Banana Trees for the Persistence in Time Series Experimentally
<|reference_start|>Banana Trees for the Persistence in Time Series Experimentally: 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.<|reference_end|>
@article{ost2024banana,
    title={Banana Trees for the Persistence in Time Series Experimentally},
    author={Lara Ost and Sebastiano Cultrera di Montesano and Herbert Edelsbrunner},
    journal={arXiv preprint arXiv:2405.17920},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.17920},
    primaryClass={cs.DS}
}