A logifold structure on measure space

TL;DR

This paper introduces a novel measure-theoretic framework using network models as local charts to analyze datasets, aiming to uncover fuzzy domains and enhance classification accuracy.

Contribution

It develops the mathematical foundations for a logifold structure on measure spaces and demonstrates its practical utility in data analysis and classification.

Findings

Effective identification of fuzzy domains in datasets

Improved accuracy in data classification tasks

Mathematical foundation for measure-theoretic dataset analysis

Abstract

In this paper,we develop a local-to-global and measure-theoretical approach to understand datasets. The idea is to take network models with restricted domains as local charts of datasets. We develop the mathematical foundations for these structures, and show in experiments how it can be used to find fuzzy domains and to improve accuracy in data classification problems.