Logifold: A Geometrical Foundation of Ensemble Machine Learning

TL;DR

This paper introduces logifolds, a geometric and measure-theoretic framework for understanding datasets and ensemble models, leading to improved accuracy by identifying fuzzy domains and providing a mathematical foundation for ensemble learning.

Contribution

It develops the concept of logifolds as a new geometric foundation for ensemble machine learning, connecting local models to dataset structure.

Findings

Logifolds can identify fuzzy domains within datasets.

Implementing logifolds improves ensemble accuracy.

Theoretical example highlights the importance of domain restrictions.

Abstract

We present a local-to-global and measure-theoretical approach to understanding datasets. The core idea is to formulate a logifold structure and to interpret network models with restricted domains as local charts of datasets. In particular, this provides a mathematical foundation for ensemble machine learning. Our experiments demonstrate that logifolds can be implemented to identify fuzzy domains and improve accuracy compared to taking average of model outputs. Additionally, we provide a theoretical example of a logifold, highlighting the importance of restricting to domains of classifiers in an ensemble.