$p$-adic Bi-Filtrations for Topological Machine Learning on Genomic Sequences
We introduce pVR, a topological machine learning framework for alignment-free genomic sequence classification that combines $p$-adic numbers with topological data analysis. Each DNA sequence is encoded along two complementary axes: a $p$-adic distance on $k$-mer prefixes, which captures hierarchical positional structure, and a compositional $L_1$ distance on $k$-mer frequencies, which captures local sequence content. The two distances jointly parameterise a bi-filtered Vietoris--Rips complex, and per-sequence topological summaries from this bi-filtration serve as features for standard machine learning classifiers. We establish theoretical guarantees for the construction: stability under m...
| Authors | Tirtharaj Dash, Gunja Sachdeva |
|---|---|
| Primary category | q-bio.QM |
| Published | 4 June 2026 |
| Last updated at source | 4 June 2026 |
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