mlsanityData to 7 Oct 2026

GeomNet: A Neural Network Based on Riemannian Geometries of SPD Matrix Space and Cholesky Space for 3D Skeleton-Based Interaction Recognition

arXiv 2111.13089 ↗First posted 25 Nov 2021cs.CV cs.LG stat.MLcited by 27

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Abstract (arXiv)

In this paper, we propose a novel method for representation and classification of two-person interactions from 3D skeleton sequences. The key idea of our approach is to use Gaussian distributions to capture statistics on R n and those on the space of symmetric positive definite (SPD) matrices. The main challenge is how to parametrize those distributions. Towards this end, we develop methods for embedding Gaussian distributions in matrix groups based on the theory of Lie groups and Riemannian symmetric spaces. Our method relies on the Riemannian geometry of the underlying manifolds and has the advantage of encoding high-order statistics from 3D joint positions. We show that the proposed method achieves competitive results in two-person interaction recognition on three benchmarks for 3D human activity understanding.

Key facts. Cited by 27 papers in the map (data through 7 Oct 2026). Builds on 24 of its 68 references that are in the map. First posted on arXiv 25 Nov 2021.

Builds on

24 of 68 references.

References · 24

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2018Spatial Temporal Graph Convolutional Networks for Skeleton-Based Action Recognitioncited by 1,199
  3. 2016NTU RGB+D: A Large Scale Dataset for 3D Human Activity Analysiscited by 683
  4. 2019NTU RGB+D 120: A Large-Scale Benchmark for 3D Human Activity Understandingcited by 530
  5. 2017A simple neural network module for relational reasoningcited by 345
  6. 2019Actional-Structural Graph Convolutional Networks for Skeleton-based Action Recognitioncited by 228
  7. 2018Riemannian Adaptive Optimization Methodscited by 187
  8. 2016A Riemannian Network for SPD Matrix Learningcited by 162
  9. 2019An Attention Enhanced Graph Convolutional LSTM Network for Skeleton-Based Action Recognitioncited by 151
  10. 2017A New Representation of Skeleton Sequences for 3D Action Recognitioncited by 125
  11. 2019Riemannian batch normalization for SPD neural networkscited by 72
  12. 2018geomstats: a Python Package for Riemannian Geometry in Machine Learningcited by 71
12 more
  1. 2016Co-occurrence Feature Learning for Skeleton based Action Recognition using Regularized Deep LSTM Networkscited by 63
  2. 2016Building Deep Networks on Grassmann Manifoldscited by 58
  3. 2017Skeleton-Based Action Recognition Using Spatio-Temporal LSTM Network with Trust Gatescited by 54
  4. 2017Modeling Temporal Dynamics and Spatial Configurations of Actions Using Two-Stream Recurrent Neural Networkscited by 48
  5. 2019A neural network based on SPD manifold learning for skeleton-based hand gesture recognitioncited by 46
  6. 2020A Survey on 3D Skeleton-Based Action Recognition Using Learning Methodcited by 46
  7. 2017Is Second-order Information Helpful for Large-scale Visual Recognition?cited by 44
  8. 2016Deep Learning on Lie Groups for Skeleton-based Action Recognitioncited by 42
  9. 2019Interaction Relational Network for Mutual Action Recognitioncited by 27
  10. 2018Parallel Transport on the Cone Manifold of SPD Matrices for Domain Adaptationcited by 20
  11. 2018Spatio-Temporal Graph Convolution for Skeleton Based Action Recognitioncited by 15
  12. 2017Statistics on the (compact) Stiefel manifold: Theory and Applicationscited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 4; 2023: 9; 2024: 5; 2025: 5; 2026: 3.

27 papers.

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  1. 2022Riemannian Local Mechanism for SPD Neural Networkscited by 22
  2. 2021COMPOSER: Compositional Reasoning of Group Activity in Videos with Keypoint-Only Modalitycited by 19
  3. 2023Building Neural Networks on Matrix Manifolds: A Gyrovector Space Approachcited by 18
  4. 2023Adaptive Log-Euclidean Metrics for SPD Matrix Learningcited by 13
  5. 2023SPD-DDPM: Denoising Diffusion Probabilistic Models in the Symmetric Positive Definite Spacecited by 13
  6. 2024Matrix Manifold Neural Networks++cited by 13
  7. 2023A numerical approximation method for the Fisher-Rao distance between multivariate normal distributionscited by 11
  8. 2023Riemannian Multinomial Logistics Regression for SPD Neural Networkscited by 11
  9. 2022ERA: Expert Retrieval and Assembly for Early Action Predictioncited by 9
  10. 2024Understanding Matrix Function Normalizations in Covariance Pooling through the Lens of Riemannian Geometrycited by 9
  11. 2024RMLR: Extending Multinomial Logistic Regression into General Geometriescited by 8
  12. 2022Two-person Graph Convolutional Network for Skeleton-based Human Interaction Recognitioncited by 7
15 more
  1. 2025Learning to Normalize on the SPD Manifold under Bures-Wasserstein Geometrycited by 7
  2. 2023Video-based Contrastive Learning on Decision Trees: from Action Recognition to Autism Diagnosiscited by 5
  3. 2025Wrapped Gaussian on the manifold of Symmetric Positive Definite Matricescited by 5
  4. 2026Neural Networks on Symmetric Spaces of Noncompact Typecited by 5
  5. 2024SMLNet: A SPD Manifold Learning Network for Infrared and Visible Image Fusioncited by 4
  6. 2022Efficient and Accurate Skeleton-Based Two-Person Interaction Recognition Using Inter- and Intra-body Graphscited by 2
  7. 2025DFNN: A Deep Fr'echet Neural Network Framework for Learning Metric-Space-Valued Responsescited by 2
  8. 2023Cross-view Action Recognition via Contrastive View-invariant Representationcited by 1
  9. 2023SkeleTR: Towrads Skeleton-based Action Recognition in the Wildcited by 1
  10. 2025Learning Adaptive Node Selection with External Attention for Human Interaction Recognitioncited by 1
  11. 2025Siegel Neural Networkscited by 1
  12. 2023Two-stream Multi-level Dynamic Point Transformer for Two-person Interaction Recognitioncited by 0
  13. 2024An Improved Graph Pooling Network for Skeleton-Based Action Recognitioncited by 0
  14. 2026E2E-GNet: An End-to-End Skeleton-based Geometric Deep Neural Network for Human Motion Recognitioncited by 0
  15. 2026ReManNet: A Riemannian Manifold Network for Monocular 3D Lane Detectioncited by 0