$p$-ClustVal: A Novel $p$-Adic Approach for Enhanced Clustering of High-Dimensional scRNASeq Data (Extended Abstract)

This paper introduces <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$p$</tex>-ClustVal, a novel data transformation technique inspired by p-adic number theory that significantly enhances cluster discernibility in genomics data, specifically Single Cell RNA Sequencing (scRNASeq). By lever-aging p-adic-valuation, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$p$</tex>-ClustVal integrates with and augments widely used clustering algorithms and dimension reduction techniques, amplifying their effectiveness in discovering meaningful structure from data. The transformation uses a data-centric heuristic to determine optimal parameters, without relying on ground truth labels, making it more user-friendly. <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$p$</tex>-ClustVal reduces overlap between clusters by employing alternate metric spaces inspired by p-adic-valuation, a significant shift from conventional methods. Our comprehensive evaluation spanning 30 experiments and over 1200 observations, shows that <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$p$</tex>-ClustVal improves performance in 91% of cases, and boosts the performance of classical and state of the art (SOTA) methods. This work contributes to data analytics and genomics by introducing a unique data transformation approach, enhancing downstream clustering algorithms, and providing empirical evidence of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$p$</tex>-ClustVal's efficacy.