Faster Binary Mean Computation Under Dynamic Time Warping

TL;DR

This paper introduces faster algorithms for computing binary means under dynamic time warping, improving efficiency and demonstrating practical effectiveness through experiments, while exploring special cases and properties of solutions.

Contribution

It presents improved algorithms for binary mean computation under dynamic time warping, including linear-time solutions for specific cases and empirical analysis of solution properties.

Findings

Significantly improved worst-case running time algorithms.

Practical algorithms validated on real-world and synthetic data.

Identification of special cases solvable in linear time.

Abstract

Many consensus string problems are based on Hamming distance. We replace Hamming distance by the more flexible (e.g., easily coping with different input string lengths) dynamic time warping distance, best known from applications in time series mining. Doing so, we study the problem of finding a mean string that minimizes the sum of (squared) dynamic time warping distances to a given set of input strings. While this problem is known to be NP-hard (even for strings over a three-element alphabet), we address the binary alphabet case which is known to be polynomial-time solvable. We significantly improve on a previously known algorithm in terms of worst-case running time. Moreover, we also show the practical usefulness of one of our algorithms in experiments with real-world and synthetic data. Finally, we identify special cases solvable in linear time (e.g., finding a mean of only two binary input strings) and report some empirical findings concerning combinatorial properties of optimal means.