Fast optimization of Multithreshold Entropy Linear Classifier

TL;DR

This paper proposes methods to accelerate the optimization process of the Multithreshold Entropy Linear Classifier by using approximate solutions, adaptive parameter selection, and standard optimizers, validated on real datasets.

Contribution

It introduces approximate optimization techniques and adaptive schemes for MELC, enabling faster training while maintaining accuracy, and demonstrates their effectiveness on real-world data.

Findings

Significant speed-up in MELC optimization process.

Adaptive parameter selection improves efficiency.

Validated methods on 10 real datasets from UCI.

Abstract

Multithreshold Entropy Linear Classifier (MELC) is a density based model which searches for a linear projection maximizing the Cauchy-Schwarz Divergence of dataset kernel density estimation. Despite its good empirical results, one of its drawbacks is the optimization speed. In this paper we analyze how one can speed it up through solving an approximate problem. We analyze two methods, both similar to the approximate solutions of the Kernel Density Estimation querying and provide adaptive schemes for selecting a crucial parameters based on user-specified acceptable error. Furthermore we show how one can exploit well known conjugate gradients and L-BFGS optimizers despite the fact that the original optimization problem should be solved on the sphere. All above methods and modifications are tested on 10 real life datasets from UCI repository to confirm their practical usability.