The DOI matches its Crossref record; 27 of the 27 references it cites were found in a registry or an index.
Stochastic Gradient Descent on Riemannian Manifolds
Open accessAbstract
Stochastic gradient descent is a simple approach to find the local minima of a cost function whose evaluations are corrupted by noise. In this paper, we develop a procedure extending stochastic gradient descent algorithms to the case where the function is defined on a Riemannian manifold. We prove that, as in the Euclidian case, the gradient descent algorithm converges to a critical point of the cost function. The algorithm has numerous potential applications, and is illustrated here by four examples. In particular a novel gossip algorithm on the set of covariance matrices is derived and tested numerically.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The cited source says what the claim attributes to it.
In the citing paper
“We also compute an analytic closed-form expression for the exponential map in the n -dimensional Poincar´ e ball, allowing us to perform full Riemannian optimization (Bonnabel, 2013) in the Poincar´ e ball, as opposed to the approximate optimization method used by (Nickel & Kiela, 2017).”
From Hyperbolic Entailment Cones for Learning Hierarchical Embeddings (2018) · cites this paper as Bonnabel, 2013
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
A Stochastic Approximation Method
Robbins, H., & Monro, S. (1951) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177729586 · Cited by 9,643
The Geometry of Algorithms with Orthogonality Constraints
Edelman, A. S., Arias, T. A., & Smith, S. T. (1998) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/s0895479895290954 · Cited by 2,741
Stability of multiagent systems with time-dependent communication links
Moreau, L. (2005) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2004.841888 · Cited by 2,667
Boyd, S., Ghosh, A., Prabhakar, B., & Shah, D. (2006) · IEEE Transactions on Information Theory · doi:10.1109/tit.2006.874516 · Cited by 2,439
Distributed asynchronous deterministic and stochastic gradient optimization algorithms
Tsitsiklis, J., Bertsekas, D., & Athans, M. (1986) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1986.1104412 · Cited by 1,967
Faraut, J., & Korányi, A. (1994) · doi:10.1093/oso/9780198534778.001.0001 · Cited by 1,659
A Riemannian Framework for Tensor Computing
Pennec, X., Fillard, P., & Ayache, N. (2005) · International Journal of Computer Vision · doi:10.1007/s11263-005-3222-z · Cited by 1,553
Analysis of recursive stochastic algorithms
Ljung, L. (1977) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1977.1101561 · Cited by 1,485
Principal components, minor components, and linear neural networks
Oja, E. (1992) · Neural Networks · doi:10.1016/s0893-6080(05)80089-9 · Cited by 826
Candès, E. J., & Plan, Y. (2011) · IEEE Transactions on Information Theory · doi:10.1109/tit.2011.2111771 · Cited by 602
Research works printed but not linked: 10
- tsuda, 2005, Matrix exponentiated gradient updates for online learning and Bregman projection, J Mach Learn Res, 36, 995
- higham, 1989, Matrix Nearness Problems and Applications
- o'neill, 1983, Semi-Riemaniann Geometry
- amari, 1998, Natural Gradient Works Efficiently in Learning
- barbaresco, 2008, Innovative tools for radar signal processing based on Cartan's geometry of symmetric positive-definite matrices and information geometry, Proc IEEE Radar Conf RADAR'08, 1
- bonnabel, 2011, Convergence des m�thodes de gradient stochastique sur les vari�t�s riemanniennes, Proc XIII i�me Colloque GRETSI Bordeaux
- bottou, 1998, Online Algorithms and Stochastic Approximations
- absil, 2007, Optimization Algorithms on Matrix Manifolds
- meyer, 2011, Geometric optimization algorithms for linear regression on fixed-rank matrices
- oja, 1983, Subspace Methods of Pattern Recognition
Cited by
Sorted by citations
Items 201–300 of 536
On the Local Linear Rate of Consensus on the Stiefel Manifold
Chen, S., Garcia, A., Hong, M., & Shahrampour, S. (2023) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2023.3330735 · Cited by 11
Probabilistic PCA From Heteroscedastic Signals: Geometric Framework and Application to Clustering
Collas, A., Bouchard, F., Breloy, A., Ginolhac, G., Ren, C., & Ovarlez, J. (2021) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2021.3130997 · Cited by 11
Mei, Z., & Yin, Z. (2022) · IEEE Geoscience and Remote Sensing Letters · doi:10.1109/lgrs.2022.3168722 · Cited by 11
Hyperbolic Personalized Tag Recommendation
Zhao, W., Zhang, A., Shang, L., Yu, Y., Li, Z., Wang, C., Chen, J., & Yin, H. (2022) · Lecture notes in computer science · doi:10.1007/978-3-031-00126-0_14 · Cited by 11
Statistics on the space of trajectories for longitudinal data analysis
Chakraborty, R., Banerjee, M., & Vemuri, B. C. (2017) · IEEE International Symposium on Biomedical Imaging (ISBI) · doi:10.1109/isbi.2017.7950684 · Cited by 11
Solis, C. U., Clempner, J. B., & Poznyak, A. S. (2018) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.4408 · Cited by 11
Accelerated Levenberg–Marquardt Algorithm for Radial Basis Function Neural Network
Ma, M.-L., Wu, X., & Honggui, H. (2020) · Chinese Automation Congress · doi:10.1109/cac51589.2020.9327740 · Cited by 11
Embedding Heterogeneous Information Network in Hyperbolic Spaces
Zhang, Y., Wang, X. S., Liu, N., & Shi, C. (2021) · ACM Transactions on Knowledge Discovery from Data · doi:10.1145/3468674 · Cited by 11
Riemannian stochastic variance reduced gradient on Grassmann manifoldPreprint
Kasai, H., Sato, H., & Mishra, B. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1605.07367 · Cited by 11
Computationally Tractable Riemannian Manifolds for Graph Embeddings
Cruceru, C., Bécigneul, G., & Ganea, O.-E. (2021) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v35i8.16877 · Cited by 10
Fast, Asymptotically Efficient, Recursive Estimation in a Riemannian Manifold
Zhou, J., & Said, S. (2019) · Entropy · doi:10.3390/e21101021 · Cited by 10
Riemannian Stochastic Recursive Momentum Method for non-Convex Optimization
Han, A., & Gao, J. (2021) · International Joint Conference on Artificial Intelligence · doi:10.24963/ijcai.2021/345 · Cited by 12
Liao, X., Chen, C., Liu, W., Zhou, P., Zhu, H., Shen, S., Wang, W., Hu, M., Tan, Y., & Zheng, X. (2023) · ACM International Conference on Multimedia (ACM MM) · doi:10.1145/3581783.3612178 · Cited by 10
Stochastic Primal-Dual Method on Riemannian Manifolds of Bounded Sectional Curvature
Khuzani, M. B., & Li, N. (2017) · International Conference on Machine Learning and Applications · doi:10.1109/icmla.2017.0-167 · Cited by 10
Cascade Residual Capsule Network for Hyperspectral Image Classification
Mei, Z., Yin, Z., Kong, X., Wang, L., & Ren, H. (2022) · IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing · doi:10.1109/jstars.2022.3166972 · Cited by 10
Interpretable domain adaptation via optimization over the Stiefel manifold
Pölitz, C., Duivesteijn, W., & Morik, K. J. (2016) · Machine Learning · doi:10.1007/s10994-016-5577-5 · Cited by 10
Fast stochastic optimization on Riemannian manifolds.Preprint
Zhang, H., Reddi, S. J., & Sra, S. (2016) · arXiv (Cornell University) · Cited by 10
Statistics on the (compact) Stiefel manifold: Theory and ApplicationsPreprint
Chakraborty, R., & Vemuri, B. C. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1708.00045 · Cited by 10
The Extended Kalman Filter is a Natural Gradient Descent in Trajectory SpacePreprint
Ollivier, Y. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1901.00696 · Cited by 21
Nonsmooth Optimization over Stiefel Manifold: Riemannian Subgradient Methods.Preprint
Li, X., Chen, S., Deng, Z., Qu, Q., Zhu, Z., & So, A. M. (2019) · arXiv (Cornell University) · Cited by 10
Relative gradient optimization of the Jacobian term in unsupervised deep learningPreprint
Gresele, L., Fissore, G., Javaloy, A., Schölkopf, B., & Hyvärinen, A. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2006.15090 · Cited by 11
On Riemannian Optimization over Positive Definite Matrices with the Bures-Wasserstein GeometryPreprint
Han, A., Mishra, B., Jawanpuria, P., & Gao, J. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2106.00286 · Cited by 10
A Riemannian approach to large-scale constrained least-squares with symmetries
Mishra, B. (2014) · ORBi (University of Liège) · Cited by 10
Deep hyperbolic convolutional model for knowledge graph embedding
Lu, M., Li, Y., Zhang, J., Ren, H., & Zhang, X. (2024) · Knowledge-Based Systems · doi:10.1016/j.knosys.2024.112183 · Cited by 10
Deep metric learning in projected-hypersphere space
Xu, Y., Chen, Z., & Hu, J. (2024) · Pattern Recognition · doi:10.1016/j.patcog.2024.111245 · Cited by 9
Scalable Container-Based Time Synchronization for Smart Grid Data Center Networks
Okafor, K. C., Okafor, W. O., Longe, O. M., Ayogu, I. I., Anoh, K., & Adebisi, B. (2025) · Technologies · doi:10.3390/technologies13030105 · Cited by 9
Noise Adaptive Kalman Filtering With Stochastic Natural Gradient Variational Inference
Lan, H., Zhao, S., Mao, Y., Wang, Z., Cheng, Q., & Liu, Z. (2025) · IEEE Transactions on Aerospace and Electronic Systems · doi:10.1109/taes.2025.3559523 · Cited by 9
Ancestor Search: Generalized Open Set Recognition via Hyperbolic Side Information Learning
Dengxiong, X., & Kong, Y. (2023) · IEEE Winter Conference on Applications of Computer Vision · doi:10.1109/wacv56688.2023.00399 · Cited by 9
Multimodal Deep Fusion in Hyperbolic Space for Mild Cognitive Impairment Study
Zhang, L., Na, S., Liu, T., Zhu, D., & Huang, J. (2023) · Lecture notes in computer science · doi:10.1007/978-3-031-43904-9_65 · Cited by 9
Li, X., Andrei, V. C., Mönich, U. J., & Boche, H. (2023) · Globecom · doi:10.1109/globecom54140.2023.10437293 · Cited by 9
A stochastic algorithm finding $p$-means on the circle
Arnaudon, M., & Miclo, L. (2016) · Bernoulli · doi:10.3150/15-bej728 · Cited by 9
Riemannian L p Averaging on Lie Group of Nonzero Quaternions
Angulo, J. (2013) · Advances in Applied Clifford Algebras · doi:10.1007/s00006-013-0432-2 · Cited by 9
Xing, L., Ma, Q., Gao, J., & Chen, S. (2018) · IEEE Access · doi:10.1109/access.2018.2822839 · Cited by 9
Recent Advances in Stochastic Riemannian Optimization
Hosseini, R., & Sra, S. (2020) · Springer eBooks · doi:10.1007/978-3-030-31351-7_19 · Cited by 9
Poincaré Embedding Reveals Edge-Based Functional Networks of the Brain
Gao, S., Mishne, G., & Scheinost, D. (2020) · Lecture notes in computer science · doi:10.1007/978-3-030-59728-3_44 · Cited by 9
A stochastic algorithm finding generalized means on compact manifolds
Arnaudon, M., & Miclo, L. (2014) · Stochastic Processes and their Applications · doi:10.1016/j.spa.2014.05.011 · Cited by 9
Riemannian Stochastic Proximal Gradient Methods for Nonsmooth Optimization over the Stiefel ManifoldPreprint
Wang, B., Ma, S., & Xue, L. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2005.01209 · Cited by 9
Hyperbolic Deep Neural Networks: A SurveyPreprint
Peng, W., Varanka, T., Mostafa, A., Shi, H., & Zhao, G. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2101.04562 · Cited by 9
Class Incremental Learning With Less Forgetting Direction and Equilibrium Point
Wen, H., Qiu, H., Wang, L., Cheng, H., & Li, H. (2024) · IEEE Transactions on Circuits and Systems for Video Technology · doi:10.1109/tcsvt.2024.3477951 · Cited by 10
Learning to Normalize on the SPD Manifold under Bures-Wasserstein Geometry
Wang, R., Jin, S.-H., Chen, Z., Luo, X., & Wu, X.-J. (2025) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr52734.2025.00776 · Cited by 8
Hybrid hyperplane gradient learning algorithm for RBF neural network
Ma, M.-L., Huang, Z., Liao, Y., Zhou, L., Jia, L., Liang, C., & Guo, Z. (2024) · Neurocomputing · doi:10.1016/j.neucom.2024.127626 · Cited by 8
Nasr, M. C. B., de Araujo-Filho, P. F., Kaddoum, G., & Mourad, A. (2024) · IEEE Internet of Things Journal · doi:10.1109/jiot.2024.3439440 · Cited by 9
HKF: Hierarchical Kalman Filtering With Online Learned Evolution Priors for Adaptive ECG Denoising
Revach, G., Locher, T., Shlezinger, N., van Sloun, R. J. G., & Vullings, R. (2024) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2024.3443875 · Cited by 12
Understanding and Mitigating Hyperbolic Dimensional Collapse in Graph Contrastive Learning
Zhang, Y., Zhu, H., Yang, M., Liu, J., Ying, R., King, I., & Koniusz, P. (2025) · ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD) · doi:10.1145/3690624.3709249 · Cited by 8
Tracking and Regret Bounds for Online Zeroth-Order Euclidean and Riemannian Optimization
Maass, A. I., Manzie, C. G., Nešić, D., Manton, J. H., & Shames, I. (2022) · SIAM Journal on Optimization · doi:10.1137/21m1405551 · Cited by 8
ROLE: Rotated Lorentzian Graph Embedding Model for Asymmetric Proximity
Feng, S., Chen, L., Zhao, K., Wei, W., Song, X., Shang, S., Kalnis, P., & Shao, L. (2022) · IEEE Transactions on Knowledge and Data Engineering · doi:10.1109/tkde.2022.3221929 · Cited by 8
Convergence Analysis of Gradient Descent for Eigenvector Computation
Xu, Z., Cao, X., & Gao, X. (2018) · International Joint Conference on Artificial Intelligence · doi:10.24963/ijcai.2018/407 · Cited by 8
Neural Architecture Search of SPD Manifold Networks
Sukthanker, R. S., Huang, Z., Kumar, S., Endsjo, E. G., Wu, Y. X., & Gool, L. V. (2021) · International Joint Conference on Artificial Intelligence · doi:10.24963/ijcai.2021/413 · Cited by 8
Deep Learning on Lie Groups for Skeleton-based Action RecognitionPreprint
Huang, Z., Wan, C., Probst, T., & Gool, L. V. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1612.05877 · Cited by 8
Interactive Teaching System for Remote Vocal Singing Based on Decision Tree Algorithm
Wang, X., & Liu, X. (2022) · Mathematical Problems in Engineering · doi:10.1155/2022/4957353 · Cited by 7
Zheng, P., Wu, W., Hu, J. Y., & Deng, K. (2023) · Applied Mathematics & Optimization · doi:10.1007/s00245-023-10061-x · Cited by 7
Low-Complexity Multi-Target Detection in ELAA ISAC
Galappaththige, D., Zargari, S., Tellambura, C., & Li, G. Y. (2025) · IEEE Communications Letters · doi:10.1109/lcomm.2025.3537457 · Cited by 7
Node2LV: Squared Lorentzian Representations for Node Proximity
Feng, S., Chen, L., Zhao, K., Wei, W., Li, F., & Shang, S. (2021) · IEEE International Conference on Data Engineering (ICDE) · doi:10.1109/icde51399.2021.00193 · Cited by 7
The Fisher–Rao Geometry of CES Distributions
Bouchard, F., Breloy, A., Collas, A., Renaux, A., & Ginolhac, G. (2024) · Springer eBooks · doi:10.1007/978-3-031-52116-4_2 · Cited by 7
Riemannian Natural Gradient Methods
Hu, J. J., Ao, R., So, A. M., Yang, M., & Wen, Z. (2024) · SIAM Journal on Scientific Computing · doi:10.1137/22m1509643 · Cited by 7
Chen, Y., Zhu, L., Gao, Z., Li, W., & Wu, J. (2024) · Structural Health Monitoring · doi:10.1177/14759217241243111 · Cited by 7
Coordinate Descent on the Orthogonal Group for Recurrent Neural Network Training
Massart, E. M., & Abrol, V. (2022) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v36i7.20742 · Cited by 7
Lu, M., Liu, Y., Li, H., Tan, D., He, X., Bi, W., & Li, W. (2019) · Symmetry · doi:10.3390/sym11020254 · Cited by 7
A Coordinate-Free Construction of Scalable Natural GradientPreprint
Luk, K., & Grosse, R. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1808.10340 · Cited by 7
RIS-Enabled SCLAM: An Approach for Simultaneous Radio Communication, Localization, and Mapping
Zhao, J., Bai, Z., Guo, S., Ma, D., Li, N., & Kwak, K. S. (2025) · IEEE Internet of Things Journal · doi:10.1109/jiot.2025.3526688 · Cited by 6
Random pairwise gossip on CAT(0) metric spaces
Bellachehab, A., & Jakubowicz, J. (2014) · IEEE Conference on Decision and Control (CDC) · doi:10.1109/cdc.2014.7040264 · Cited by 6
Lorentz equivariant model for knowledge-enhanced hyperbolic collaborative filtering
Huang, B., Yu, W., Xie, R., Luo, J., Xiao, J., & Huang, J. (2024) · Knowledge-Based Systems · doi:10.1016/j.knosys.2024.111590 · Cited by 6
Knowledge graph completion model based on hyperbolic hierarchical attention network
Luo, J.-H., & Song, C. (2024) · International Journal of Machine Learning and Cybernetics · doi:10.1007/s13042-024-02126-2 · Cited by 6
Effective Phoneme Decoding With Hyperbolic Neural Networks for High-Performance Speech BCIs
Tan, X., Lian, Q., Zhu, J., Zhang, J., Wang, Y., & Qi, Y. (2024) · IEEE Transactions on Neural Systems and Rehabilitation Engineering · doi:10.1109/tnsre.2024.3457313 · Cited by 6
On Truly Block Eigensolvers via Riemannian Optimization
Xu, Z., & Gao, X. (2018) · King Abdullah University of Science and Technology Repository (King Abdullah University of Science and Technology) · Cited by 6
Zeroth-order Optimization on Riemannian Manifolds
Li, J., Balasubramanian, K., & Ma, S. (2020) · Cited by 5
An Interface between Grassmann manifolds and vector spaces
de Souza, L. S., Sogi, N., Gatto, B. B., Kobayashi, T., & Fukui, K. (2020) · IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW) · doi:10.1109/cvprw50498.2020.00431 · Cited by 6
A Survey of Graph Curvature and Embedding in Non-Euclidean Spaces
Saxena, C., Liu, T., & King, I. (2020) · Lecture notes in computer science · doi:10.1007/978-3-030-63833-7_11 · Cited by 6
Cao, X. (2023) · Pattern Recognition · doi:10.1016/j.patcog.2023.109302 · Cited by 6
Analyzing animal escape data with circular nonparametric multimodal regression
Alonso‐Pena, M., & Crujeiras, R. M. (2023) · The Annals of Applied Statistics · doi:10.1214/22-aoas1619 · Cited by 6
Hyperbolic Mutual Learning for Bundle Recommendation
Ke, H., Li, L., Wang, P., Yuan, J., & Tao, X. (2023) · Lecture notes in computer science · doi:10.1007/978-3-031-30672-3_28 · Cited by 6
Zhang, C., Zhang, A., Li, Z., Yu, Y., Zhao, W., & Geng, H. (2023) · IEEE Access · doi:10.1109/access.2023.3347249 · Cited by 6
Representation of Multirelations of Geographic Scenes Based on Hyperbolic Space
Cui, W., Xu, X., Chen, J., Feng, Z., Zhao, H., Hao, Y., Tian, Y., Wang, J., & Xia, C. (2024) · IEEE Transactions on Geoscience and Remote Sensing · doi:10.1109/tgrs.2024.3407843 · Cited by 6
MASAGA: A Linearly-Convergent Stochastic First-Order Method for Optimization on Manifolds
Babanezhad, R., Laradji, I., Shafaei, A., & Schmidt, M. (2019) · Lecture notes in computer science · doi:10.1007/978-3-030-10928-8_21 · Cited by 5
Prerequisite Relation Learning for Course Concepts Based on Hyperbolic Deep Representation
Liu, L., Lin, F., Wang, B., Li, K., Xiao, M., Xiahou, J., & Wu, P. (2020) · IEEE Access · doi:10.1109/access.2020.2979555 · Cited by 6
Manifold Optimization-Assisted Gaussian Variational Approximation
Zhong, B., Gao, J., Tran, M., & Gerlach, R. (2021) · Journal of Computational and Graphical Statistics · doi:10.1080/10618600.2021.1923516 · Cited by 6
Online Change Point Detection on Riemannian Manifolds with Karcher Mean Estimates
Wang, X., Borsoi, R. A., & Richard, C. (2023) · European Signal Processing Conference (EUSIPCO) · doi:10.23919/eusipco58844.2023.10289744 · Cited by 6
Training CNNs With Normalized Kernels
Özay, M., & Okatani, T. (2018) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v32i1.11624 · Cited by 7
From Node Embedding To Community Embedding : A Hyperbolic ApproachPreprint
Gerald, T., Zaatiti, H., Hajri, H., Baskiotis, N., & Schwander, O. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1907.01662 · Cited by 6
Symmetric Spaces for Graph Embeddings: A Finsler-Riemannian ApproachPreprint
López, F., Pozzetti, B., Trettel, S., Strube, M., & Wienhard, A. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2106.04941 · Cited by 6
Fine-Grained Entity Typing in Hyperbolic Space
López, F., Heinzerling, B., & Strube, M. (2019) · Workshop on Representation Learning for NLP (RepL4NLP) · doi:10.18653/v1/w19-4319 · Cited by 32
Adaptive curvature exploration geometric graph neural network
Fu, X., Li, J., Wu, J. X., Qin, J., Sun, Q., Ji, C., Wang, S., Peng, H. M., & Yu, P. S. (2023) · Knowledge and Information Systems · doi:10.1007/s10115-022-01811-4 · Cited by 7
Sundriyal, M., Singh, P., Akhtar, M. S., Sengupta, S., & Chakraborty, T. (2021) · ACM International Conference on Information and Knowledge Management (CIKM) · doi:10.1145/3459637.3482423 · Cited by 8
Efficient Riemannian Meta-Optimization by Implicit Differentiation
Fan, X., Wu, Y., Gao, Z. F., Jia, Y., & Harandi, M. T. (2022) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v36i4.20287 · Cited by 5
Adaptive filter with Riemannian manifold constraint
Mejia, J. M., Mederos, B., Gordillo, N., & Ortega, L. (2023) · Scientific Reports · doi:10.1038/s41598-023-36127-y · Cited by 5
A Universal Framework for Learning the Elliptical Mixture Model
Li, S., Yu, Z., & Mandic, D. P. (2020) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2020.3010198 · Cited by 5
Some Limit Properties of Markov Chains Induced by Recursive Stochastic Algorithms
Gupta, A., Chen, H., Pi, J., & Tendolkar, G. (2020) · SIAM Journal on Mathematics of Data Science · doi:10.1137/19m1258104 · Cited by 5
Multi-task Learning with Riemannian Optimization
Cai, T., Song, L., Li, G., & Liao, M. (2021) · Lecture notes in computer science · doi:10.1007/978-3-030-84529-2_42 · Cited by 5
Network Consensus in the Wasserstein Metric Space of Probability Measures
Bishop, A. N., & Arnaud Doucet, B. (2021) · SIAM Journal on Control and Optimization · doi:10.1137/19m1268252 · Cited by 5
Cohen, K., Nedić, A., & Srikant, R. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1606.03000 · Cited by 5
Distributed Optimization on Riemannian Manifolds for multi-agent networksPreprint
Shah, S. M. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1711.11196 · Cited by 5
Directed Graph Embeddings in Pseudo-Riemannian ManifoldsPreprint
Sim, A., Wiatrak, M., Brayne, A., Creed, P., & Paliwal, S. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2106.08678 · Cited by 5
Multi-Prototype Hyperbolic Learning Guided by Class Hierarchy
Berg, P., Buecher, L., Michele, B., Pham, M., Chapel, L., & Courty, N. (2025) · International Journal of Computer Vision · doi:10.1007/s11263-025-02571-8 · Cited by 6
Prediction of the Behaviour from Discharge Points for Solid Waste Management
Moratilla, S. D. L. M., Martínez, J. M. G., Castillo-Martínez, A., & Caro‐Álvaro, S. (2024) · Machine Learning and Knowledge Extraction · doi:10.3390/make6030066 · Cited by 5
Hyperbolic Self-Paced Multi-Expert Network for Cross-Domain Few-Shot Facial Expression Recognition
Chen, X., Yan, Y., Xue, J., Shu, C., & Wang, H. (2025) · IEEE Transactions on Image Processing · doi:10.1109/tip.2025.3612281 · Cited by 4
Solis, C. U., Clempner, J. B., & Poznyak, A. S. (2019) · International Journal of Control · doi:10.1080/00207179.2019.1662940 · Cited by 4
Hole Inpainting Algorithm for Half-Organized Point Cloud Obtained by Structured-Light Section System
Cui, B., Shao, Z., Tao, W., & Zhao, H. Z. (2022) · IEEE Transactions on Multimedia · doi:10.1109/tmm.2022.3233254 · Cited by 4
Kojima, T., Arikawa, K., Koyama, S., & Saruwatari, H. (2023) · European Signal Processing Conference (EUSIPCO) · doi:10.23919/eusipco58844.2023.10289919 · Cited by 4
Hyperbolic multichannel graph convolutional network for social recommendation
Yang, X., Chang, M., Yu, J., Wang, D., & Dang, Z. (2024) · Journal of Intelligent & Fuzzy Systems · doi:10.3233/jifs-235266 · Cited by 4
Matrix eigen-decomposition via doubly stochastic riemannian optimization
Xu, Z., Zhao, P., Cao, J., & Li, X. (2016) · International Conference on Machine Learning · Cited by 4
Metadata
- Authors
- Bonnabel, S.
- Affiliations
- Centre de Robotique (FR)
- Corresponding author
- Bonnabel, Silvere
- Venue
- IEEE Transactions on Automatic Control
- Published
- 2013-09
- Volume
- 58
- Issue
- 9
- Pages
- 2217-2229
- ISSN
- 0018-9286 (ISSN-L)
- 1558-2523
- OpenAlex
- W2138674039
- Cited by
- 540
- References
- 27
- Citations by year
- 2026: 33 · 2025: 52 · 2024: 56 · 2023: 51 · 2022: 52 · 2021: 80 · 2020: 64 · 2019: 53 · 2018: 26 · 2017: 24 · 2016: 22 · 2015: 12 · 2014: 8 · 2013: 4
- FWCI
- 16.96
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- IEEE Transactions on Automatic Control (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Stochastic Gradient Optimization Techniques
- Physical Sciences › Engineering › Control and Systems Engineering › Distributed Control Multi-Agent Systems
- Physical Sciences › Mathematics › Numerical Analysis › Advanced Optimization Algorithms Research
- Keywords
- stochastic gradient descent, Riemannian manifolds, gossip algorithms, covariance matrix, distributed optimization, Riemannian optimization
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
