Towards a theoretical foundation for Laplacian-based manifold methods

[1]  Mikhail Belkin,et al.  Consistency of spectral clustering , 2008, 0804.0678.

[2]  Stephen Smale,et al.  Finding the Homology of Submanifolds with High Confidence from Random Samples , 2008, Discret. Comput. Geom..

[3]  V. Koltchinskii,et al.  Empirical graph Laplacian approximation of Laplace–Beltrami operators: Large sample results , 2006, math/0612777.

[4]  A. Singer.  From graph to manifold Laplacian: The convergence rate , 2006 .

[5]  A. Singer.  Spectral independent component analysis , 2006 .

[6]  Ulrike von Luxburg,et al.  From Graphs to Manifolds - Weak and Strong Pointwise Consistency of Graph Laplacians , 2005, COLT.

[7]  Ann B. Lee,et al.  Geometric diffusions as a tool for harmonic analysis and structure definition of data: diffusion maps. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[8]  Vikas Sindhwani,et al.  On Manifold Regularization , 2005, AISTATS.

[9]  H. Weizsäcker,et al.  Chernoff's Theorem and Discrete Time Approximations of Brownian Motion on Manifolds , 2004, math/0409155.

[10]  Guillermo Sapiro,et al.  Comparing point clouds , 2004, SGP '04.

[11]  Afra Zomorodian,et al.  Computing Persistent Homology , 2004, SCG '04.

[12]  Matthias Hein,et al.  Measure Based Regularization , 2003, NIPS.

[13]  Bernhard Schölkopf,et al.  Learning with Local and Global Consistency , 2003, NIPS.

[14]  Nicolas Le Roux,et al.  Out-of-Sample Extensions for LLE, Isomap, MDS, Eigenmaps, and Spectral Clustering , 2003, NIPS.

[15]  Zoubin Ghahramani,et al.  Combining active learning and semi-supervised learning using Gaussian fields and harmonic functions , 2003, ICML 2003.

[16]  Mikhail Belkin,et al.  Laplacian Eigenmaps for Dimensionality Reduction and Data Representation , 2003, Neural Computation.

[17]  D. Donoho,et al.  Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[18]  Mikhail Belkin,et al.  Problems of learning on manifolds , 2003 .

[19]  D. Donoho,et al.  Hessian Eigenmaps : new locally linear embedding techniques for high-dimensional data , 2003 .

[20]  Alexander J. Smola,et al.  Kernels and Regularization on Graphs , 2003, COLT.

[21]  John D. Lafferty,et al.  Diffusion Kernels on Graphs and Other Discrete Input Spaces , 2002, ICML.

[22]  Mikhail Belkin,et al.  Using Manifold Stucture for Partially Labeled Classification , 2002, NIPS.

[23]  Mikhail Belkin,et al.  Using manifold structure for partially labelled classification , 2002, NIPS 2002.

[24]  Bernhard Schölkopf,et al.  Cluster Kernels for Semi-Supervised Learning , 2002, NIPS.

[25]  Michael I. Jordan,et al.  On Spectral Clustering: Analysis and an algorithm , 2001, NIPS.

[26]  Tommi S. Jaakkola,et al.  Partially labeled classification with Markov random walks , 2001, NIPS.

[27]  J. Tenenbaum,et al.  A global geometric framework for nonlinear dimensionality reduction. , 2000, Science.

[28]  S T Roweis,et al.  Nonlinear dimensionality reduction by locally linear embedding. , 2000, Science.

[29]  Santosh S. Vempala,et al.  On clusterings-good, bad and spectral , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[30]  H. Weizsäcker,et al.  Brownian motion on a manifold as a limit of stepwise conditioned standard Brownian motions , 2000 .

[31]  Jianbo Shi,et al.  Learning Segmentation by Random Walks , 2000, NIPS.

[32]  Vin de Silva,et al.  Graph approximations to geodesics on embedded manifolds , 2000 .

[33]  Jitendra Malik,et al.  Normalized cuts and image segmentation , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[34]  S. Rosenberg.  The Laplacian on a Riemannian Manifold: The Laplacian on a Riemannian Manifold , 1997 .

[35]  Shang-Hua Teng,et al.  Spectral partitioning works: planar graphs and finite element meshes , 1996, Proceedings of 37th Conference on Foundations of Computer Science.

[36]  I. Holopainen.  Riemannian Geometry , 1927, Nature.