TOTOPO: Classifying univariate and multivariate time series with Topological Data Analysis

TL;DR

TOTOPO introduces a topological data analysis method for classifying univariate and multivariate time series, outperforming many existing methods and demonstrating robustness to data perturbations.

Contribution

The paper presents TOTOPO, a novel approach that extracts topological descriptors for time series classification, addressing previous limitations in benchmarking and state-of-the-art comparisons.

Findings

TOTOPO significantly outperforms existing baselines in accuracy.

It is the best method on 20% of univariate and 40% of multivariate datasets.

TDA-based approaches are robust to small data perturbations and effective for shape-based discrimination.

Abstract

This work is devoted to a comprehensive analysis of topological data analysis fortime series classification. Previous works have significant shortcomings, such aslack of large-scale benchmarking or missing state-of-the-art methods. In this work,we propose TOTOPO for extracting topological descriptors from different types ofpersistence diagrams. The results suggest that TOTOPO significantly outperformsexisting baselines in terms of accuracy. TOTOPO is also competitive with thestate-of-the-art, being the best on 20% of univariate and 40% of multivariate timeseries datasets. This work validates the hypothesis that TDA-based approaches arerobust to small perturbations in data and are useful for cases where periodicity andshape help discriminate between classes.