## 2019 |

Adaptive Geometric Multiscale Approximations for Intrinsically Low-dimensional Data Journal Article Journal of machine learning Research, 20 (98), pp. 1-63, 2019. |

## 2017 |

Multiscale Strategies for Discrete Optimal Transport Journal Article Journ. Mach. Learn. Res., (72), pp. 1–32, 2017. |

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). |

## 2013 |

Multiscale dictionaries, transforms, and learning in high-dimensions Inproceedings Proc. SPIE conference Optics and Photonics, 2013. |

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 |

Geometric Multiscale Reduction for Autonomous and Controlled Nonlinear Systems Inproceedings IEEE Conference on Decision and Control (CDC), 2012. |

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

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. |

Diffusion polynomial frames on metric measure spaces Journal Article ACHA, 3 , pp. 329–353, 2008. |

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. |

## 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)). |

Multiscale Analysis of Document Corpora Unpublished 2006, (Technical Report).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

## 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. |

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. |

Multi-Scale Approximation with Hierarchical Radial Basis Functions Networks, Journal Article IEEE Trans. on Neural Networks, 15 (1), pp. 178–188, 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.