Influence functions for a linear subspace method

A linear subspace method, which is one of discriminant methods, was proposed as a pattern recognition method and was studied. Because the method and its extensions do not encounter the situation of singular covariance matrix, we need not consider extensions such as generalized ridge discrimination, even when treating a high dimensional and sparse dataset. In addition, classifiers based on a multi-class discrimination method can function faster because of the simple decision procedure. Therefore, they have been widely used for face and speech recognition. However, it seems that sufficient studies have not been conducted about the statistical assessment of training data performance for classifier in terms of prediction accuracy. In statistics, influence functions for statistical discriminant analysis were derived and the assessments for analysis result were performed. These studies indicate that influence functions are useful for detecting large influential observations for analysis results by using discrimination methods and they contribute to enhancing the performance of a target classifier. In this paper, we propose the statistical diagnostics of a classifier on the basis of an influence function by using the linear subspace method. We first propose the discriminant score for the linear subspace method. Next, we derive the sample and empirical influence functions for the average of the discriminant scores to detect large influential observations for the misclassification rate. Finally, through a simulation study and a real data analysis, we detect the outliers in the training dataset using the derived influence function and develop a highly sophisticated classifier in the linear subspace method.