# Quasi Zigzag Persistence: A Topological Framework for Analyzing Time-Varying Data

arXiv: https://arxiv.org/abs/2502.16049 · HTML: https://mlsanity.com/paper/2502.16049/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 70 references that are in the map.
- First posted on arXiv 22 Feb 2025.

## Builds on (most cited first, 30 of 43)

- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Improving Graph Neural Network Expressivity via Subgraph Isomorphism Counting](https://mlsanity.com/paper/2006.09252/) (2020)
- [Spatio-temporal Self-Supervised Representation Learning for 3D Point Clouds](https://mlsanity.com/paper/2109.00179/) (2021)
- [DeepSleepNet: a Model for Automatic Sleep Stage Scoring based on Raw Single-Channel EEG](https://mlsanity.com/paper/1703.04046/) (2017)
- [PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures](https://mlsanity.com/paper/1904.09378/) (2019)
- [Multivariate LSTM-FCNs for Time Series Classification](https://mlsanity.com/paper/1801.04503/) (2018)
- [MeteorNet: Deep Learning on Dynamic 3D Point Cloud Sequences](https://mlsanity.com/paper/1910.09165/) (2019)
- [TransMOT: Spatial-Temporal Graph Transformer for Multiple Object Tracking](https://mlsanity.com/paper/2104.00194/) (2021)
- [SeqSleepNet: End-to-End Hierarchical Recurrent Neural Network for Sequence-to-Sequence Automatic Sleep Staging](https://mlsanity.com/paper/1809.10932/) (2018)
- [Topological Graph Neural Networks](https://mlsanity.com/paper/2102.07835/) (2021)
- [A Topology Layer for Machine Learning](https://mlsanity.com/paper/1905.12200/) (2019)
- [Graph Filtration Learning](https://mlsanity.com/paper/1905.10996/) (2019)
- [PSTNet: Point Spatio-Temporal Convolution on Point Cloud Sequences](https://mlsanity.com/paper/2205.13713/) (2022)
- [Z-GCNETs: Time Zigzags at Graph Convolutional Networks for Time Series Forecasting](https://mlsanity.com/paper/2105.04100/) (2021)
- [A Topological Regularizer for Classifiers via Persistent Homology](https://mlsanity.com/paper/1806.10714/) (2018)
- [A deep learning architecture for temporal sleep stage classification using multivariate and multimodal time series](https://mlsanity.com/paper/1707.03321/) (2017)
- [Multivariate Time Series Classification with WEASEL+MUSE](https://mlsanity.com/paper/1711.11343/) (2017)
- [CaSPR: Learning Canonical Spatiotemporal Point Cloud Representations](https://mlsanity.com/paper/2008.02792/) (2020)
- [Omni-Scale CNNs: a simple and effective kernel size configuration for time series classification](https://mlsanity.com/paper/2002.10061/) (2020)
- [Multi-View Spatial-Temporal Graph Convolutional Networks with Domain Generalization for Sleep Stage Classification](https://mlsanity.com/paper/2109.01824/) (2021)
- [FC-GAGA: Fully Connected Gated Graph Architecture for Spatio-Temporal Traffic Forecasting](https://mlsanity.com/paper/2007.15531/) (2020)
- [Sign Language Translation with Hierarchical Spatio-TemporalGraph Neural Network](https://mlsanity.com/paper/2111.07258/) (2021)
- [Mixed Neural Network Approach for Temporal Sleep Stage Classification](https://mlsanity.com/paper/1610.06421/) (2016)
- [Interactive Visualization of 2-D Persistence Modules](https://mlsanity.com/paper/1512.00180/) (2015)
- [Topological Optimization with Big Steps](https://mlsanity.com/paper/2203.16748/) (2022)
- [TodyNet: Temporal Dynamic Graph Neural Network for Multivariate Time Series Classification](https://mlsanity.com/paper/2304.05078/) (2023)
- [Stable Vectorization of Multiparameter Persistent Homology using Signed Barcodes as Measures](https://mlsanity.com/paper/2306.03801/) (2023)
- [A Kernel for Multi-Parameter Persistent Homology](https://mlsanity.com/paper/1809.10231/) (2018)
- [Euler Characteristic Tools For Topological Data Analysis](https://mlsanity.com/paper/2303.14040/) (2023)

## Built on by (most cited first, 1 of 1)

- [A differentiability framework for zigzag persistent homology via linear interpolation](https://mlsanity.com/paper/2609.39242/) (2026)

## Abstract (arXiv)

In this paper, we propose Quasi Zigzag Persistent Homology (QZPH) as a framework for analyzing time-varying data by integrating multiparameter persistence and zigzag persistence. To this end, we introduce a stable topological invariant that captures both static and dynamic features at different scales. We present an algorithm to compute this invariant efficiently. We show that it enhances the machine learning models when applied to tasks such as sleep-stage detection, demonstrating its effectiveness in capturing the evolving patterns in time-varying datasets.