Quasi Zigzag Persistence: A Topological Framework for Analyzing Time-Varying Data
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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.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 43 of its 70 references that are in the map. First posted on arXiv 22 Feb 2025.
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43 of 70 references.
References · 43
- 2017Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecastingcited by 1,125
- 2020Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networkscited by 563
- 2020Improving Graph Neural Network Expressivity via Subgraph Isomorphism Countingcited by 312
- 2021Spatio-temporal Self-Supervised Representation Learning for 3D Point Cloudscited by 180
- 2017DeepSleepNet: a Model for Automatic Sleep Stage Scoring based on Raw Single-Channel EEGcited by 154
- 2019PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signaturescited by 125
- 2018Multivariate LSTM-FCNs for Time Series Classificationcited by 120
- 2019MeteorNet: Deep Learning on Dynamic 3D Point Cloud Sequencescited by 117
- 2021TransMOT: Spatial-Temporal Graph Transformer for Multiple Object Trackingcited by 93
- 2018SeqSleepNet: End-to-End Hierarchical Recurrent Neural Network for Sequence-to-Sequence Automatic Sleep Stagingcited by 90
- 2021Topological Graph Neural Networkscited by 86
- 2019A Topology Layer for Machine Learningcited by 79
31 more
- 2019Graph Filtration Learningcited by 68
- 2022PSTNet: Point Spatio-Temporal Convolution on Point Cloud Sequencescited by 68
- 2021Z-GCNETs: Time Zigzags at Graph Convolutional Networks for Time Series Forecastingcited by 67
- 2018A Topological Regularizer for Classifiers via Persistent Homologycited by 62
- 2017A deep learning architecture for temporal sleep stage classification using multivariate and multimodal time seriescited by 58
- 2017Multivariate Time Series Classification with WEASEL+MUSEcited by 53
- 2020CaSPR: Learning Canonical Spatiotemporal Point Cloud Representationscited by 51
- 2020Omni-Scale CNNs: a simple and effective kernel size configuration for time series classificationcited by 47
- 2021Multi-View Spatial-Temporal Graph Convolutional Networks with Domain Generalization for Sleep Stage Classificationcited by 37
- 2020FC-GAGA: Fully Connected Gated Graph Architecture for Spatio-Temporal Traffic Forecastingcited by 30
- 2021Sign Language Translation with Hierarchical Spatio-TemporalGraph Neural Networkcited by 26
- 2016Mixed Neural Network Approach for Temporal Sleep Stage Classificationcited by 23
- 2015Interactive Visualization of 2-D Persistence Modulescited by 18
- 2023TodyNet: Temporal Dynamic Graph Neural Network for Multivariate Time Series Classificationcited by 16
- 2022Topological Optimization with Big Stepscited by 15
- 2023Stable Vectorization of Multiparameter Persistent Homology using Signed Barcodes as Measurescited by 15
- 2023Euler Characteristic Tools For Topological Data Analysiscited by 13
- 2023GRIL: A 2-parameter Persistence Based Vectorization for Machine Learningcited by 13
- 2018A Kernel for Multi-Parameter Persistent Homologycited by 12
- 2022Temporal Network Analysis Using Zigzag Persistencecited by 9
- 2021Euler Characteristic Surfacescited by 8
- 2016Algebraic Stability of Zigzag Persistence Modulescited by 7
- 2018Generalized Persistence Diagrams for Persistence Modules over Posetscited by 6
- 2022Fast Computation of Zigzag Persistencecited by 6
- 2024Graphcode: Learning from multiparameter persistent homology using graph neural networkscited by 6
- 2024Differentiability and Optimization of Multiparameter Persistent Homologycited by 6
- 2024GEFL: Extended Filtration Learning for Graph Classificationcited by 5
- 2024D-GRIL: End-to-End Topological Learning with 2-parameter Persistencecited by 5
- 2021Computing Generalized Rank Invariant for 2-Parameter Persistence Modules via Zigzag Persistence and its Applicationscited by 4
- 2024Time-Aware Knowledge Representations of Dynamic Objects with Multidimensional Persistencecited by 2
- 2023ZigzagNetVis: Suggesting temporal resolutions for graph visualization using zigzag persistencecited by 1
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