## 2019 |

Multiscale regression on intrinsically low-dimensional sets Journal Article in preparation, 2019. |

## 2017 |

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). |

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). |

## 2016 |

Learning adaptive multiscale approximations to data and functions near low-dimensional sets Inproceedings Proceedings of the IEEE Information Theory Workshop, 2016, (Cambridge, UK). |

Multiscale Dictionary Learning: Non-asymptotic Bounds and Robustness Journal Article J. Mach. Learn. Res., 17 (1), pp. 43–93, 2016, ISSN: 1532-4435. |

## 2013 |

Learning of intrinsically low-dimensional stochastic systems in high-dimensions, I Technical Report 2013, (in preparation). |

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). |

## 2012 |

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. |

## 2011 |

Multi-Resolution Geometric Analysis for data in high dimensions Journal Article Proc. FFT 2011, 2011. |

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). |

Polymer reversal rate calculated via locally scaled diffusion map Journal Article J. Chem. Phys., (134), pp. 144108, 2011. |

Determination of reaction coordinates via locally scaled diffusion map Journal Article J. Chem. Phys., (134), pp. 124116, 2011. |

Multiscale Geometric Dictionaries for Point-Cloud Data Inproceedings Proc. SampTA, 2011. |

Multiscale Geometric and Spectral Analysis of Plane Arrangements Inproceedings Conference on Computer Vision and Pattern Recognition, 2011. |

## 2010 |

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). |

Multiscale Geometric Methods for Data Sets III: multiple planes Journal Article in preparation, 2010. |

Multiscale Geometric Wavelets for the Analysis of Point Clouds Journal Article Proc. CISS 2010, 2010. |

## 2009 |

Multiscale Estimation of Intrinsic Dimensionality of Data Sets Inproceedings Proc. A.A.A.I., 2009. |

Estimation of intrinsic dimensionality of samples from noisy low-dimensional manifolds in high dimensions with multiscale $SVD$ Inproceedings Proc. S.S.P., 2009. |

## 2008 |

Geometry Analysis and Signal Processing on Digital Data, Emergent Structures, and Knowledge Building Miscellaneous SIAM News, 2008. |

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)). |

Manifold parametrizations by eigenfunctions of the Laplacian and heat kernels Journal Article Proc. Nat. Acad. Sci., 105 (6), pp. 1803–1808, 2008. |

## 2007 |

Multiscale Data Analysis with Diffusion Wavelets Journal Article Proc. SIAM Bioinf. Workshop, Minneapolis, 2007. |

Proto-value Functions: A Spectral Framework for Solving Markov Decision Processes Journal Article JMLR, 8 , pp. 2169–2231, 2007. |

## 2006 |

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

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

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. |

Multiscale Analysis of Document Corpora Unpublished 2006, (Technical Report). |

Fast Direct Policy Evaluation using Multiscale Analysis of Markov Diffusion Processes Inproceedings ICML 2006, pp. 601–608, 2006. |

Simultaneous Learning of Representation and Control In Continuous Domains Inproceedings AAAI, AAAI Press, 2006. |

## 2005 |

Geometric diffusions for the analysis of data from sensor networks Journal Article Curr Opin Neurobiol, 15 (5), pp. 576–84, 2005. |

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. |

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. |

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. |

Biorthogonal diffusion wavelets for multiscale representations on manifolds and graphs Conference 5914 (1), SPIE, San Diego, CA, USA, 2005. |

Diffusion-driven multiscale analysis on manifolds and graphs: top-down and bottom-up constructions Conference 5914-1 , SPIE, San Diego, CA, USA, 2005. |

## 2004 |

Multiresolution Analysis associated to diffusion semigroups: construction and fast algorithms Technical Report Dept. Comp. Sci., Yale University (YALE/DCS/TR-1289), 2004. |

- 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.