Classification of Stochastic Processes with Topological Data Analysis

TL;DR

This paper demonstrates that topological data analysis features improve the classification of time series from different stochastic processes compared to traditional statistical features.

Contribution

It introduces the use of engineered topological features for classifying stochastic processes and shows their superiority over statistical and raw features.

Findings

Topological features outperform statistical features in classification accuracy.

Engineered topological features are effective across balanced and unbalanced sampling.

Machine learning models using topological features show consistent performance improvements.

Abstract

In this study, we examine if engineered topological features can distinguish time series sampled from different stochastic processes with different noise characteristics, in both balanced and unbalanced sampling schemes. We compare our classification results against the results of the same classification tasks built on statistical and raw features. We conclude that in classification tasks of time series, different machine learning models built on engineered topological features perform consistently better than those built on standard statistical and raw features.