Publications

Extended persistence is a technique from topological data analysis to obtain global multiscale topological information from a graph. This includes information about connected components and cycles that are captured by the so-called persistence barcodes. We introduce extended persistence into a supervised learning framework for graph classification. Global topological information, in the form of a barcode with four different types of bars and their explicit cycle representatives, is combined into the model by the readout function which is computed by extended persistence. The entire model is end-to-end differentiable

Denoising noisy datasets is a crucial task in this data-driven world. In this paper, we develop a persistence-guided discrete Morse …

Identifying differences between cytometry data seen as a point cloud can be complicated by random variations in data collection and data sources. We apply persistent homology used in topological data analysis to describe the shape and structure of the data representing immune cells in healthy donors and COVID-19 patients. By looking at how the shape and structure differ between healthy donors and COVID-19 patients, we are able to definitively conclude how these groups differ despite random variations in the data. Furthermore, these results are novel in their ability to capture shape and structure of cytometry data, something not described by other analyses.

We show that the representative cycles we compute have an unsupervised inclination towards phenotype labels. This work thus shows that topological signatures are able to comprehend gene expression levels and classify cohorts accordingly.