Deterministic Bridge Regression for Compressive Classification

TL;DR

This paper introduces a deterministic bridge regression method for compressive classification, providing analytic solutions suitable for different data dimensions and validating its effectiveness through numerical experiments.

Contribution

It proposes an analytic bridge solution for compressive classification using an approximated $ ext{ell}_p$-norm, applicable to both over- and under-determined systems.

Findings

Effective in simulated data

Validated on real-world data

Suitable for high and low-dimensional problems

Abstract

Pattern classification with compact representation is an important component in machine intelligence. In this work, an analytic bridge solution is proposed for compressive classification. The proposal has been based upon solving a penalized error formulation utilizing an approximated $\ell_p$-norm. The solution comes in a primal form for over-determined systems and in a dual form for under-determined systems. While the primal form is suitable for problems of low dimension with large data samples, the dual form is suitable for problems of high dimension but with a small number of data samples. The solution has also been extended for problems with multiple classification outputs. Numerical studies based on simulated and real-world data validated the effectiveness of the proposed solution.