A Neurodynamical System for finding a Minimal VC Dimension Classifier

Abstract: The recently proposed Minimal Complexity Machine (MCM) finds a hyperplane classifier by minimizing an exact bound on the Vapnik-Chervonenkis (VC) dimension. The VC dimension measures the capacity of a learning machine, and a smaller VC dimension leads to improved generalization. On many benchmark datasets, the MCM generalizes better than SVMs and uses far fewer support vectors than the number used by SVMs. In this paper, we describe a neural network based on a linear dynamical system, that converges to the MCM solution. The proposed MCM dynamical system is conducive to an analogue circuit implementation on a chip or simulation using Ordinary Differential Equation (ODE) solvers. Numerical experiments on benchmark datasets from the UCI repository show that the proposed approach is scalable and accurate, as we obtain improved accuracies and fewer number of support vectors (upto 74.3% reduction) with the MCM dynamical system.