Fetching the paper…
Reading the bibliography…
Graph Laplacians computed from weighted adjacency matrices are widely used to identify geometric structure in data, and clusters in particular; their spectral properties play a central role in a number of unsupervised and semi-supervised learning algorithms.
A nonparametric estimate of a multivariate density function
D. O. Loftsgaarden, C. P. Quesenberry, et al · 1965
Earlier work this paper cites.
Variable kernel density estimation
G. R. Terrell and D. W. Scott · 1992
Earlier work this paper cites.
Perturbation theory for linear operators
T. Kato · 1995
Earlier work this paper cites.
Spectral partitioning works: Planar graphs and finite element meshes
D. A. Spielmat and S.-H. Teng · 1996
Earlier work this paper cites.
Computation of essential molecular dynamics by subdivision techniques
P. Deuflhard, M. Dellnitz, O. Junge, and C. Schütte · 1999
Earlier work this paper cites.
Identification of almost invariant aggregates in reversible nearly uncoupled Markov chains
P. Deuflhard, W. Huisinga, A. Fischer, and C. Schütte · 2000
Earlier work this paper cites.
Strongly elliptic systems and boundary integral equations
W. McLean · 2000
Earlier work this paper cites.
Normalized cuts and image segmentation
J. Shi and J. Malik · 2000
Earlier work this paper cites.
Transfer operator approach to conformational dynamics in biomolecular systems
C. Schütte, W. Huisinga, and P. Deuflhard · 2001
Earlier work this paper cites.
On spectral clustering: Analysis and an algorithm
A. Y. Ng, M. I. Jordan, and Y. Weiss · 2002
Earlier work this paper cites.
Sobolev spaces
R. A. Adams and J. J. Fournier · 2003
Earlier work this paper cites.
Laplacian eigenmaps for dimensionality reduction and data representation
M. Belkin and P. Niyogi · 2003
Earlier work this paper cites.
Semi-supervised learning using Gaussian fields and harmonic functions
X. Zhu, Z. Ghahramani, and J. D. Lafferty · 2003
Earlier work this paper cites.
Metastability in reversible diffusion processes i: Sharp asymptotics for capacities and exit times
A. Bovier, M. Eckhoff, V. Gayrard, and M. Klein · 2004
Earlier work this paper cites.
Phase transitions and metastability in Markovian and molecular systems
W. Huisinga, S. Meyn, and C. Schütte · 2004
Earlier work this paper cites.
Metastability in reversible diffusion processes ii: Precise asymptotics for small eigenvalues
A. Bovier, V. Gayrard, and M. Klein · 2005
Cited alongside, same era.
Self-tuning spectral clustering
L. Zelnik-Manor and P. Perona · 2005
Cited alongside, same era.
Convergence of laplacian eigenmaps
M. Belkin and P. Niyogi · 2006
Cited alongside, same era.
Diffusion maps
R. R. Coifman and S. Lafon · 2006
Cited alongside, same era.
Empirical graph laplacian approximation of laplace–beltrami operators: Large sample results
E. Giné, V. Koltchinskii, et al · 2006
Cited alongside, same era.
A tutorial on spectral clustering
U. von Luxburg · 2007
Cited alongside, same era.
The geometry of kernelized spectral clustering
G. Schiebinger, M. J. Wainwright, B. Yu, et al · 2015
Later among the works it cites.
Variable bandwidth diffusion kernels
T. Berry and J. Harlim · 2016
Later among the works it cites.
Uncertainty quantification in graph-based classification of high dimensional data
A. L. Bertozzi, X. Luo, A. M. Stuart, and K. C. Zygalakis · 2018
Later among the works it cites.
N. García Trillos, M. Gerlach, M. Hein, and D. Slepčev · 2018
Later among the works it cites.
A variational approach to the consistency of spectral clustering
N. García Trillos and D. Slepčev · 2018
Later among the works it cites.
PETSc users manual
S. Balay, S. Abhyankar, M. F. Adams, J. Brown, P. Brune, K. Buschelman, L. Dalcin, A. Dener, V. Eijkhout, W. D. Gropp, D. Karpeyev, D. Kaushik, M. G. Knepley, D. A. May, L. C. McInnes, R. T. Mills, T. Munson, K. Rupp, P. Sanan, B. F. Smith, S. Zampini, H. Zhang, and H. Zhang · 2019
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
M. Belkin and P. Niyogi · 2008
Cited alongside, same era.
Consistency of spectral clustering
U. von Luxburg, M. Belkin, and O. Bousquet · 2008
Cited alongside, same era.
Data spectroscopy: Eigenspaces of convolution operators and clustering
T. Shi, M. Belkin, B. Yu, et al · 2009
Cited alongside, same era.
Partial differential equations
L. C. Evans · 2010
Cited alongside, same era.
Diffuse interface models on graphs for classification of high dimensional data
A. L. Bertozzi and A. Flenner · 2012
Cited alongside, same era.
Automated solution of differential equations by the finite element method: The FEniCS book
A. Logg, K.-A. Mardal, and G. Wells · 2012
Cited alongside, same era.
Closest in time.
Improved spectral convergence rates for graph Laplacians on ϵ \epsilon -graphs and k k -NN graphs
J. Calder and N. G. Trillos · 2019
Closest in time.
Large data and zero noise limits of graph-based semi-supervised learning algorithms
M. M. Dunlop, D. Slepčev, A. M. Stuart, and M. Thorpe · 2019
Closest in time.
Geometric structure of graph laplacian embeddings
N. García Trillos, F. Hoffmann, and B. Hosseini · 2019
Closest in time.
Consistency of graphical semi-supervised learning algorithms in the continuum limit: The probit method
F. Hoffmann, B. Hosseini, A. Oberai, and A. Stuart · 2019
Closest in time.
Consistency of semi-supervised learning algorithms on graphs: probit and one-hot methods
F. Hoffmann, B. Hosseini, Z. Ren, and A. M. Stuart · 2019
Closest in time.
Analysis of p p -Laplacian regularization in semisupervised learning
D. Slepčev and M. Thorpe · 2019
Closest in time.
Consistency of anchor-based spectral clustering
H.-L. de Kergorlay and D. J. Higham · 2020
Closest in time.
Spectral convergence of diffusion maps: improved error bounds and an alternative normalisation
C. L. Wormell and S. Reich · 2020
Closest in time.