On $p$-adic Classification

TL;DR

This paper introduces a $p$-adic adaptation of the split-LBG classification method that computes clusterings and centers minimizing an energy function, with results largely independent of the prime $p$, and applies it to $p$-adic learning classifiers.

Contribution

It presents a novel $p$-adic version of the split-LBG classification method, extending clustering techniques into the $p$-adic setting with independence from the prime $p$ for fixed datasets.

Findings

Outcome is independent of prime $p$ for fixed datasets

Method effectively constructs $p$-adic classifiers

Applicable to learning contexts

Abstract

A $p$-adic modification of the split-LBG classification method is presented in which first clusterings and then cluster centers are computed which locally minimise an energy function. The outcome for a fixed dataset is independent of the prime number $p$ with finitely many exceptions. The methods are applied to the construction of $p$-adic classifiers in the context of learning.