vectors of data as well as their components are assumed to be independent. The system is designed to implement a plug-in log-likelihood ratio test with maximum likelihood estimates of the unknown parameters instead of the true parameters. Because a small amount of data is available to estimate the parameters, the performance of such a system is strongly degraded relative to the performance with known parameters. To improve the performance of the system we deene a thresholding function that, when incorporated into the plug-in log-likelihood ratio, signiicantly decreases the probability of error for binary and multiple hypothesis testing problems for the exponential class of populations. We analyze the modiied test statistic and present the results of Monte-Carlo simulation. Special attention is paid to complex Gaussian model with zero mean and unknown variances.