## 2020 |

Okada, David Jason Miller; Jonathan Chrispin; Adityo Prakosa; Natalia Trayanova; Steven Jones; Mauro Maggioni; Katherine Wu David R ; C R Substrate Spatial Complexity Analysis for the Prediction of Ventricular Arrhythmias in Patients with Ischemic Cardiomyopathy Journal Article Circulation: Arrhythmia and Electrophysiology, 2020. Links | BibTeX | Tags: imaging, Laplacian eigenfunctions, medical imaging @article{SpatialComplexity1, title = {Substrate Spatial Complexity Analysis for the Prediction of Ventricular Arrhythmias in Patients with Ischemic Cardiomyopathy}, author = {David Jason Miller; Jonathan Chrispin; Adityo Prakosa; Natalia Trayanova; Steven Jones; Mauro Maggioni; Katherine Wu R ; C David R. Okada}, url = {https://www.ahajournals.org/doi/epub/10.1161/CIRCEP.119.007975}, year = {2020}, date = {2020-01-01}, journal = {Circulation: Arrhythmia and Electrophysiology}, keywords = {imaging, Laplacian eigenfunctions, medical imaging}, pubstate = {published}, tppubtype = {article} } |

## 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 @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} } |

## 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} } |

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 @article{MM:DiffusionPolynomialFrames, title = {Diffusion polynomial frames on metric measure spaces}, author = {Mauro Maggioni and Hrushikesh Mhaskar}, year = {2008}, date = {2008-05-01}, journal = {ACHA}, volume = {3}, pages = {329–353}, keywords = {approximation theory, diffusion geometry, heat kernels, Laplacian eigenfunctions, multiscale analysis}, pubstate = {published}, tppubtype = {article} } |

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 @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} } |

Coifman, Ronald R; Kevrekidis, Ioannis G; Lafon, Stephane; Maggioni, Mauro; Nadler, Boaz Diffusion Maps, reduction coordinates and low dimensional representation of stochastic systems Journal Article SIAM J.M.M.S., 7 (2), pp. 842–864, 2008. BibTeX | Tags: diffusion geometry, dynamical systems, Laplacian eigenfunctions, Machine learning, model reduction, stochastic systems @article{CKLMN:DiffusionMapsReductionCoordinates, title = {Diffusion Maps, reduction coordinates and low dimensional representation of stochastic systems}, author = {Ronald R Coifman and Ioannis G Kevrekidis and Stephane Lafon and Mauro Maggioni and Boaz Nadler}, year = {2008}, date = {2008-01-01}, journal = {SIAM J.M.M.S.}, volume = {7}, number = {2}, pages = {842–864}, keywords = {diffusion geometry, dynamical systems, Laplacian eigenfunctions, Machine learning, model reduction, stochastic systems}, pubstate = {published}, tppubtype = {article} } |

## 2007 |

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 @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; 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 @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 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 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 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} } |

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 @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} } |

- 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.