Pattern Recognition with Gaussian Mixture Models of Marginal Distributions

Precise estimation of data distribution with a small number of sample patterns is an important and challenging problem in the field of statistical pattern recognition. In this paper, we propose a novel method for estimating multimodal data distribution based on the Gaussian mixture model. In the proposed method, multiple random vectors are generated after classifying the elements of the feature vector into subsets so that there is no correlation between any pair of subsets. The Gaussian mixture model for each subset is then constructed independently. As a result, the constructed model is represented as the product of the Gaussian mixture models of marginal distributions. To make the classification of the elements effective, a graph cut technique is used for rearranging the elements of the feature vectors to gather elements with a high correlation into the same subset. The proposed method is applied to a character recognition problem that requires high-dimensional feature vectors. Experiments with a public handwritten digit database show that the proposed method improves the accuracy of classification. In addition, the effect of classifying the elements of the feature vectors is shown by visualizing the distribution. key words: pattern recognition, Gaussian mixture model, graph cut, small sample size problem, character recognition