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Geometric Deep Learning: Going beyond Euclidean data
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Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains, such as graphs and manifolds. The purpose of this article is to overview different examples of geometric deep-learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field.
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Deep Residual Learning for Image Recognition
He, K., Zhang, X., Ren, S., & Sun, J. (2016) · 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr.2016.90 · Cited by 235,474
Very Deep Convolutional Networks for Large-Scale Image Recognition
Simonyan, K., & Zisserman, A. (2014) · arXiv · doi:10.48550/arxiv.1409.1556 · Cited by 114,148
ImageNet classification with deep convolutional neural networks
Krizhevsky, A., Sutskever, I., & Hinton, G. E. (2017) · Communications of the ACM · doi:10.1145/3065386 · Cited by 112,155
LeCun, Y., Bengio, Y., & Hinton, G. (2015) · Nature · doi:10.1038/nature14539 · Cited by 84,126
Self-citation(2008) · Journal of Machine Learning Research · Cited by 33,051
Efficient Estimation of Word Representations in Vector Space
Mikolov, T., Chen, K., Corrado, G., & Dean, J. (2013) · arXiv · doi:10.48550/arxiv.1301.3781 · Cited by 26,568
Semi-supervised classification with graph convolutional networks
Kipf, T. N., & Welling, M. (2016) · arXiv · doi:10.48550/arxiv.1609.02907 · Cited by 24,853
Distributed Representations of Words and Phrases and their Compositionality
Mikolov, T., Sutskever, I., Chen, K., Corrado, G., & Dean, J. (2013) · arXiv · doi:10.48550/arxiv.1310.4546 · Cited by 24,533
Sequence to Sequence Learning with Neural Networks
Sutskever, I., Vinyals, O., & Le, Q. V. (2014) · arXiv · doi:10.48550/arxiv.1409.3215 · Cited by 17,766
A Wavelet Tour of Signal Processing
Mallat, S. (1999) · Elsevier eBooks · doi:10.1016/b978-0-12-466606-1.x5000-4 · Cited by 16,329
Nonlinear Dimensionality Reduction by Locally Linear Embedding
Roweis, S. T., & Saul, L. K. (2000) · Science · doi:10.1126/science.290.5500.2323 · Cited by 14,965
A Global Geometric Framework for Nonlinear Dimensionality Reduction
Tenenbaum, J. B., Silva, V. D., & Langford, J. C. (2000) · Science · doi:10.1126/science.290.5500.2319 · Cited by 13,585
Backpropagation Applied to Handwritten Zip Code Recognition
LeCun, Y., Boser, B., Denker, J. S., Henderson, D., Howard, R. E., Hubbard, W., & Jackel, L. D. (1989) · Neural Computation · doi:10.1162/neco.1989.1.4.541 · Cited by 11,891
Self-citationFortunato, S. (2010) · Physics Reports · doi:10.1016/j.physrep.2009.11.002 · Cited by 11,293
Matrix Factorization Techniques for Recommender Systems
Koren, Y., Bell, R. M., & Volinsky, C. (2009) · Computer · doi:10.1109/mc.2009.263 · Cited by 11,232
A tutorial on spectral clustering
Ulrike Von Luxburg, A. (2007) · Statistics and Computing · doi:10.1007/s11222-007-9033-z · Cited by 10,787
Hinton, G., Deng, L., Yu, D., Dahl, G., Mohamed, A.-R., Jaitly, N., Senior, A., Vanhoucke, V., Nguyen, P., Sainath, T., et al. (2012) · IEEE Signal Processing Magazine · doi:10.1109/msp.2012.2205597 · Cited by 10,260
DeepWalk: online learning of social representations
Perozzi, B., Al-Rfou, R., & Skiena, S. (2014) · Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining · doi:10.1145/2623330.2623732 · Cited by 10,123
Object Detection with Discriminatively Trained Part-Based Models
Felzenszwalb, P. F., Girshick, R. B., McAllester, D., & Ramanan, D. (2010) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2009.167 · Cited by 9,853
The graph neural network model
Scarselli, F., Gori, M., Tsoi, A. C., Hagenbuchner, M., & Monfardini, G. (2009) · IEEE Transactions on Neural Networks · doi:10.1109/tnn.2008.2005605 · Cited by 9,582
Extended-Connectivity Fingerprints
Rogers, D. O. W., & Hahn, M. (2010) · Journal of Chemical Information and Modeling · doi:10.1021/ci100050t · Cited by 7,925
Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
Belkin, M., & Niyogi, P. (2003) · Neural Computation · doi:10.1162/089976603321780317 · Cited by 7,562
Network motifs: simple building blocks of complex networks.
Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D., & Alon, U. (2002) · Science · doi:10.1126/science.298.5594.824 · Cited by 7,368
Advances In Deep Learning On Graphs (Gsp'18 Workshop)Preprint
Defferrard, M., Bresson, X., & Vandergheynst, P. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1606.09375 · Cited by 7,021
Self-citationDeepFace: Closing the Gap to Human-Level Performance in Face Verification
Taigman, Y., Yang, M., Ranzato, M., & Wolf, L. (2014) · 2014 IEEE Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2014.220 · Cited by 6,542
LINE: Large-scale Information Network Embedding
Tang, J., Qu, M., Wang, M., Zhang, M., Yan, J., & Mei, Q. (2015) · Proceedings of the 24th International Conference on World Wide Web · doi:10.1145/2736277.2741093 · Cited by 5,416
3D ShapeNets: A deep representation for volumetric shapes
Wu, Z., Song, S., Khosla, A., Yu, F., Zhang, L., Tang, X., & Xiao, J. (2015) · 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/cvpr.2015.7298801 · Cited by 5,413
Dimensionality Reduction by Learning an Invariant Mapping
Hadsell, R., Chopra, S., & LeCun, Y. (2006) · 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 2 (CVPR'06) · doi:10.1109/cvpr.2006.100 · Cited by 5,336
Self-citationJaderberg, M., Simonyan, K., Zisserman, A., & Kavukcuoglu, K. (2015) · arXiv · doi:10.48550/arxiv.1506.02025 · Cited by 5,137
Advances In Deep Learning On Graphs (Gsp'18 Workshop)
Defferrard, M. (2016) · Figshare · doi:10.5281/zenodo.1286817 · Cited by 4,977
WaveNet: a generative model for raw audio
Oord, A. V. D., Dieleman, S., Zen, H., Simonyan, K., Vinyals, O., Graves, A., Kalchbrenner, N., Senior, A., & Kavukcuoglu, K. (2016) · arXiv · doi:10.48550/arxiv.1609.03499 · Cited by 4,911
Shuman, D. I., Narang, S. K., Frossard, P., Ortega, A., & Vandergheynst, P. (2013) · IEEE Signal Processing Magazine · doi:10.1109/msp.2012.2235192 · Cited by 4,421
Self-citationFlownet: Learning optical flow with convolutional networks
Dosovitskiy, A., Fischer, P., Ilg, E., Hausser, P., Hazirbas, C., Golkov, V., Smagt, P. V. D., Cremers, D., & Brox, T. (2015) · 2015 IEEE International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2015.316 · Cited by 4,313
Deep Residual Learning for Image Recognition
He, K., Zhang, X., Ren, S., & Sun, J. (2015) · arXiv · doi:10.48550/arxiv.1512.03385 · Cited by 4,196
Spectral Networks and Locally Connected Networks on Graphs
Bruna, J., Zaremba, W., Szlam, A., & LeCun, Y. (2013) · arXiv · doi:10.48550/arxiv.1312.6203 · Cited by 3,983
Self-citationMulti-view Convolutional Neural Networks for 3D Shape Recognition
Su, H., Maji, S., Kalogerakis, E., & Miller, E. G. (2015) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2015.114 · Cited by 3,608
Deep Learning: Methods and Applications
Deng, L., & Yu, D. (2014) · Foundations and Trends® in Signal Processing · doi:10.1561/2000000039 · Cited by 3,480
Striving for Simplicity: The All Convolutional Net
Springenberg, J. T., Dosovitskiy, A., Brox, T., & Riedmiller, M. (2014) · arXiv · doi:10.48550/arxiv.1412.6806 · Cited by 3,447
Lazer, D., Pentland, A., Adamic, L., Aral, S., Barabási, A.-L., Brewer, D., Christakis, N., Contractor, N., Fowler, J., Gutmann, M., et al. (2009) · Science · doi:10.1126/science.1167742 · Cited by 3,365
Gated Graph Sequence Neural NetworksPreprint
Li, Y., Tarlow, D., Brockschmidt, M., & Zemel, R. S. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1511.05493 · Cited by 3,329
Collective Classification in Network Data
Sen, P., Namata, G., Bilgic, M., Getoor, L., Gallagher, B., & Eliassi‐Rad, T. (2008) · AI Magazine · doi:10.1609/aimag.v29i3.2157 · Cited by 3,293
Cho, E., Myers, S. A., & Leskovec, J. (2011) · ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD) · doi:10.1145/2020408.2020579 · Cited by 2,910
Predicting the sequence specificities of DNA- and RNA-binding proteins by deep learning
Alipanahi, B., Delong, A., Weirauch, M. T., & Frey, B. J. (2015) · Nature Biotechnology · doi:10.1038/nbt.3300 · Cited by 2,873
Convolutional Networks on Graphs for Learning Molecular Fingerprints
Duvenaud, D., Maclaurin, D., Aguilera-Iparraguirre, J., Gómez-Bombarelli, R., Hirzel, T., Aspuru-Guzik, A., & Adams, R. P. (2015) · arXiv · doi:10.48550/arxiv.1509.09292 · Cited by 2,628
Learning Hierarchical Features for Scene Labeling
Farabet, C., Couprie, C., Najman, L., & LeCun, Y. (2013) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2012.231 · Cited by 2,620
Self-citationNatural Image Statistics and Neural Representation
Simoncelli, E. P., & Olshausen, B. A. (2001) · Annual Review of Neuroscience · doi:10.1146/annurev.neuro.24.1.1193 · Cited by 2,460
Coifman, R. R., & Lafon, S. (2006) · Applied and Computational Harmonic Analysis · doi:10.1016/j.acha.2006.04.006 · Cited by 2,380
Convolutional networks and applications in vision
LeCun, Y., Kavukcuoglu, K., & Farabet, C. (2010) · Proceedings of 2010 IEEE International Symposium on Circuits and Systems · doi:10.1109/iscas.2010.5537907 · Cited by 2,213
Self-citationA new model for learning in graph domains
Gori, M., Monfardini, G., & Scarselli, F. (2006) · Proceedings. 2005 IEEE International Joint Conference on Neural Networks, 2005. · doi:10.1109/ijcnn.2005.1555942 · Cited by 2,075
Geometric Deep Learning on Graphs and Manifolds Using Mixture Model CNNs
Monti, F., Boscaini, D., Masci, J., Rodola, E., Svoboda, J., & Bronstein, M. M. (2017) · 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr.2017.576 · Cited by 1,820
Self-citationDeep Learning: Methods and Applications
Deng, L. (2014) · now publishers, Inc. eBooks · doi:10.1561/9781601988157 · Cited by 1,789
Morgan, H. L. (1965) · Journal of Chemical Documentation · doi:10.1021/c160017a018 · Cited by 1,716
Recommender systems with social regularization
Ma, H., Zhou, D., Liu, C., Lyu, M. R.-T., & King, I. (2011) · ACM International Conference on Web Search and Data Mining (WSDM) · doi:10.1145/1935826.1935877 · Cited by 1,669
Invariant Scattering Convolution Networks
Bruna, J., & Mallat, S. (2013) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2012.230 · Cited by 1,633
Self-citationCao, S., Lu, W., & Xu, Q. (2015) · ACM International Conference on Information and Knowledge Management (CIKM) · doi:10.1145/2806416.2806512 · Cited by 1,609
A genomic regulatory network for development
Davidson, E. H., Rast, J. P., Oliveri, P., Ransick, A., Calestani, C., Yuh, C.-H., Minokawa, T., Amore, G., Hinman, V., Arenas-Mena, C., et al. (2002) · Science · doi:10.1126/science.1069883 · Cited by 1,567
Volumetric and Multi-view CNNs for Object Classification on 3D Data
Qi, C. R., Su, H., NieBner, M., Dai, A., Yan, M., & Guibas, L. J. (2016) · 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/cvpr.2016.609 · Cited by 1,527
Unique Signatures of Histograms for Local Surface Description
Tombari, F., Salti, S., & Di Stefano, L. (2010) · Lecture Notes in Computer Science · doi:10.1007/978-3-642-15558-1_26 · Cited by 1,480
A Concise and Provably Informative Multi‐Scale Signature Based on Heat Diffusion
Sun, J. Z., Ovsjanikov, M., & Guibas, L. J. (2009) · Computer Graphics Forum · doi:10.1111/j.1467-8659.2009.01515.x · Cited by 1,466
Learning Fast Approximations of Sparse Coding
Gregor, K., & LeCun, Y. (2010) · Cited by 1,416
Self-citationComputing Discrete Minimal Surfaces and Their Conjugates
Pinkall, U., & Polthier, K. (1993) · Experimental Mathematics · doi:10.1080/10586458.1993.10504266 · Cited by 1,278
Deep Convolutional Networks on Graph-Structured Data
Henaff, M., Bruna, J., & LeCun, Y. (2015) · arXiv · doi:10.48550/arxiv.1506.05163 · Cited by 1,255
Self-citationMallat, S. (2012) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.21413 · Cited by 1,127
Exact matrix completion via convex optimization
Candès, E. J., & Recht, B. (2012) · Communications of the ACM · doi:10.1145/2184319.2184343 · Cited by 1,011
The Imbedding Problem for Riemannian Manifolds
Nash, J. (1956) · Annals of Mathematics · doi:10.2307/1969989 · Cited by 1,006
Interaction Networks for Learning about Objects, Relations and Physics
Battaglia, P. W., Pascanu, R., Lai, M., Rezende, D., & Kavukcuoglu, K. (2016) · arXiv · doi:10.48550/arxiv.1612.00222 · Cited by 969
Goodfellow, I. J., Warde-Farley, D., Mirza, M., Courville, A., & Bengio, Y. (2013) · arXiv · doi:10.48550/arxiv.1302.4389 · Cited by 935
Diffusion-Convolutional Neural Networks
Atwood, J. R., & Towsley, D. (2016) · neural information processing systems · Cited by 925
11. The Imbedding Problem for Riemannian Manifolds
Nash, J. (2002) · Princeton University Press eBooks · doi:10.1515/9781400884087-013 · Cited by 838
Biological network comparison using graphlet degree distribution
Pržulj, N. (2007) · Bioinformatics · doi:10.1093/bioinformatics/btl301 · Cited by 820
Net2Net: Accelerating Learning via Knowledge TransferPreprint
Chen, T.-Q., Goodfellow, I., & Shlens, J. (2015) · International Conference on Learning Representations · doi:10.48550/arxiv.1511.05641 · Cited by 819
Bronstein, A. M., Bronstein, M. M., Guibas, L. J., & Ovsjanikov, M. (2011) · ACM Transactions on Graphics · doi:10.1145/1899404.1899405 · Cited by 811
Self-citationOvsjanikov, M., Ben‐Chen, M., Solomon, J., Butscher, A., & Guibas, L. J. (2012) · ACM Transactions on Graphics · doi:10.1145/2185520.2185526 · Cited by 736
The Loss Surfaces of Multilayer Networks
Choromanska, A., Henaff, M., Mathieu, M., Arous, G. B., & LeCun, Y. (2014) · arXiv · doi:10.48550/arxiv.1412.0233 · Cited by 733
Self-citationUnderstanding deep convolutional networks
Mallat, S. (2016) · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rsta.2015.0203 · Cited by 733
Geodesic Convolutional Neural Networks on Riemannian Manifolds
Masci, J., Boscaini, D., Bronstein, M. M., & Vandergheynst, P. (2015) · 2015 IEEE International Conference on Computer Vision Workshop (ICCVW) · doi:10.1109/iccvw.2015.112 · Cited by 721
Self-citationScale-invariant heat kernel signatures for non-rigid shape recognition
Bronstein, M. M., & Kokkinos, I. (2010) · 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/cvpr.2010.5539838 · Cited by 690
Self-citationLearning Multiagent Communication with BackpropagationPreprint
Sukhbaatar, S., Szlam, A. D., & Fergus, R. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1605.07736 · Cited by 649
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Kawaguchi, K. (2016) · arXiv · doi:10.48550/arxiv.1605.07110 · Cited by 592
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Monti, F., Bronstein, M., & Bresson, X. (2017) · Neural Information Processing Systems · doi:10.48550/arxiv.1704.06803 · Cited by 558
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Bronstein, A. M., Bronstein, M. M., & Kimmel, R. (2006) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0508601103 · Cited by 555
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Atwood, J. R., & Towsley, D. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1511.02136 · Cited by 544
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Boscaini, D., Masci, J., Rodolà, E., & Bronstein, M. (2016) · Neural Information Processing Systems · doi:10.48550/arxiv.1605.06437 · Cited by 540
Self-citationStrategies for training large scale neural network language models
Mikolov, T., Deoras, A., Povey, D., Burget, L., & Černocký, J. (2011) · IEEE Workshop on Automatic Speech Recognition and Understanding (ASRU) · doi:10.1109/asru.2011.6163930 · Cited by 516
Coifman, R. R., & Maggioni, M. (2006) · Applied and Computational Harmonic Analysis · doi:10.1016/j.acha.2006.04.004 · Cited by 491
SyncSpecCNN: Synchronized Spectral CNN for 3D Shape Segmentation
Yi, L., Su, H., Guo, X., & Guibas, L. (2017) · 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr.2017.697 · Cited by 461
The Laplacian on a Riemannian Manifold
Rosenberg, S. (1997) · Cambridge University Press eBooks · doi:10.1017/cbo9780511623783 · Cited by 451
A committee of neural networks for traffic sign classification
Ciresan, D. C., Meier, U., Masci, J., & Schmidhuber, J. (2011) · International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn.2011.6033458 · Cited by 387
Vertex-frequency analysis on graphs
Shuman, D. I., Ricaud, B., & Vandergheynst, P. (2016) · Applied and Computational Harmonic Analysis · doi:10.1016/j.acha.2015.02.005 · Cited by 349
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Chang, M. B., Ullman, T. D., Torralba, A. B., & Tenenbaum, J. B. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1612.00341 · Cited by 340
Kim, V. G., Lipman, Y., & Funkhouser, T. A. (2011) · ACM SIGGRAPH Conference (SIGGRAPH) · doi:10.1145/1964921.1964974 · Cited by 311
Deep Functional Maps: Structured Prediction for Dense Shape Correspondence
Litany, O., Remez, T., Rodolà, E., Bronstein, A. M., & Bronstein, M. M. (2017) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2017.603 · Cited by 298
Self-citationKim, V. G., Lipman, Y., & Funkhouser, T. (2011) · ACM Transactions on Graphics · doi:10.1145/2010324.1964974 · Cited by 298
Multi-view Convolutional Neural Networks for 3D Shape RecognitionPreprint
Su, H., Maji, S., Kalogerakis, E., et al. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1505.00880 · Cited by 278
Learning to Generate Chairs, Tables and Cars with Convolutional Networks
Dosovitskiy, A., Springenberg, J. T., Tatarchenko, M., & Brox, T. (2016) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2016.2567384 · Cited by 267
Lim, L. (2020) · SIAM Review · doi:10.1137/18m1223101 · Cited by 234
Boscaini, D., Masci, J., Melzi, S., Bronstein, M. M., Castellani, U., & Vandergheynst, P. (2015) · Computer Graphics Forum · doi:10.1111/cgf.12693 · Cited by 205
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Rosenberg, S. (1997) · Cited by 202
Collaborative filtering with graph information: consistency and scalable methods
Rao, N., Yu, H., Ravikumar, P., & Dhillon, I. S. (2015) · Cited by 201
Discrete laplace operators: no free lunch
Wardetzky, M., Mathur, S., Kälberer, F., & Grinspun, E. (2007) · doi:10.5555/1281991.1281995 · Cited by 196
Ktena, S. I., Parisot, S., Ferrante, E., Rajchl, M., Lee, M., Glocker, B., & Rueckert, D. (2017) · Lecture notes in computer science · doi:10.1007/978-3-319-66182-7_54 · Cited by 196
Kovnatsky, A., Bronstein, M. M., Bronstein, A. M., Glashoff, K., & Kimmel, R. (2013) · Computer Graphics Forum · doi:10.1111/cgf.12064 · Cited by 189
Self-citationLearning Spectral Descriptors for Deformable Shape Correspondence
Litman, R., & Bronstein, A. M. (2013) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2013.148 · Cited by 189
Dense Human Body Correspondences Using Convolutional Networks
Wei, L., Qi-xing Huang, A., Ceylan, D., Vouga, E., & Li, H. (2016) · 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/cvpr.2016.171 · Cited by 184
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Arie-Nachimson, M., Kovalsky, S. Z., Kemelmacher-Shlizerman, I., Singer, A., & Basri, R. (2012) · International Conference on 3D Imaging, Modeling, Processing, Visualization & Transmission · doi:10.1109/3dimpvt.2012.46 · Cited by 174
Gavish, M., Nadler, B., & Coifman, R. R. (2010) · Cited by 169
Map-based exploration of intrinsic shape differences and variability
Rustamov, R., Ovsjanikov, M., Azencot, O., Ben-Chen, M., Chazal, F., & Guibas, L. (2013) · ACM Transactions on Graphics · doi:10.1145/2461912.2461959 · Cited by 166
Dense Non-rigid Shape Correspondence Using Random Forests
Rodolà, E., Bulò, S. R., Windheuser, T., Vestner, M., & Cremers, D. (2014) · 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/cvpr.2014.532 · Cited by 157
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Kalofolias, V., Bresson, X., Bronstein, M. M., & Vandergheynst, P. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1408.1717 · Cited by 154
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Mehta, P. D., & Schwab, D. J. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1410.3831 · Cited by 142
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Coates, A. (2024) · doi:10.57702/4h3zav33 · Cited by 138
Recent Trends, Applications, and Perspectives in 3D Shape Similarity Assessment
Biasotti, S., Cerri, A., Bronstein, A. M., & Bronstein, M. M. (2015) · Computer Graphics Forum · doi:10.1111/cgf.12734 · Cited by 131
Self-citationAnisotropic Diffusion Descriptors
Boscaini, D., Masci, J., Rodolà, E., Bronstein, M. M., & Cremers, D. (2016) · Computer Graphics Forum · doi:10.1111/cgf.12844 · Cited by 119
Self-citationSur l'uniformisation des fonctions analytiques
Poincaré, H. (1908) · Acta Mathematica · doi:10.1007/bf02415442 · Cited by 115
Wardetzky, M., Mathur, S., Kälberer, F., & Grinspun, E. (2008) · ACM SIGGRAPH Conference and Exhibition on Computer Graphics and Interactive Techniques in Asia (SIGGRAPH Asia) · doi:10.1145/1508044.1508063 · Cited by 103
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Freeman, C. D., & Bruna, J. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1611.01540 · Cited by 96
Self-citationA mathematical motivation for complex-valued convolutional networks
Tygert, M., Bruna, J., Chintala, S., LeCun, Y., Piantino, S., & Szlam, A. (2016) · Neural Computation · doi:10.1162/neco_a_00824 · Cited by 88 · cited 2×
“These statistical properties have been related to physics [16] and formalized in specific classes of convolutional neural networks (CNNs) [17], [18], [19].”
BackgroundSelf-citationWhat The Statistics Of Natural Images Tell Us About Visual Coding
Field, D. J. (1989) · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · doi:10.1117/12.952724 · Cited by 81
Multimodal Manifold Analysis by Simultaneous Diagonalization of Laplacians
Eynard, D., Kovnatsky, A., Bronstein, M. M., Glashoff, K., & Bronstein, A. M. (2015) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2015.2408348 · Cited by 64
Self-citationIn silicogrouping of peptide/HLA class I complexes using structural interaction characteristics
Tong, J. C., Tan, T. W., & Ranganathan, S. (2006) · Bioinformatics · doi:10.1093/bioinformatics/btl563 · Cited by 62
Anisotropic Laplace-Beltrami Operators for Shape Analysis
Andreux, M., Rodolà, E., Aubry, M., & Cremers, D. (2015) · Lecture notes in computer science · doi:10.1007/978-3-319-16220-1_21 · Cited by 61
Which Spatial Partition Trees are Adaptive to Intrinsic Dimension?Preprint
Verma, N., Kpotufe, S., & Dasgupta, S. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1205.2609 · Cited by 60
The multiscale structure of non-differentiable image manifolds
Wakin, M. B., Donoho, D. L., Choi, H., & Baraniuk, R. G. (2005) · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · doi:10.1117/12.617822 · Cited by 58
Wavelets on Graphs via Deep Learning
Rustamov, R. M., & Guibas, L. J. (2018) · Signals and communication technology · doi:10.1007/978-3-030-03574-7_5 · Cited by 57
Diffusion-driven multiscale analysis on manifolds and graphs: top-down and bottom-up constructions
Szlam, A. D., Maggioni, M., Coifman, R. R., & BremerJr., J. C. (2005) · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · doi:10.1117/12.616931 · Cited by 53
Self-citationConvergence of the Cotangent Formula: An Overview
Wardetzky, M. (2008) · Oberwolfach Seminars · doi:10.1007/978-3-7643-8621-4_15 · Cited by 47
Shape‐from‐Operator: Recovering Shapes from Intrinsic Operators
Boscaini, D., Eynard, D., Kourounis, D., & Bronstein, M. M. (2015) · Computer Graphics Forum · doi:10.1111/cgf.12558 · Cited by 47
Self-citationKtena, S. I., Parisot, S., Ferrante, E., et al. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1703.02161 · Cited by 27
Cheng, X., Chen, X., & Mallat, S. (2016) · Information and Inference A Journal of the IMA · doi:10.1093/imaiai/iaw007 · Cited by 26
Hodge Laplacians on graphsPreprint
Lim, L. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1507.05379 · Cited by 24
Search-Convolutional Neural NetworksPreprint
Atwood, J. R., & Towsley, D. (2015) · arXiv (Cornell University) · Cited by 21
Learning to Generate Chairs, Tables and Cars with Convolutional NetworksPreprint
Dosovitskiy, A., Springenberg, J. T., Tatarchenko, M., & Brox, T. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1411.5928 · Cited by 19
Learning the 2-D Topology of Images
Roux, N. L., Bengio, Y., Lamblin, P., Joliveau, M., & Kégl, B. (2007) · HAL · Cited by 15
On the Quality of the Initial Basin in Overspecified Neural NetworksPreprint
Safran, I., & Shamir, O. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1511.04210 · Cited by 7
A Harmonic Extension Approach for Collaborative RankingPreprint
Kuang, D., Shi, Z., Osher, S., & Bertozzi, A. L. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1602.05127 · Cited by 3
Chen, T., Wang, Z., Li, L., Li, D., Li, Z., Chang, X., Bian, P., Liang, G., Wang, Q., & Xie, T. (2025) · Schloss Dagstuhl – Leibniz-Zentrum für Informatik · doi:10.4230/lipics.ecoop.2025.6
Deep Functional Maps: Structured Prediction for Dense Shape Correspondence
Litany, O., Remez, T., Rodolà, E., Bronstein, A. M., & Bronstein, M. M. (2017) · arXiv · doi:10.48550/arxiv.1704.08686
Self-citation
Flagged first, then by citations
Research works printed but not linked: 6
- defferrard, 0, Convolutional neural networks on graphs with fast localized spectral filtering, Proc Int Conf Neural Information Processing Systems (NIPS), 3844
- chang, 2016, A compositional object-based approach to learning physical dynamics
- goodfellow, 2016, Deep Learning
- glem, 2006, The generation of a unique machine description for chemical structure, Investigational Drugs, 9, 199
- preti, 2016, The dynamic functional connectome State-of-the-art and perspectives Science
- battaglia, 0, Interaction networks for learning about objects, relations and physics, Proc Int Conf Neural Information Processing Systems (NIPS), 4502
Cited by
Sorted by citations
A Comprehensive Survey on Graph Neural Networks
Wu, Z., Pan, S., Chen, F., Long, G., Zhang, C., & Yu, P. S. (2021) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2020.2978386 · Cited by 11,000
Physics-informed machine learning
Karniadakis, G. E., Kevrekidis, I. G., Lu, L., Perdikaris, P., Wang, S., & Yang, L. (2021) · Nature Reviews Physics · doi:10.1038/s42254-021-00314-5 · Cited by 8,718
Dynamic Graph CNN for Learning on Point Clouds
Wang, Y., Sun, Y., Liu, Z., Sarma, S. E., Bronstein, M. M., & Solomon, J. M. (2019) · ACM Transactions on Graphics · doi:10.1145/3326362 · Cited by 7,199
Self-citationGraph neural networks: A review of methods and applications
Zhou, J., Cui, G., Hu, S., Zhang, Z., Yang, C., Liu, Z., Wang, L., Li, C., & Sun, M. (2020) · AI Open · doi:10.1016/j.aiopen.2021.01.001 · Cited by 6,880
Graph Convolutional Neural Networks for Web-Scale Recommender Systems
Ying, R., He, R., Chen, K., Eksombatchai, P., Hamilton, W. L., & Leskovec, J. (2018) · Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining · doi:10.1145/3219819.3219890 · Cited by 3,733
Metadata
- Authors
- Bronstein, M. M., Bruna, J., LeCun, Y., Szlam, A., & Vandergheynst, P.
- Affiliations
- Tel Aviv University (IL)
- Courant Institute of Mathematical Sciences (US)
- Meta (United Kingdom) (GB)
- Meta (United States) (US)
- École Polytechnique Fédérale de Lausanne (CH)
- Venue
- IEEE Signal Processing Magazine
- Published
- 2017-07
- Volume
- 34
- Issue
- 4
- Pages
- 18-42
- ISSN
- 1053-5888 (ISSN-L)
- 1558-0792
- OpenAlex
- W2558748708
- Cited by
- 3,661
- References
- 137
- Citations by year
- 2026: 350 · 2025: 412 · 2024: 388 · 2023: 428 · 2022: 462 · 2021: 567 · 2020: 493 · 2019: 353 · 2018: 181 · 2017: 25
- FWCI
- 169.40
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- IEEE Signal Processing Magazine (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- HAL (submittedVersion)
- Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion)
- Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion, cc-by-nc-nd)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Advanced Graph Neural Networks
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Topological and Geometric Data Analysis
- Physical Sciences › Computer Science › Computer Graphics and Computer-Aided Design › 3D Shape Modeling and Analysis
- Keywords
- geometric deep learning, non-Euclidean data, graph neural networks, manifold learning, structured data, deep neural network
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.
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