Graphical lasso quadratic discriminant function and its application to character recognition

Multivariate Gaussian distribution is a popular assumption in many pattern recognition tasks. The quadratic discriminant function (QDF) is an effective classification approach based on this assumption. An improved algorithm, called modified QDF (or MQDF in short) has achieved great success and is widely recognized as the state-of-the-art method in character recognition. However, because both of the two approaches estimate the mean and covariance by the maximum-likelihood estimation (MLE), they often lead to the loss of the classification accuracy when the number of the training samples is small. To attack this problem, in this paper, we engage the graphical lasso method to estimate the covariance and propose a new classification method called the graphical lasso quadratic discriminant function (GLQDF). By exploiting a coordinate descent procedure for the lasso, GLQDF can estimate the covariance matrix (and its inverse) more precisely. Experimental results demonstrate that the proposed method can perform better than the competitive methods on two artificial and nine real datasets (including both benchmark digit and Chinese character data).