# Mauro Maggioni

- Research Professor of Mathematics

**External address:**117 Physics Bldg, Office #293, Durham, NC 27708

**Internal office address:**319 Gross Hall, Information Initiative at Duke, Durham, NC 27708

**Phone:**(919) 660-2825

### Research Areas and Keywords

##### Analysis

##### Computational Mathematics

##### PDE & Dynamical Systems

##### Probability

I am interested in novel constructions inspired by classical harmonic analysis that allow to analyse the geometry of manifolds and graphs and functions on such structures. These constructions are motivated by several important applications across many fields. In many situations we are confronted with large amounts of apparently unstructured high-dimensional data. I find fascinating to study the intrinsic geometry of such data, and exploiting in order to study, explore, visualize, characterize statistical properties of the data. Oftentimes such data is modeled as a manifold (or something "close to a manifold") or a graph, and functions on these spaces need to approximated or "learned" from the data and experiments on the data. For example each data point could be a document, a graph associated with the documents could be given by for example hyperlinks, or by similarity of word frequencies, and a function on the set of documents would be how interesting I personally score a document. One may wish to learn how to predict how much I would score documents I have not seen yet. This can be cast as an approximation problem on the graph of documents, and it turns out that one can generalize Euclidean-type approximation techniques (in particular multiscale regression techniques) to tackle this problem. An application of the above techniques that I find particularly interesting is Markov Decision Processes and Reinforcement Learning, where the problem of learning a behaviour from experience is cast in a rather general optimization and learning framework that involves approximations of functions and operators on graphs and manifolds. I am also interested in imaging, in particular I am working on novel classes of nonlinear denoising algorithms, based on diffusion processes on graphs of features built from images. Another interest is in the geometry of multiscale dynamical systems, and the construction of algorithms for the empirical construction of approximate equations for such systems. I also work on hyperspectral imaging, in particular in building automatic classifiers for discriminating normal from cancerous biopsies, for automated diagnostics and pathology.

AMS Fellow. AMS. January 2013

Sloan Fellowship. Sloan Foundation. March 2008

Dimension Reduction for Open Quantum Systems awarded by Stanford University (Principal Investigator). 2016 to 2020

BIGDATA:Collaborative Research:F:From Data Geometries to Information Networks awarded by National Science Foundation (Principal Investigator). 2016 to 2019

Statistical learning for high-dimensional stochastic dynamical systems awarded by National Science Foundation (Principal Investigator). 2015 to 2018

EMSW21-RTG: Geometric, Topological awarded by National Science Foundation (Co-Principal Investigator). 2011 to 2018

Collaborative Research: SI2-CHE-ExTASY Extensible Tools for Advanced Sampling and AnalYsis awarded by National Science Foundation (Principal Investigator). 2013 to 2017

ATD: Online Multiscale Algorithms for Geometric Density Estimation in High-Dimensions and Persistent Homology of Data fo awarded by National Science Foundation (Principal Investigator). 2012 to 2017

Structured Dictionary Models and Learning for High Resolution Images awarded by National Science Foundation (Principal Investigator). 2013 to 2017

Geometric Approximation and Estimation of Probability Measures in High Dimensions awarded by Air Force Office of Scientific Research (Principal Investigator). 2013 to 2016

Multiscale Analysis of Dynamic Graphs awarded by Office of Naval Research (Principal Investigator). 2012 to 2016

X-Ray Scatter and Phase Imaging for Explosive Detection awarded by US Department of Homeland Security (Co-Principal Investigator). 2011 to 2015

## Pages

Chen, G, Little, AV, and Maggioni, M. "Multi-resolution geometric analysis for data in high dimensions." *Excursions in Harmonic Analysis: The February Fourier Talks at the Norbert Wiener Center.* January 1, 2013. 259-285.
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Little, AV, Maggioni, M, and Rosasco, L. "Multiscale geometric methods for data sets I: Multiscale SVD, noise and curvature (Accepted)." *Applied and Computational Harmonic Analysis* 43.3 (November 2017): 504-567.
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Bongini, M, Fornasier, M, Hansen, M, and Maggioni, M. "Inferring interaction rules from observations of evolutive systems I: The variational approach." *Mathematical Models and Methods in Applied Sciences* 27.05 (May 2017): 909-951.
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Crosskey, M, and Maggioni, M. "ATLAS: A Geometric Approach to Learning High-Dimensional Stochastic Systems Near Manifolds." *Multiscale Modeling & Simulation* 15.1 (January 2017): 110-156.
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Wang, Y, Chen, G, and Maggioni, M. "High-Dimensional Data Modeling Techniques for Detection of Chemical Plumes and Anomalies in Hyperspectral Images and Movies." *IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing* 9.9 (September 2016): 4316-4324.
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Goetzmann, WN, Jones, PW, Maggioni, M, and Walden, J. "Beauty is in the bid of the beholder: An empirical basis for style." *Research in Economics* 70.3 (September 2016): 388-402.
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Maggioni, M, Minsker, S, and Strawn, N. "Multiscale dictionary learning: Non-asymptotic bounds and robustness." *Journal of Machine Learning Research* 17 (January 1, 2016).

Maggioni, M. "Geometry of Data and Biology." *Notices of the American Mathematical Society* 62.10 (November 1, 2015): 1185-1188.
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Altemose, N, Miga, KH, Maggioni, M, and Willard, HF. "Genomic characterization of large heterochromatic gaps in the human genome assembly." *PLoS computational biology* 10.5 (May 15, 2014): e1003628-.
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Coppola, A, Wenner, BR, Ilkayeva, O, Stevens, RD, Maggioni, M, Slotkin, TA, Levin, ED, and Newgard, CB. "Branched-chain amino acids alter neurobehavioral function in rats." *Am J Physiol Endocrinol Metab* 304.4 (February 15, 2013): E405-E413.
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Maggioni, M. "Geometric estimation of probability measures in high-dimensions." *Conference Record - Asilomar Conference on Signals, Systems and Computers* (January 1, 2013): 1363-1367.
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## Pages

Tomita, TM, Maggioni, M, and Vogelstein, JT. "ROFLMAO: Robust oblique forests with linear MAtrix operations." January 1, 2017.

Liao, W, Maggioni, M, and Vigogna, S. "Learning adaptive multiscale approximations to data and functions near low-dimensional sets." October 21, 2016. Full Text

Yin, R, Monson, E, Honig, E, Daubechies, I, and Maggioni, M. "Object recognition in art drawings: Transfer of a neural network." May 18, 2016. Full Text

Maggioni, M, Minsker, S, and Strawn, N. "Geometric multi-resolution analysis for dictionary learning." January 1, 2015. Full Text

Gerber, S, and Maggioni, M. "Multiscale dictionaries, transforms, and learning in high-dimensions." 2013. Full Text

Chen, G, Iwen, MA, Chin, S, and Maggioni, M. "A fast multiscale framework for data in high-dimensions: Measure estimation, anomaly detection, and compressive measurements." IEEE, 2012. Full Text

Bouvrie, JV, and Maggioni, M. "Geometric multiscale reduction for autonomous and controlled nonlinear systems." IEEE, 2012. Full Text