Banana Trees for the Persistence in Time Series Experimentally

TL;DR

This paper explores the banana tree data structure for efficiently maintaining persistent homology in dynamic time series data, demonstrating its effectiveness and potential practical utility through experimental evaluation.

Contribution

We implement and experimentally evaluate banana trees, showing they outperform static algorithms for dynamic persistent homology computation in certain scenarios.

Findings

Banana trees outperform static algorithms with unbiased random data.

Real-world time series share properties with unbiased random walks.

Banana trees are effective for dynamic topological data analysis.

Abstract

In numerous fields, dynamic time series data require continuous updates, necessitating efficient data processing techniques for accurate analysis. This paper examines the banana tree data structure, specifically designed to efficiently maintain persistent homology -- a multi-scale topological descriptor -- for dynamically changing time series data. We implement this data structure and conduct an experimental study to assess its properties and runtime for update operations. Our findings indicate that banana trees are highly effective with unbiased random data, outperforming state-of-the-art static algorithms in these scenarios. Additionally, our results show that real-world time series share structural properties with unbiased random walks, suggesting potential practical utility for our implementation.