# Persistent Homology of Coarse Grained State Space Networks

arXiv: https://arxiv.org/abs/2206.02530 · HTML: https://mlsanity.com/paper/2206.02530/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 75 references that are in the map.
- First posted on arXiv 20 May 2022.

## Builds on (most cited first, 14 of 14)

- [A roadmap for the computation of persistent homology](https://mlsanity.com/paper/1506.08903/) (2015)
- [Persistent Homology of Complex Networks for Dynamic State Detection](https://mlsanity.com/paper/1904.07403/) (2019)
- [A persistent homology approach to heart rate variability analysis with an application to sleep-wake classification](https://mlsanity.com/paper/1908.06856/) (2019)
- [Using Zigzag Persistent Homology to Detect Hopf Bifurcations in Dynamical Systems](https://mlsanity.com/paper/2009.08972/) (2020)
- [Novel Features for Time Series Analysis: A Complex Networks Approach](https://mlsanity.com/paper/2110.09888/) (2021)
- [Enhanced Hierarchical Music Structure Annotations via Feature Level Similarity Fusion](https://mlsanity.com/paper/1902.01023/) (2019)
- [Topological Feature Vectors for Chatter Detection in Turning Processes](https://mlsanity.com/paper/1905.08671/) (2019)
- [On Transfer Learning of Traditional Frequency and Time Domain Features in Turning](https://mlsanity.com/paper/2008.12691/) (2020)
- [On Transfer Learning For Chatter Detection in Turning Using Wavelet Packet Transform and Empirical Mode Decomposition](https://mlsanity.com/paper/1905.01982/) (2019)
- [Data-driven and Automatic Surface Texture Analysis Using Persistent Homology](https://mlsanity.com/paper/2110.10005/) (2021)
- [Stable Topological Summaries for Analyzing the Organization of Cells in a Packed Tissue](https://mlsanity.com/paper/1902.06467/) (2019)
- [Chatter Detection in Turning Using Machine Learning and Similarity Measures of Time Series via Dynamic Time Warping](https://mlsanity.com/paper/1908.01678/) (2019)
- [Adaptive Partitioning for Template Functions on Persistence Diagrams](https://mlsanity.com/paper/1910.08506/) (2019)
- [Topological Signal Processing using the Weighted Ordinal Partition Network](https://mlsanity.com/paper/2205.08349/) (2022)

## Built on by (most cited first, 2 of 2)

- [Persistent Homology for High-dimensional Data Based on Spectral Methods](https://mlsanity.com/paper/2311.03087/) (2023)
- [Persistent Homology of Time Series through Complex Networks](https://mlsanity.com/paper/2605.01624/) (2026)

## Abstract (arXiv)

This work is dedicated to the topological analysis of complex transitional networks for dynamic state detection. Transitional networks are formed from time series data and they leverage graph theory tools to reveal information about the underlying dynamic system. However, traditional tools can fail to summarize the complex topology present in such graphs. In this work, we leverage persistent homology from topological data analysis to study the structure of these networks. We contrast dynamic state detection from time series using a coarse-grained state-space network (CGSSN) and topological data analysis (TDA) to two state of the art approaches: ordinal partition networks (OPNs) combined with TDA and the standard application of persistent homology to the time-delay embedding of the signal. We show that the CGSSN captures rich information about the dynamic state of the underlying dynamical system as evidenced by a significant improvement in dynamic state detection and noise robustness in comparison to OPNs. We also show that because the computational time of CGSSN is not linearly dependent on the signal's length, it is more computationally efficient than applying TDA to the time-delay embedding of the time series.