Multiscale Geometric Methods for Data Sets II: Geometric Multi-Resolution Analysis

[1]  M. Maggioni,et al.  Determination of reaction coordinates via locally scaled diffusion map. , 2011, The Journal of chemical physics.

[2]  Wolfgang Dahmen,et al.  Fast high-dimensional approximation with sparse occupancy trees , 2011, J. Comput. Appl. Math..

[3]  Robert H. Halstead,et al.  Matrix Computations , 2011, Encyclopedia of Parallel Computing.

[4]  Guangliang Chen,et al.  Data representation and exploration with Geometric Wavelets , 2010, 2010 IEEE Symposium on Visual Analytics Science and Technology.

[5]  Guillermo Sapiro,et al.  Online Learning for Matrix Factorization and Sparse Coding , 2009, J. Mach. Learn. Res..

[6]  Guillermo Sapiro,et al.  Non-Parametric Bayesian Dictionary Learning for Sparse Image Representations , 2009, NIPS.

[7]  Arthur Szlam,et al.  Asymptotic regularity of subdivisions of Euclidean domains by iterated PCA and iterated 2-means , 2009 .

[8]  Mauro Maggioni,et al.  Multiscale Estimation of Intrinsic Dimensionality of Data Sets , 2009, AAAI Fall Symposium: Manifold Learning and Its Applications.

[9]  M. Maggioni,et al.  Estimation of intrinsic dimensionality of samples from noisy low-dimensional manifolds in high dimensions with multiscale SVD , 2009, 2009 IEEE/SP 15th Workshop on Statistical Signal Processing.

[10]  Guillermo Sapiro,et al.  Discriminative k-metrics , 2009, ICML '09.

[11]  Michael L. Littman,et al.  Proceedings of the 26th Annual International Conference on Machine Learning, ICML 2009, Montreal, Quebec, Canada, June 14-18, 2009 , 2009, International Conference on Machine Learning.

[12]  Guillermo Sapiro,et al.  Online dictionary learning for sparse coding , 2009, ICML '09.

[13]  Richard G. Baraniuk,et al.  Random Projections of Smooth Manifolds , 2009, Found. Comput. Math..

[14]  Mark Tygert,et al.  A Randomized Algorithm for Principal Component Analysis , 2008, SIAM J. Matrix Anal. Appl..

[15]  Ronald R. Coifman,et al.  Regularization on Graphs with Function-adapted Diffusion Processes , 2008, J. Mach. Learn. Res..

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

[17]  M. Maggioni,et al.  Manifold parametrizations by eigenfunctions of the Laplacian and heat kernels , 2008, Proceedings of the National Academy of Sciences.

[18]  Sridhar Mahadevan,et al.  Proto-value Functions: A Laplacian Framework for Learning Representation and Control in Markov Decision Processes , 2007, J. Mach. Learn. Res..

[19]  M. Maggioni,et al.  Universal Local Parametrizations via Heat Kernels and Eigenfunctions of the Laplacian , 2007, 0709.1975.

[20]  Robert M. Haralick,et al.  Nonlinear Manifold Clustering By Dimensionality , 2006, 18th International Conference on Pattern Recognition (ICPR'06).

[21]  Arthur D. Szlam,et al.  Diffusion wavelet packets , 2006 .

[22]  John Langford,et al.  Cover trees for nearest neighbor , 2006, ICML.

[23]  Sridhar Mahadevan,et al.  Fast direct policy evaluation using multiscale analysis of Markov diffusion processes , 2006, ICML.

[24]  Ronald R. Coifman,et al.  Geometries of sensor outputs, inference, and information processing , 2006, SPIE Defense + Commercial Sensing.

[25]  Ronald R. Coifman,et al.  Qeeg-Based Classification With Wavelet Packet and Microstate Features for Triage Applications in the ER , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.

[26]  Stéphane Lafon,et al.  Diffusion maps , 2006 .

[27]  Wolfgang Dahmen,et al.  Universal Algorithms for Learning Theory Part I : Piecewise Constant Functions , 2005, J. Mach. Learn. Res..

[28]  Michael Elad,et al.  Submitted to Ieee Transactions on Image Processing Image Decomposition via the Combination of Sparse Representations and a Variational Approach , 2022 .

[29]  Ronald R. Coifman,et al.  Biorthogonal diffusion wavelets for multiscale representations on manifolds and graphs , 2005, SPIE Optics + Photonics.

[30]  Ronald R. Coifman,et al.  Diffusion-driven multiscale analysis on manifolds and graphs: top-down and bottom-up constructions , 2005, SPIE Optics + Photonics.

[31]  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.

[32]  R R Coifman,et al.  Geometric diffusions as a tool for harmonic analysis and structure definition of data: multiscale methods. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[33]  Michael Elad,et al.  K-SVD : DESIGN OF DICTIONARIES FOR SPARSE REPRESENTATION , 2005 .

[34]  Peter Schröder,et al.  Multiscale Representations for Manifold-Valued Data , 2005, Multiscale Model. Simul..

[35]  H. Zha,et al.  Principal manifolds and nonlinear dimensionality reduction via tangent space alignment , 2004, SIAM J. Sci. Comput..

[36]  Alfred O. Hero,et al.  Learning intrinsic dimension and intrinsic entropy of high-dimensional datasets , 2004, 2004 12th European Signal Processing Conference.

[37]  Ronald A. DeVore,et al.  Fast computation in adaptive tree approximation , 2004, Numerische Mathematik.

[38]  Francesco Camastra,et al.  Intrinsic Dimension Estimation of Data: An Approach Based on Grassberger–Procaccia's Algorithm , 2001, Neural Processing Letters.

[39]  David R. Larson,et al.  Wavelets, frames and operator theory : Focused Research Group Workshop on Wavelets, Frames and Operator Theory, January 15-21, 2003, University of Maryland, College Park, Maryland , 2004 .

[40]  R. Coifman,et al.  Diffusion Wavelets , 2004 .

[41]  P. Casazza,et al.  Frames of subspaces , 2003, math/0311384.

[42]  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.

[43]  Hongyuan Zha,et al.  Principal Manifolds and Nonlinear Dimension Reduction via Local Tangent Space Alignment , 2022 .

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

[45]  O. Christensen An introduction to frames and Riesz bases , 2002 .

[46]  A. Vinciarelli,et al.  Estimating the Intrinsic Dimension of Data with a Fractal-Based Method , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

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

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

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

[50]  S. Semmes,et al.  Uniform rectifiability and quasiminimizing sets of arbitrary codimension , 2000 .

[51]  E. Candès,et al.  Curvelets: A Surprisingly Effective Nonadaptive Representation for Objects with Edges , 2000 .

[52]  Vipin Kumar,et al.  A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs , 1998, SIAM J. Sci. Comput..

[53]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..

[54]  S. Mallat A wavelet tour of signal processing , 1998 .

[55]  David J. Field,et al.  Sparse coding with an overcomplete basis set: A strategy employed by V1? , 1997, Vision Research.

[56]  Yair Bartal,et al.  Probabilistic approximation of metric spaces and its algorithmic applications , 1996, Proceedings of 37th Conference on Foundations of Computer Science.

[57]  R. Tibshirani Regression Shrinkage and Selection via the Lasso , 1996 .

[58]  D. Donoho,et al.  Translation-Invariant De-Noising , 1995 .

[59]  Ronald R. Coifman,et al.  Signal processing and compression with wavelet packets , 1994 .

[60]  Yves Meyer,et al.  Progress in wavelet analysis and applications , 1993 .

[61]  S. Semmes,et al.  Analysis of and on uniformly rectifiable sets , 1993 .

[62]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[63]  G. David Wavelets and Singular Integrals on Curves and Surfaces , 1991 .

[64]  The Traveling Salesman problem and Harmonic analysis , 1991 .

[65]  Peter W. Jones Rectifiable sets and the Traveling Salesman Problem , 1990 .

[66]  Michael Christ,et al.  A T(b) theorem with remarks on analytic capacity and the Cauchy integral , 1990 .

[67]  S. Mallat Multiresolution approximations and wavelet orthonormal bases of L^2(R) , 1989 .

[68]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..