A weighted angle distance on strings

TL;DR

This paper introduces a multi-scale string metric based on angle distances, providing theoretical properties, efficient algorithms, and benchmarking against existing methods.

Contribution

It proposes a novel weighted angle distance metric on strings, with proven properties, efficient computation, and empirical benchmarking against standard baselines.

Findings

The metric is robust under tandem-repeat stutters.

The proposed algorithm runs in linear time using suffix trees.

Benchmark results show competitive performance against edit and n-gram baselines.

Abstract

We define a multi-scale metric $d_\rho$ on strings by aggregating angle distances between all $n$-gram count vectors with exponential weights $\rho^n$. We benchmark $d_\rho$ in DBSCAN clustering against edit and $n$-gram baselines, give a linear-time suffix-tree algorithm for evaluation, prove metric and stability properties (including robustness under tandem-repeat stutters), and characterize isometries.