Mathematics Seminar - 11/04/26

Abstract: This paper introduces the ellipsoidal confidence membership score machine (EC-MSM), an advanced improvement of the membership score machine (MSM) designed for nonlinear classification of small, highly irregular datasets. The original MSM utilizes within-class clustering and principal component analysis (PCA) to capture the geometric features of the dataset, offering a robust classification through anisotropic distance measures. EC-MSM extends MSM by incorporating two novel enhancements: (1) an ellipsoidal discriminant adjustment to improve geometric representation within each class, and (2) a confidence absorption layer formulation to capture complex feature hierarchies effectively. These modifications aim to further reduce dimensionality while preserving the integrity of class-specific features, leading to improved performance in distinguishing non-globular data clusters. Numerical experiments demonstrate that EC-MSM achieves superior accuracy and generalization, particularly on highly nonlinear and challenging datasets, compared to the original MSM and other popular classifiers.