Fetching the paper…
Reading the bibliography…
We introduce submodular hypergraphs, a family of hypergraphs that have different submodular weights associated with different cuts of hyperedges.
S. H. Gould, Variational methods for eigenvalue problems . University of Toronto Press Toronto, 1966, vol. 22, no. 12
1966
Earlier work this paper cites.
P. Wolfe, “Finding the nearest point in a polytope,” Mathematical Programming , vol. 11, no. 1, pp. 128–149, 1976
1976
Earlier work this paper cites.
K.-C. Chang, “Variational methods for non-differentiable functionals and their applications to partial differential equations,” Journal of Mathematical Analysis and Applications , vol. 80, no. 1, pp. 102–129, 1981
1981
Earlier work this paper cites.
L. Lovász, “Submodular functions and convexity,” in Mathematical Programming The State of the Art . Springer, 1983, pp. 235–257
1983
Earlier work this paper cites.
F. H. Clarke, Optimization and nonsmooth analysis . Siam, 1990, vol. 5
1990
Earlier work this paper cites.
D. R. Karger, “Global min-cuts in RNC, and other ramifications of a simple min-cut algorithm,” in Proceedings of the ACM-SIAM Symposium on Discrete Algorithms , vol. 93, 1993, pp. 21–30
1993
Earlier work this paper cites.
F. R. Chung, Spectral graph theory . American Mathematical Soc., 1997, no. 92
1997
Earlier work this paper cites.
E. BrianDavies, G. L. Gladwell, J. Leydold, and P. F. Stadler, “Discrete nodal domain theorems,” Linear Algebra and its Applications , vol. 336, no. 1-3, pp. 51–60, 2001
2001
Earlier work this paper cites.
A. Y. Ng, M. I. Jordan, and Y. Weiss, “On spectral clustering: Analysis and an algorithm,” in Advances in Neural Information Processing Systems , 2002, pp. 849–856
2002
Earlier work this paper cites.
S. Amghibech, “Eigenvalues of the discrete p-Laplacian for graphs,” Ars Combinatoria , vol. 67, pp. 283–302, 2003
2003
Earlier work this paper cites.
M. Belkin and P. Niyogi, “Laplacian eigenmaps for dimensionality reduction and data representation,” Neural computation , vol. 15, no. 6, pp. 1373–1396, 2003
2003
Earlier work this paper cites.
D. Zhou, J. Huang, and B. Schölkopf, “Learning with hypergraphs: Clustering, classification, and embedding,” in Advances in Neural Information Processing Systems , 2007, pp. 1601–1608
2007
Earlier work this paper cites.
A. Asuncion and D. Newman, “UCI machine learning repository,” 2007
2007
Earlier work this paper cites.
T. Bıyıkoglu, J. Leydold, and P. F. Stadler, “Laplacian eigenvectors of graphs,” Lecture notes in mathematics , vol. 1915, 2007
2007
Earlier work this paper cites.
U. Von Luxburg, “A tutorial on spectral clustering,” Statistics and computing , vol. 17, no. 4, pp. 395–416, 2007
2007
Earlier work this paper cites.
T. Bühler and M. Hein, “Spectral clustering based on the graph p-Laplacian,” in Proceedings of the International Conference on Machine Learning . ACM, 2009, pp. 81–88
2009
Earlier work this paper cites.
A. Szlam and X. Bresson, “Total variation and cheeger cuts,” in Proceedings of the International Conference on Machine Learning , 2010, pp. 1039–1046
2010
Earlier work this paper cites.
M. Hein and T. Bühler, “An inverse power method for nonlinear eigenproblems with applications in 1-spectral clustering and sparse pca,” in Advances in Neural Information Processing Systems , 2010, pp. 847–855
2010
Cited alongside, same era.
D. K. Hammond, P. Vandergheynst, and R. Gribonval, “Wavelets on graphs via spectral graph theory,” Applied and Computational Harmonic Analysis , vol. 30, no. 2, pp. 129–150, 2011
2011
Cited alongside, same era.
C. Arora, S. Banerjee, P. Kalra, and S. Maheshwari, “Generic cuts: An efficient algorithm for optimal inference in higher order MRF-MAP,” in Proceedings of the European Conference on Computer Vision . Springer, 2012, pp. 17–30
2012
Cited alongside, same era.
V. Kolmogorov, “Minimizing a sum of submodular functions,” Discrete Applied Mathematics , vol. 160, no. 15, pp. 2246–2258, 2012
2012
Cited alongside, same era.
A. R. Benson, D. F. Gleich, and J. Leskovec, “Higher-order organization of complex networks,” Science , vol. 353, no. 6295, pp. 163–166, 2016
2016
Later among the works it cites.
K. C. Chang, “Spectrum of the 1-Laplacian and Cheeger’s constant on graphs,” Journal of Graph Theory , vol. 81, no. 2, pp. 167–207, 2016
2016
Later among the works it cites.
2016
Later among the works it cites.
M. Defferrard, X. Bresson, and P. Vandergheynst, “Convolutional neural networks on graphs with fast localized spectral filtering,” in Advances in Neural Information Processing Systems , 2016, pp. 3844–3852
2016
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
M. Hein, S. Setzer, L. Jost, and S. S. Rangapuram, “The total variation on hypergraphs-learning on hypergraphs revisited,” in Advances in Neural Information Processing Systems , 2013, pp. 2427–2435
2013
Cited alongside, same era.
A. Fix, T. Joachims, S. M. Park, and R. Zabih, “Structured learning of sum-of-submodular higher order energy functions,” in Proceedings of the IEEE International Conference on Computer Vision . IEEE, 2013, pp. 3104–3111
2013
Cited alongside, same era.
S. Jegelka, F. Bach, and S. Sra, “Reflection methods for user-friendly submodular optimization,” in Advances in Neural Information Processing Systems , 2013, pp. 1313–1321
2013
Cited alongside, same era.
D. I. Shuman, S. K. Narang, P. Frossard, A. Ortega, and P. Vandergheynst, “The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains,” IEEE Signal Processing Magazine , vol. 30, no. 3, pp. 83–98, 2013
2013
Cited alongside, same era.
F. Bach et al. , “Learning with submodular functions: A convex optimization perspective,” Foundations and Trends® in Machine Learning , vol. 6, no. 2-3, pp. 145–373, 2013
2013
Cited alongside, same era.
T. Bühler, S. S. Rangapuram, S. Setzer, and M. Hein, “Constrained fractional set programs and their application in local clustering and community detection,” in Proceedings of the International Conference on Machine Learning . JMLR. org, 2013, pp. I–624
2013
Cited alongside, same era.
R. Nishihara, S. Jegelka, and M. I. Jordan, “On the convergence rate of decomposable submodular function minimization,” in Advances in Neural Information Processing Systems , 2014, pp. 640–648
2014
Cited alongside, same era.
A. Louis, “Hypergraph markov operators, eigenvalues and approximation algorithms,” in Proceedings of the ACM symposium on Theory of computing . ACM, 2015, pp. 713–722
2015
Cited alongside, same era.
C. Zhang, S. Hu, Z. G. Tang, and T.-H. H. Chan, “Re-revisiting learning on hypergraphs: Confidence interval and subgradient method,” in Proceedings of the International Conference on Machine Learning , vol. 70, 2017, pp. 4026–4034
2017
Later among the works it cites.
P. Li and O. Milenkovic, “Inhomogeneous hypergraph clustering with applications,” in Advances in Neural Information Processing Systems , 2017, pp. 2305–2315
2017
Later among the works it cites.
C. E. Tsourakakis, J. Pachocki, and M. Mitzenmacher, “Scalable motif-aware graph clustering,” in Proceedings of the 26th International Conference on World Wide Web . International World Wide Web Conferences Steering Committee, 2017, pp. 1451–1460
2017
Later among the works it cites.
K. Chang, S. Shao, and D. Zhang, “Nodal domains of eigenvectors for 1-Laplacian on graphs,” Advances in Mathematics , vol. 308, pp. 529–574, 2017
2017
Later among the works it cites.
S. Jegelka and J. A. Bilmes, “Graph cuts with interacting edge weights: examples, approximations, and algorithms,” Mathematical Programming , vol. 162, no. 1-2, pp. 241–282, 2017
2017
Later among the works it cites.
2017
Later among the works it cites.
C. Chekuri and C. Xu, “Computing minimum cuts in hypergraphs,” in Proceedings of the ACM-SIAM Symposium on Discrete Algorithms . Society for Industrial and Applied Mathematics, 2017, pp. 1085–1100
2017
Later among the works it cites.
2018
Closest in time.
C. Yang, M. Liu, V. W. Zheng, and J. Han, “Meta-graph based hin spectral embedding: Methods, analyses, and insights,” in Proceedings of the 2018 IEEE International Conference on Data Mining , 2018
2018
Closest in time.
2018
Closest in time.
M. Mitrovic, M. Feldman, A. Krause, and A. Karbasi, “Submodularity on hypergraphs: From sets to sequences,” in International Conference on Artificial Intelligence and Statistics , 2018, pp. 1177–1184
2018
Closest in time.