Mathematics Seminar 04/1/22

Abstract:  This talk introduces a novel classification method, called the membership score machine (MSM), for highly nonlinear classification, which is particularly applicable for highly irregular/non-globular datasets of arbitrarily many classes. Given an irregular training dataset, the method utilizes within-class clustering and dimensionality reduction to extract useful geometric features, for each of classes. For data points in a class, the method first performs clustering and then apply the principal component analysis (PCA) for each cluster to form an reliable geometric representation in lower dimensions. The goal in the training stage is to draw out reliable geometric features and related anisotropic measures, one for each cluster. At the prediction stage, it calculates the membership scores based on the anisotropic measures with respect to each of the clusters; a test data point is classified for the class which contains the cluster that makes the maximum membership score. The proposed algorithm, the MSM, turns out to be more effective than existing algorithms in accuracy, especially for small and highly irregular datasets. The main idea behind the MSM is to represent the dataset geometrically by expressing it as a combination of multiple easy-to-classify clusters transformed into principal components in low dimensions. Numerical experiments are presented and compared with existing popular classifiers, to demonstrate its superior performances.