$p$-adic Principal Component Analysis

TL;DR

This paper introduces a $p$-adic optimization framework for matrix factorization and explores a heuristic method similar to principal component analysis, extending PCA concepts into the $p$-adic domain.

Contribution

It formulates a novel $p$-adic matrix factorization problem and proposes a heuristic approach analogous to PCA, bridging $p$-adic analysis and data reduction techniques.

Findings

Proposed a $p$-adic PCA-like heuristic method.

Demonstrated the feasibility of $p$-adic matrix factorization.

Extended PCA concepts into the $p$-adic setting.

Abstract

We formulate a $p$-adic optimisation problem on matrix factorisation, and investigate a heuristic method for it analogous to PCA.