Thresholding method for dimensionality reduction in recognition systems

Often recognition systems must be designed with a relatively small amount of training data. Plug-in test statistics suffer from large estimation errors, often causing the performance to degrade as the measurement vector dimension increases. Choosing a better test statistic or applying a method of dimensionality reduction are two possible solutions to this problem. In this paper, we consider a recognition problem where the data for each population are assumed to have the same parametric distribution but differ 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 (ML) 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 define a thresholding function that, when incorporated into the plug-in log-likelihood ratio, significantly decreases the probability of error for binary and multiple hypothesis testing problems for the exponential class of populations. We analyze the modified test statistic and present the results of Monte Carlo simulation. Special attention is paid to the complex Gaussian model with zero mean and unknown variances.