Multi-Scale Analysis of Spatial Clustering Methods for Tissue Domains with Persistent Homology

PerryBeamer

North Carolina State University

"Multi-Scale Analysis of Spatial Clustering Methods for Tissue Domains with Persistent Homology"

Spatial gene-expression data can be clustered to segment a tissue into distinct spatial domains representing tissue structure. Though clustering algorithms are limited to a single fixed scale (by choice of a resolution hyperparameter k), we develop new methods from topological data analysis to analyze patterns in clusters across multiple scales. Zero-dimensional persistent homology analyzes the connectivity of data by tracking changes in homology groups across a filtered simplicial complex. We build a new filtration scheme to analyze similarity between clusters generated from multiple choices of scale parameter k, where persistent components represent clusters which exist across scales. We apply these results to select optimal scale parameters for spatial gene-expression clustering. These results have potential clinical application in tumor identification, where the size and scale of cancerous domains within healthy tissue is not known a priori.
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