A new discriminant analysis for non-normally distributed data based on datawise formulation of scatter matrices

In this paper, we propose a new discrminant analysis based on datawise formulation of scatter matrices to deal with the data of non-normal distribution. Starting from original LDA, datawise formulation of scatter matrices is derived and its meaning is clarified. Based on this formulation, a new feature extraction algorithm is presented. In this formulation, assumption on distribution of data is no more necessary, so appropriate feature space can be found from the data whose distribution is non-normal, as well as multimodally normal. Limitation on the feature dimension also can be removed, and by replacing the inverse matrix of within-class scatter matrix with especially assigned weights, computational problems originating from matrix inversion of within-scatter matrix can be fundamentally avoided. As a result, good feature space for classification task can be found without the problems of LDA. Performance of this algorithm has been evaluated by using feature for real classification tasks.