This paper introduces \(p\) -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 leveraging \(p\) -adic-valuation, \(p\) -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. \(p\) -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 1400 observations shows that \(p\) -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 p-ClustVal’s efficacy. The study concludes with insights into the limitations of \(p\) -ClustVal and future research directions.
