Feature weighting for data analysis via evolutionary simulation

TL;DR

This paper presents an evolutionary algorithm for feature weighting in multi-objective data analysis, proving convergence to a unique set of optimal feature relevance weights.

Contribution

It introduces a replicator dynamic-based algorithm for feature weighting and provides a proof of its global convergence to a unique equilibrium.

Findings

The algorithm evolves feature weights based on data relevance.

Convergence to a unique interior equilibrium is proven.

The method ensures non-degenerate limiting weights.

Abstract

We analyze an algorithm for assigning weights prior to scalarization in discrete multi-objective problems arising from data analysis. The algorithm evolves weights (interpreted as the relevance of features) by a replicator-type dynamic on the standard simplex, with update indices computed from a normalized data matrix. We prove that the resulting sequence converges globally to a unique interior equilibrium, yielding non-degenerate limiting weights.