Publications

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2019

Liao, Wenjing; Maggioni, Mauro; Vigogna, S

Multiscale regression on intrinsically low-dimensional sets Journal Article

in preparation, 2019.

BibTeX | Tags: Machine learning, Manifold Learning, statistics, supervised learning

2017

Crosskey, Miles C; Maggioni, Mauro

ATLAS: A geometric approach to learning high-dimensional stochastic systems near manifolds Journal Article

Journal of Multiscale Modeling and Simulation, 15 (1), pp. 110–156, 2017, (arxiv: 1404.0667).

Links | BibTeX | Tags: diffusion geometry, Machine learning, Manifold Learning, statistics, stochastic systems

Little, Anna V; Maggioni, Mauro; Rosasco, Lorenzo

Multiscale geometric methods for data sets I: Multiscale SVD, noise and curvature Journal Article

Applied and Computational Harmonic Analysis, 43 (3), pp. 504 - 567, 2017, (Submitted: 2012, MIT-CSAIL-TR-2012-029/CBCL-310).

BibTeX | Tags: geometric wavelets, Machine learning, Manifold Learning, multiscale analysis, statistics

2016

Liao, Wenjing; Maggioni, Mauro; Vigogna, S

Learning adaptive multiscale approximations to data and functions near low-dimensional sets Inproceedings

Proceedings of the IEEE Information Theory Workshop, 2016, (Cambridge, UK).

BibTeX | Tags: Machine learning, Manifold Learning, statistics, supervised learning

Maggioni, Mauro; Minsker, Stanislav; Strawn, Nate

Multiscale Dictionary Learning: Non-asymptotic Bounds and Robustness Journal Article

J. Mach. Learn. Res., 17 (1), pp. 43–93, 2016, ISSN: 1532-4435.

Links | BibTeX | Tags: dictionary learning, Manifold Learning, multi-resolution analysis, robustness, sparsity

2013

Crosskey, Miles C; Maggioni, Mauro

Learning of intrinsically low-dimensional stochastic systems in high-dimensions, I Technical Report

2013, (in preparation).

BibTeX | Tags: Manifold Learning, stochastic systems

Iwen, Mark A; Maggioni, Mauro

Approximation of points on low-dimensional manifolds via random linear projections Journal Article

Inference and Information, 2 (1), pp. 1–31, 2013, (arXiv:1204.3337v1, 2012).

BibTeX | Tags: Machine learning, Manifold Learning, multiscale analysis

2012

Allard, William K; Chen, Guangliang; Maggioni, Mauro

Multi-scale geometric methods for data sets II: Geometric Multi-Resolution Analysis Journal Article

Applied and Computational Harmonic Analysis, 32 (3), pp. 435–462, 2012.

BibTeX | Tags: geometric wavelets, Machine learning, Manifold Learning, multiscale analysis, statistics

2011

Chen, Guangliang; Little, Anna V; Maggioni, Mauro

Multi-Resolution Geometric Analysis for data in high dimensions Journal Article

Proc. FFT 2011, 2011.

BibTeX | Tags: geometric wavelets, Machine learning, Manifold Learning, multiscale analysis

Maggioni, Mauro

Multiscale Geometric Dictionaries for Point-Cloud Data, Presented at SPARS 11, http://www.math.duke.edu/~mauro/research.html#Talks Journal Article

2011, (Presented at SPARS 11).

Links | BibTeX | Tags: dictionary learning, geometric wavelets, Machine learning, Manifold Learning, multiscale analysis

Zheng, W; Rohrdanz, M A; Maggioni, Mauro; Clementi, Cecilia

Polymer reversal rate calculated via locally scaled diffusion map Journal Article

J. Chem. Phys., (134), pp. 144108, 2011.

BibTeX | Tags: diffusion geometry, Machine learning, Manifold Learning, molecular dynamics, stochastic systems

Rohrdanz, M A; Zheng, W; Maggioni, Mauro; Clementi, Cecilia

Determination of reaction coordinates via locally scaled diffusion map Journal Article

J. Chem. Phys., (134), pp. 124116, 2011.

BibTeX | Tags: diffusion geometry, Machine learning, Manifold Learning, molecular dynamics, stochastic systems

Chen, Guangliang; Maggioni, Mauro

Multiscale Geometric Dictionaries for Point-Cloud Data Inproceedings

Proc. SampTA, 2011.

BibTeX | Tags: dictionary learning, geometric wavelets, Machine learning, Manifold Learning, multiscale analysis

Chen, Guangliang; Maggioni, Mauro

Multiscale Geometric and Spectral Analysis of Plane Arrangements Inproceedings

Conference on Computer Vision and Pattern Recognition, 2011.

BibTeX | Tags: Machine learning, Manifold Learning, multiscale analysis

2010

Jones, Peter W; Maggioni, Mauro; Schul, Raanan

Universal local manifold parametrizations via heat kernels and eigenfunctions of the Laplacian Journal Article

Ann. Acad. Scient. Fen., 35 , pp. 1–44, 2010, (http://arxiv.org/abs/0709.1975).

BibTeX | Tags: diffusion geometry, heat kernels, Laplacian eigenfunctions, Manifold Learning, multiscale analysis, random walks, spectral graph theory

Chen, Guangliang; Maggioni, Mauro

Multiscale Geometric Methods for Data Sets III: multiple planes Journal Article

in preparation, 2010.

BibTeX | Tags: Machine learning, Manifold Learning, multiscale analysis, statistics

Chen, Guangliang; Maggioni, Mauro

Multiscale Geometric Wavelets for the Analysis of Point Clouds Journal Article

Proc. CISS 2010, 2010.

BibTeX | Tags: geometric wavelets, Machine learning, Manifold Learning, multiscale analysis, spectral graph theory

2009

Little, Anna V; Jung, Y -M; Maggioni, Mauro

Multiscale Estimation of Intrinsic Dimensionality of Data Sets Inproceedings

Proc. A.A.A.I., 2009.

BibTeX | Tags: Machine learning, Manifold Learning, multiscale analysis, statistics

Little, Anna V; Lee, J; Jung, Y -M; Maggioni, Mauro

Estimation of intrinsic dimensionality of samples from noisy low-dimensional manifolds in high dimensions with multiscale $SVD$ Inproceedings

Proc. S.S.P., 2009.

BibTeX | Tags: Machine learning, Manifold Learning, multiscale analysis, statistics

2008

Coifman, Ronald R; Maggioni, Mauro

Geometry Analysis and Signal Processing on Digital Data, Emergent Structures, and Knowledge Building Miscellaneous

SIAM News, 2008.

BibTeX | Tags: diffusion geometry, heat kernels, Laplacian eigenfunctions, Manifold Learning, multiscale analysis, random walks, spectral graph theory

Szlam, Arthur D; Maggioni, Mauro; Coifman, Ronald R

Regularization on Graphs with Function-adapted Diffusion Processes Journal Article

Jour. Mach. Learn. Res., (9), pp. 1711–1739, 2008, ((YALE/DCS/TR1365, Yale Univ, July 2006)).

BibTeX | Tags: diffusion geometry, Machine learning, Manifold Learning, random walks, semisupervised learning, spectral graph theory

Jones, Peter W; Maggioni, Mauro; Schul, Raanan

Manifold parametrizations by eigenfunctions of the Laplacian and heat kernels Journal Article

Proc. Nat. Acad. Sci., 105 (6), pp. 1803–1808, 2008.

BibTeX | Tags: diffusion geometry, heat kernels, Laplacian eigenfunctions, Manifold Learning, multiscale analysis, random walks, spectral graph theory

2007

Coifman, Ronald R; Maggioni, Mauro

Multiscale Data Analysis with Diffusion Wavelets Journal Article

Proc. SIAM Bioinf. Workshop, Minneapolis, 2007.

BibTeX | Tags: diffusion geometry, diffusion wavelets, Machine learning, Manifold Learning, multiscale analysis, random walks, spectral graph theory, stochastic systems

Mahadevan, Sridhar; Maggioni, Mauro

Proto-value Functions: A Spectral Framework for Solving Markov Decision Processes Journal Article

JMLR, 8 , pp. 2169–2231, 2007.

BibTeX | Tags: diffusion geometry, Laplacian eigenfunctions, Machine learning, Manifold Learning, random walks, reinforcement learning, representation learning, spectral graph theory

2006

Coifman, Ronald R; Maggioni, Mauro

Diffusion Wavelets Journal Article

Appl. Comp. Harm. Anal., 21 (1), pp. 53–94, 2006, ((Tech. Rep. YALE/DCS/TR-1303, Yale Univ., Sep. 2004)).

BibTeX | Tags: diffusion geometry, diffusion wavelets, Machine learning, Manifold Learning, multiscale analysis, random walks, spectral graph theory, stochastic systems

Bremer, James Jr. C; Coifman, Ronald R; Maggioni, Mauro; Szlam, Arthur D

Diffusion Wavelet Packets Journal Article

Appl. Comp. Harm. Anal., 21 (1), pp. 95–112, 2006, ((Tech. Rep. YALE/DCS/TR-1304, 2004)).

BibTeX | Tags: diffusion geometry, Machine learning, Manifold Learning, multiscale analysis, random walks, spectral graph theory, stochastic systems

Coifman, Ronald R; Lafon, Stephane; Maggioni, Mauro; Keller, Y; Szlam, A D; Warner, F J; Zucker, S W

Geometries of sensor outputs, inference, and information processing Inproceedings

Athale, John Zolper; Eds. Intelligent Integrated Microsystems; Ravindra C A (Ed.): Proc. SPIE, pp. 623209, 2006.

BibTeX | Tags: diffusion geometry, Laplacian eigenfunctions, Machine learning, Manifold Learning, random walks, spectral graph theory, stochastic systems

Coifman, Ronald R; Maggioni, Mauro

Multiscale Analysis of Document Corpora Unpublished

2006, (Technical Report).

BibTeX | Tags: Machine learning, Manifold Learning, multiscale analysis, Unsupervised Learning

Maggioni, Mauro; Mahadevan, Sridhar

Fast Direct Policy Evaluation using Multiscale Analysis of Markov Diffusion Processes Inproceedings

ICML 2006, pp. 601–608, 2006.

BibTeX | Tags: diffusion geometry, Laplacian eigenfunctions, Machine learning, Manifold Learning, random walks, reinforcement learning, representation learning, spectral graph theory

Mahadevan, Sridhar; Ferguson, Kim; Osentoski, Sarah; Maggioni, Mauro

Simultaneous Learning of Representation and Control In Continuous Domains Inproceedings

AAAI, AAAI Press, 2006.

BibTeX | Tags: diffusion geometry, Laplacian eigenfunctions, Machine learning, Manifold Learning, random walks, reinforcement learning, representation learning, spectral graph theory

2005

Coifman, Ronald R; Maggioni, Mauro; Zucker, Steven W; Kevrekidis, Ioannis G

Geometric diffusions for the analysis of data from sensor networks Journal Article

Curr Opin Neurobiol, 15 (5), pp. 576–84, 2005.

BibTeX | Tags: diffusion geometry, Laplacian eigenfunctions, Machine learning, Manifold Learning, random walks, spectral graph theory, stochastic systems

Coifman, Ronald R; Lafon, Stephane; Lee, Ann B; Maggioni, Mauro; Nadler, B; Warner, Frederick; Zucker, Steven W

Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps Journal Article

Proceedings of the National Academy of Sciences of the United States of America, 102 (21), pp. 7426-7431, 2005.

BibTeX | Tags: diffusion geometry, Machine learning, Manifold Learning, random walks, spectral graph theory, stochastic systems

Coifman, Ronald R; Lafon, S; Lee, A B; Maggioni, Mauro; Nadler, B; Warner, Frederick; Zucker, Steven W

Geometric diffusions as a tool for harmonic analysis and structure definition of data: Multiscale methods Journal Article

Proceedings of the National Academy of Sciences of the United States of America, 102 (21), pp. 7432–7438, 2005.

BibTeX | Tags: diffusion geometry, Machine learning, Manifold Learning, multiscale analysis, random walks, spectral graph theory, stochastic systems

Mahadevan, Sridhar; Maggioni, Mauro

Value Function Approximation with Diffusion Wavelets and Laplacian Eigenfunctions Inproceedings

University of Massachusetts, Department of Computer Science Technical Report TR-2005-38; Proc. NIPS 2005, 2005.

BibTeX | Tags: diffusion geometry, diffusion wavelets, Laplacian eigenfunctions, Machine learning, Manifold Learning, random walks, reinforcement learning, representation learning, spectral graph theory

Maggioni, Mauro; Bremer, James Jr. C; Coifman, Ronald R; Szlam, Arthur D

Biorthogonal diffusion wavelets for multiscale representations on manifolds and graphs Conference

5914 (1), SPIE, San Diego, CA, USA, 2005.

Links | BibTeX | Tags: diffusion geometry, diffusion wavelets, Machine learning, Manifold Learning, multiscale analysis, random walks, spectral graph theory

Szlam, Arthur D; Maggioni, Mauro; Coifman, Ronald R; Bremer, James Jr. C

Diffusion-driven multiscale analysis on manifolds and graphs: top-down and bottom-up constructions Conference

5914-1 , SPIE, San Diego, CA, USA, 2005.

Links | BibTeX | Tags: diffusion geometry, diffusion wavelets, Machine learning, Manifold Learning, multiscale analysis, random walks, spectral graph theory

2004

Coifman, Ronald R; Maggioni, Mauro

Multiresolution Analysis associated to diffusion semigroups: construction and fast algorithms Technical Report

Dept. Comp. Sci., Yale University (YALE/DCS/TR-1289), 2004.

BibTeX | Tags: diffusion geometry, Machine learning, Manifold Learning, multiscale analysis, random walks, spectral graph theory, stochastic systems

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