Classification of continuous distributional data using the logratio approach

Abstract

One of the fundamental tasks in statistics is to classify observations into one of predefined classes, whether the observations are of multivariate or functional character. When considering distributional data, suitable classification methods honouring the data specificities are yet to be developed. In this work, a classification method for distributional data represented as probability density functions (PDFs) is proposed. The method uses the centred log-ratio (clr) transformation to adapt functional linear discriminant analysis to the distributional setting. Within the proposed setting, each functional observation is projected into a reduced discriminant space, and the classification itself is then based on minimizing the distance between the linear projections of the class representatives and those of the functional observations. The introduced method is demonstrated on geological data consisting of particle size distribution of 250 soil samples from four measuring sites in Moravia region, Czech Republic.