F-transform and Dimensionality Reduction: Common and Different

Abstract

This contribution is focused on the connection between two theories: Dimensionality reduction and the F-transform. We show how the graph Laplacian can be extracted from a fuzzy partition and how the Laplacian eigenmaps can be associated with the F-transform components in their functional forms. We analyse the spectrum of the graph Laplacian and its dependence on basic functions in a fuzzy partition. We support our theoretical results by numerical experiments.