Feature weighting for data analysis via evolutionary simulation

2025-11-09

AI Summary

This paper addresses the challenge of feature weight assignment in discrete multi-objective data analysis. We propose a dynamic feature weighting method grounded in evolutionary game theory, modeling feature weights as population states on the standard simplex and employing analytically tractable replicator dynamics to iteratively evolve weights over a normalized data matrix. We rigorously prove global convergence to a unique non-degenerate interior equilibrium, thereby eliminating the weight collapse commonly observed in conventional approaches. Our key contribution is the first application of an evolutionary game-theoretic framework to feature weighting—yielding a method that guarantees theoretical convergence, offers intuitive interpretability, and ensures numerical stability. This establishes a novel paradigm for multi-objective feature selection, bridging rigorous mathematical foundations with practical applicability.

Technology Category

• Machine Learning: Evolutionary Learning
• Search and Optimization: Evolutionary Computation
• Game Theory and Economic Paradigms: Cooperative Game Theory

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

We analyze an algorithm for assigning weights prior to scalarization in discrete multi-objective problems arising from data analysis. The algorithm evolves the weights (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. The method, originally inspired by evolutionary game theory, differs from standard weighting schemes in that it is analytically tractable with provable convergence.

Problem

• Develops evolutionary algorithm for feature weighting in multi-objective data analysis
• Proves global convergence to unique interior equilibrium with non-degenerate weights
• Provides analytically tractable alternative to standard feature weighting schemes

Innovation

• Evolutionary simulation evolves feature weights dynamically
• Replicator dynamics ensure convergence to interior equilibrium
• Method provides analytically tractable weighting with provable convergence