A study of regularized Gaussian classifier in high-dimension small sample set case based on MDL principle with application to spectrum recognition

In classifying high-dimensional patterns such as stellar spectra by a Gaussian classifier, the covariance matrix estimated with a small-number sample set becomes unstable, leading to degraded classification accuracy. In this paper, we investigate the covariance matrix estimation problem for small-number samples with high dimension setting based on minimum description length (MDL) principle. A new covariance matrix estimator is developed, and a formula for fast estimation of regularization parameters is derived. Experiments on spectrum pattern recognition are conducted to investigate the classification accuracy with the developed covariance matrix estimator. Higher classification accuracy results are obtained and demonstrated in our new approach.