This work introduces IsUMap, a novel manifold learning technique that enhances data
representation by integrating aspects of UMAP and Isomap with Vietoris-Rips filtrations. We …

In this survey, we provide an overview of category theory-derived machine learning from four
mainstream perspectives: gradient-based learning, probability-based learning, invariance …

The objective of this thesis is to show that studying the underlying compositional and
functorial structure in machine learning systems allows us to better understand them. In …

We draw some squares and apply some homology in the hope of classifying different flavors
of functors in a neat way. Our wishes are granted and we obtain homological measures of …

In this article, we expand upon the concepts introduced in\cite {Spivak09} about the
relationship between the category $\mathbf {UM} $ of uber metric spaces and the category …

Rolling bearing is a key component of rotating machinery, which affects the reliability of the
equipment. In order to make the equipment intelligent, facilitate the maintenance of the …

(A. 2) On the other hand, we use those theoretical clarifications to put the UMAP algorithm
developed by [MHM18], that heavily draws upon those category theoretical concepts, on a …