What is an ultrametric distance?

It is a distance metric satisfying the strong triangle inequality, where the distance between two points is always less than or equal to the maximum of their distances to a third point, rather than the sum.

Which programming languages are supported?

The skill provides implementation patterns and code examples for both Python and Julia, including sup-norm and p-adic valuation functions.

What is p-adic valuation in this context?

P-adic valuation is a method used to determine the highest power of a prime number that divides a difference between two integers, forming the basis for non-Archimedean metric spaces.

Can this skill analyze Git history?

Yes, it calculates the 'distance' between two commits based on the depth of their common ancestor, allowing for topological analysis of code evolution.

How is this used in hierarchical clustering?

It uses the UPGMA algorithm to build trees (dendrograms) where the distance between nodes represents a hierarchy, ensuring that all points within a cluster are equally distant from points outside the cluster.

Ultrametric Distance Metrics

Name: Ultrametric Distance Metrics
Author: plurigrid

byplurigrid

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Data Science & ML

Computes non-Archimedean distance metrics for hierarchical clustering, p-adic analysis, and version control ancestry.

About

The Ultrametric Distance skill implements specialized mathematical functions where the strong triangle inequality holds, providing a robust framework for analyzing hierarchical structures. By treating data points within a non-Archimedean space, this skill enables precise p-adic valuation, UPGMA (Unweighted Pair Group Method with Arithmetic Mean) clustering, and the calculation of evolutionary distances. It is an essential tool for developers and data scientists working with phylogenetic trees, topological data analysis, and complex branching version control systems where traditional Euclidean metrics are insufficient to describe nested relationships.

Key Features

Implementation of p-adic distance and valuation algorithms
Git commit ancestry distance calculation via merge-base depth
2 GitHub stars
Mapping of ultrametric distances to GF(3) trits for logical categorization
UPGMA hierarchical clustering for automated dendrogram generation
Ultrametric property verification for arbitrary distance functions

Use Cases

Performing number-theoretic computations and p-adic analysis in cryptography
Constructing phylogenetic trees in bioinformatics and evolutionary biology
Analyzing branching structures and ancestor proximity in large Git repositories

About

Key Features

Implementation of p-adic distance and valuation algorithms
Git commit ancestry distance calculation via merge-base depth
2 GitHub stars
Mapping of ultrametric distances to GF(3) trits for logical categorization
UPGMA hierarchical clustering for automated dendrogram generation
Ultrametric property verification for arbitrary distance functions

Use Cases

Performing number-theoretic computations and p-adic analysis in cryptography
Constructing phylogenetic trees in bioinformatics and evolutionary biology
Analyzing branching structures and ancestor proximity in large Git repositories