Sequents, barcodes, and homology

TL;DR

This paper introduces sequent barcodes, a new topological data analysis tool inspired by logic, demonstrating their stability and application in cancer genomics data analysis.

Contribution

It presents a novel notion of sequent barcodes, establishing their stability and linking them to persistent homology, with practical application in genomics.

Findings

Sequent barcodes are stable under data perturbations.

They can be interpreted via persistent homology of specific filtrations.

Application demonstrated in cancer genomics discovery tasks.

Abstract

We consider the problem of generating hypothesis from data based on ideas from logic. We introduce a notion of barcodes, which we call sequent barcodes, that mirrors the barcodes in persistent homology theory in topological data analysis. We prove a theoretical result on the stability of these barcodes in analogy with similar results in persistent homology theory. Additionally we show that our new notion of barcodes can be interpreted in terms of a persistent homology of a particular filtration of topological spaces induced by the data. Finally, we discuss a concrete application of the sequent barcodes in a discovery problem arising from the area of cancer genomics.