Publications

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2019

Liao, Wenjing; Maggioni, Mauro

Adaptive Geometric Multiscale Approximations for Intrinsically Low-dimensional Data Journal Article

Journal of machine learning Research, 20 (98), pp. 1-63, 2019.

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

2017

Gerber, Sam; Maggioni, Mauro

Multiscale Strategies for Discrete Optimal Transport Journal Article

Journ. Mach. Learn. Res., (72), pp. 1–32, 2017.

BibTeX | Tags: multiscale analysis, optimal transport, optimization

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

2013

Gerber, S; Maggioni, Mauro

Multiscale dictionaries, transforms, and learning in high-dimensions Inproceedings

Proc. SPIE conference Optics and Photonics, 2013.

BibTeX | Tags: dictionary learning, imaging, Machine learning, multiscale analysis

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

Bouvrie, Jake; Maggioni, Mauro

Geometric Multiscale Reduction for Autonomous and Controlled Nonlinear Systems Inproceedings

IEEE Conference on Decision and Control (CDC), 2012.

BibTeX | Tags: control theory, geometric wavelets, Machine learning, multiscale analysis

Bouvrie, Jake; Maggioni, Mauro

Multiscale Markov Decision Problems: Compression, Solution, and Transfer Learning Journal Article

2012.

Links | BibTeX | Tags: Machine learning, multiscale analysis, reinforcement learning, representation learning, spectral graph theory, transfer learning

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

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

Maggioni, Mauro; Mhaskar, Hrushikesh

Diffusion polynomial frames on metric measure spaces Journal Article

ACHA, 3 , pp. 329–353, 2008.

BibTeX | Tags: approximation theory, diffusion geometry, heat kernels, Laplacian eigenfunctions, multiscale analysis

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

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; Maggioni, Mauro

Multiscale Analysis of Document Corpora Unpublished

2006, (Technical Report).

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

2005

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

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

Ferrari, S; Maggioni, Mauro; Borghese, N A

Multi-Scale Approximation with Hierarchical Radial Basis Functions Networks, Journal Article

IEEE Trans. on Neural Networks, 15 (1), pp. 178–188, 2004.

BibTeX | Tags: approximation theory, multiscale analysis, radial basis functions

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