Penalized Discriminant Analysis

fisher's linear discriminant analysis (LDA) is a popular data- analytic tool for studying the relationship between a set of predictors and a categorical response. In this paper we describe a penalized version of LDA which has applications in two different. scenarios. The first scenario occurs when there are many highly correlated predictors, such as those obtained by discretizing a function, or the greyscale values of the pixels in a series of images. In cases such as these it is natural and efficient to impose a spatial smoothness constraint on the coefficients, both for improved prediction performance and interpretability.