### 2012

Bouvrie, Jake; Maggioni, Mauro

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

In: 2012.

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

@article{BM:MMDPs,

title = {Multiscale Markov Decision Problems: Compression, Solution, and Transfer Learning},

author = {Jake Bouvrie and Mauro Maggioni},

url = {http://arxiv.org/abs/1212.1143},

year = {2012},

date = {2012-01-01},

keywords = {Machine learning, multiscale analysis, reinforcement learning, representation learning, spectral graph theory, transfer learning},

pubstate = {published},

tppubtype = {article}

}

### 2011

Lee, J; Maggioni, Mauro

Multiscale Analysis of Time Series of Graphs Conference

Proc. SampTA, 2011.

BibTeX | Tags: random walks, spectral graph theory

@conference{LM:sampta11,

title = {Multiscale Analysis of Time Series of Graphs},

author = {J Lee and Mauro Maggioni},

year = {2011},

date = {2011-01-01},

booktitle = {Proc. SampTA},

keywords = {random walks, spectral graph theory},

pubstate = {published},

tppubtype = {conference}

}

### 2010

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

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

In: 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

@article{jms:UniformizationEigenfunctions2,

title = {Universal local manifold parametrizations via heat kernels and eigenfunctions of the Laplacian},

author = {Peter W Jones and Mauro Maggioni and Raanan Schul},

year = {2010},

date = {2010-01-01},

journal = {Ann. Acad. Scient. Fen.},

volume = {35},

pages = {1--44},

note = {http://arxiv.org/abs/0709.1975},

keywords = {diffusion geometry, heat kernels, Laplacian eigenfunctions, Manifold Learning, multiscale analysis, random walks, spectral graph theory},

pubstate = {published},

tppubtype = {article}

}

Chen, Guangliang; Maggioni, Mauro

Multiscale Geometric Wavelets for the Analysis of Point Clouds Journal Article

In: Proc. CISS 2010, 2010.

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

@article{CM:geometricwaveletsciss,

title = {Multiscale Geometric Wavelets for the Analysis of Point Clouds},

author = {Guangliang Chen and Mauro Maggioni},

year = {2010},

date = {2010-01-01},

journal = {Proc. CISS 2010},

keywords = {geometric wavelets, Machine learning, Manifold Learning, multiscale analysis, spectral graph theory},

pubstate = {published},

tppubtype = {article}

}

### 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

@misc{CM:SiamNews,

title = {Geometry Analysis and Signal Processing on Digital Data, Emergent Structures, and Knowledge Building},

author = {Ronald R Coifman and Mauro Maggioni},

year = {2008},

date = {2008-11-01},

howpublished = {SIAM News},

keywords = {diffusion geometry, heat kernels, Laplacian eigenfunctions, Manifold Learning, multiscale analysis, random walks, spectral graph theory},

pubstate = {published},

tppubtype = {misc}

}

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

Regularization on Graphs with Function-adapted Diffusion Processes Journal Article

In: 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

@article{SMC:GeneralFrameworkAdaptiveRegularization,

title = {Regularization on Graphs with Function-adapted Diffusion Processes},

author = {Arthur D Szlam and Mauro Maggioni and Ronald R Coifman},

year = {2008},

date = {2008-08-01},

journal = {Jour. Mach. Learn. Res.},

number = {9},

pages = {1711--1739},

note = {(YALE/DCS/TR1365, Yale Univ, July 2006)},

keywords = {diffusion geometry, Machine learning, Manifold Learning, random walks, semisupervised learning, spectral graph theory},

pubstate = {published},

tppubtype = {article}

}

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

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

In: 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

@article{jms:UniformizationEigenfunctions,

title = {Manifold parametrizations by eigenfunctions of the Laplacian and heat kernels},

author = {Peter W Jones and Mauro Maggioni and Raanan Schul},

year = {2008},

date = {2008-02-01},

journal = {Proc. Nat. Acad. Sci.},

volume = {105},

number = {6},

pages = {1803--1808},

keywords = {diffusion geometry, heat kernels, Laplacian eigenfunctions, Manifold Learning, multiscale analysis, random walks, spectral graph theory},

pubstate = {published},

tppubtype = {article}

}

### 2007

Coifman, Ronald R; Maggioni, Mauro

Multiscale Data Analysis with Diffusion Wavelets Journal Article

In: 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

@article{CM:MsDataDiffWavelets,

title = {Multiscale Data Analysis with Diffusion Wavelets},

author = {Ronald R Coifman and Mauro Maggioni},

year = {2007},

date = {2007-04-01},

journal = {Proc. SIAM Bioinf. Workshop, Minneapolis},

keywords = {diffusion geometry, diffusion wavelets, Machine learning, Manifold Learning, multiscale analysis, random walks, spectral graph theory, stochastic systems},

pubstate = {published},

tppubtype = {article}

}

Mahadevan, Sridhar; Maggioni, Mauro

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

In: 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

@article{smmm:jmrl1,

title = {Proto-value Functions: A Spectral Framework for Solving Markov Decision Processes},

author = {Sridhar Mahadevan and Mauro Maggioni},

year = {2007},

date = {2007-01-01},

journal = {JMLR},

volume = {8},

pages = {2169--2231},

keywords = {diffusion geometry, Laplacian eigenfunctions, Machine learning, Manifold Learning, random walks, reinforcement learning, representation learning, spectral graph theory},

pubstate = {published},

tppubtype = {article}

}

### 2006

Coifman, Ronald R; Maggioni, Mauro

Diffusion Wavelets Journal Article

In: 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

@article{CMDiffusionWavelets,

title = {Diffusion Wavelets},

author = {Ronald R Coifman and Mauro Maggioni},

year = {2006},

date = {2006-07-01},

journal = {Appl. Comp. Harm. Anal.},

volume = {21},

number = {1},

pages = {53--94},

note = {(Tech. Rep. YALE/DCS/TR-1303, Yale Univ., Sep. 2004)},

keywords = {diffusion geometry, diffusion wavelets, Machine learning, Manifold Learning, multiscale analysis, random walks, spectral graph theory, stochastic systems},

pubstate = {published},

tppubtype = {article}

}

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

Diffusion Wavelet Packets Journal Article

In: 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

@article{DiffusionWaveletPackets,

title = {Diffusion Wavelet Packets},

author = {James Jr. C Bremer and Ronald R Coifman and Mauro Maggioni and Arthur D Szlam},

year = {2006},

date = {2006-07-01},

journal = {Appl. Comp. Harm. Anal.},

volume = {21},

number = {1},

pages = {95--112},

note = {(Tech. Rep. YALE/DCS/TR-1304, 2004)},

keywords = {diffusion geometry, Machine learning, Manifold Learning, multiscale analysis, random walks, spectral graph theory, stochastic systems},

pubstate = {published},

tppubtype = {article}

}

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

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

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

@inproceedings{CLMKSWZ:GeometrySensorOutputs,

title = {Geometries of sensor outputs, inference, and information processing},

author = {Ronald R Coifman and Stephane Lafon and Mauro Maggioni and Y Keller and A D Szlam and F J Warner and S W Zucker},

editor = {John Zolper; Eds. C Intelligent Integrated Microsystems; Ravindra A. Athale},

year = {2006},

date = {2006-05-01},

booktitle = {Proc. SPIE},

volume = {6232},

pages = {623209},

keywords = {diffusion geometry, Laplacian eigenfunctions, Machine learning, Manifold Learning, random walks, spectral graph theory, stochastic systems},

pubstate = {published},

tppubtype = {inproceedings}

}

Maggioni, Mauro; Mahadevan, Sridhar

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

In: 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

@inproceedings{smmm:FastDirectMDP,

title = {Fast Direct Policy Evaluation using Multiscale Analysis of Markov Diffusion Processes},

author = {Mauro Maggioni and Sridhar Mahadevan},

year = {2006},

date = {2006-01-01},

booktitle = {ICML 2006},

pages = {601--608},

keywords = {diffusion geometry, Laplacian eigenfunctions, Machine learning, Manifold Learning, random walks, reinforcement learning, representation learning, spectral graph theory},

pubstate = {published},

tppubtype = {inproceedings}

}

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

Simultaneous Learning of Representation and Control In Continuous Domains Inproceedings

In: AAAI, AAAI Press, 2006.

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

@inproceedings{smkfsomm:SimLearningReprControlContinuous,

title = {Simultaneous Learning of Representation and Control In Continuous Domains},

author = {Sridhar Mahadevan and Kim Ferguson and Sarah Osentoski and Mauro Maggioni},

year = {2006},

date = {2006-01-01},

booktitle = {AAAI},

publisher = {AAAI Press},

keywords = {diffusion geometry, Laplacian eigenfunctions, Machine learning, Manifold Learning, random walks, reinforcement learning, representation learning, spectral graph theory},

pubstate = {published},

tppubtype = {inproceedings}

}

### 2005

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

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

In: 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

@article{CMZK:CONB,

title = {Geometric diffusions for the analysis of data from sensor networks},

author = {Ronald R Coifman and Mauro Maggioni and Steven W Zucker and Ioannis G Kevrekidis},

year = {2005},

date = {2005-10-01},

journal = {Curr Opin Neurobiol},

volume = {15},

number = {5},

pages = {576--84},

keywords = {diffusion geometry, Laplacian eigenfunctions, Machine learning, Manifold Learning, random walks, spectral graph theory, stochastic systems},

pubstate = {published},

tppubtype = {article}

}

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

In: 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

@article{DiffusionPNAS,

title = {Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps},

author = {Ronald R Coifman and Stephane Lafon and Ann B Lee and Mauro Maggioni and B Nadler and Frederick Warner and Steven W Zucker},

year = {2005},

date = {2005-01-01},

journal = {Proceedings of the National Academy of Sciences of the United States of America},

volume = {102},

number = {21},

pages = {7426-7431},

keywords = {diffusion geometry, Machine learning, Manifold Learning, random walks, spectral graph theory, stochastic systems},

pubstate = {published},

tppubtype = {article}

}

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

In: 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

@article{DiffusionPNAS2,

title = {Geometric diffusions as a tool for harmonic analysis and structure definition of data: Multiscale methods},

author = {Ronald R Coifman and S Lafon and A B Lee and Mauro Maggioni and B Nadler and Frederick Warner and Steven W Zucker},

year = {2005},

date = {2005-01-01},

journal = {Proceedings of the National Academy of Sciences of the United States of America},

volume = {102},

number = {21},

pages = {7432--7438},

keywords = {diffusion geometry, Machine learning, Manifold Learning, multiscale analysis, random walks, spectral graph theory, stochastic systems},

pubstate = {published},

tppubtype = {article}

}

Mahadevan, Sridhar; Maggioni, Mauro

Value Function Approximation with Diffusion Wavelets and Laplacian Eigenfunctions Inproceedings

In: 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

@inproceedings{smmm:ValueFunction,

title = {Value Function Approximation with Diffusion Wavelets and Laplacian Eigenfunctions},

author = {Sridhar Mahadevan and Mauro Maggioni},

year = {2005},

date = {2005-01-01},

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

keywords = {diffusion geometry, diffusion wavelets, Laplacian eigenfunctions, Machine learning, Manifold Learning, random walks, reinforcement learning, representation learning, spectral graph theory},

pubstate = {published},

tppubtype = {inproceedings}

}

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

@conference{MBCS:BiorthogonalDiffusionWavelets,

title = {Biorthogonal diffusion wavelets for multiscale representations on manifolds and graphs},

author = {Mauro Maggioni and James Jr. C Bremer and Ronald R Coifman and Arthur D Szlam},

editor = {Manos Papadakis and Andrew F Laine and Michael A Unser},

url = {http://link.aip.org/link/?PSI/5914/59141M/1},

year = {2005},

date = {2005-01-01},

journal = {Wavelets XI},

volume = {5914},

number = {1},

pages = {59141M},

publisher = {SPIE},

address = {San Diego, CA, USA},

keywords = {diffusion geometry, diffusion wavelets, Machine learning, Manifold Learning, multiscale analysis, random walks, spectral graph theory},

pubstate = {published},

tppubtype = {conference}

}

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

@conference{MSCB:MultiscaleManifoldMethods,

title = {Diffusion-driven multiscale analysis on manifolds and graphs: top-down and bottom-up constructions},

author = {Arthur D Szlam and Mauro Maggioni and Ronald R Coifman and James Jr. C Bremer},

editor = {Manos Papadakis and Andrew F Laine and Michael A Unser},

url = {http://link.aip.org/link/?PSI/5914/59141D/1},

year = {2005},

date = {2005-01-01},

journal = {Wavelets XI},

volume = {5914-1},

pages = {59141D},

publisher = {SPIE},

address = {San Diego, CA, USA},

keywords = {diffusion geometry, diffusion wavelets, Machine learning, Manifold Learning, multiscale analysis, random walks, spectral graph theory},

pubstate = {published},

tppubtype = {conference}

}

### 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

@techreport{CMTech,

title = {Multiresolution Analysis associated to diffusion semigroups: construction and fast algorithms},

author = {Ronald R Coifman and Mauro Maggioni},

year = {2004},

date = {2004-05-01},

number = {YALE/DCS/TR-1289},

institution = {Dept. Comp. Sci., Yale University},

keywords = {diffusion geometry, Machine learning, Manifold Learning, multiscale analysis, random walks, spectral graph theory, stochastic systems},

pubstate = {published},

tppubtype = {techreport}

}

- Lectures at Summer School at Peking University, July 2017.
- PCMI Lectures, Summer 2016: Lecture 1, Lecture 2, Problems/discussion points
- Google Scholar
- Papers on the ArXiv
- Papers on MathsciNet
- Tutorials on diffusion geometry and multiscale analysis on graphs at the MRA Internet Program at IPAM: Part I and Part II.
- Diffusion Geometries, Diffusion Wavelets and Harmonic Analysis of large data sets, IPAM, Multiscale Geometric Analysis Program, Fall 2004.
- Diffusion Geometries, global and multiscale, IPAM, 2005.