Michael J. Catanzaro

Hello!

I am a mathematician turned data scientist interested in solving problems in big data and machine learning. Lately I’ve been working on simplifying machine learning problems using the tools of algebraic topology. Before this, I studied topological data analysis and its applications on a variety of applied problems, ranging from understanding deep perception models to analyzing fMRI data. Once upon a time, I studied stochastic topology and empirical currents as they arise in physics and statistical mechanics.

I am currently a Senior Scientist at Geometric Data Analytics, Inc. Prior to this, I was an Assistant Professor in the mathematics department at Iowa State University, a postdoc at the Unviersity of Florida, and a graduate student at Wayne State University. I earned my PhD in 2016 under the supervision of John Klein and Vladimir Chernyak and was mentored by Peter Bubenik as a postdoc.

I like to do lots of other things besides math, machine learning, and physics.

selected publications

Implications of Data Topology for Deep Generative Models

Jin Yinzhu, Rory McDaniel, Joseph N. Tatro, Michael J. Catanzaro, Abraham D. Smith, Paul Bendich, Matthew B. Dwyer, and P. Thomas Fletcher

Frontiers in Computer Science, 2024

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Topological Parallax: A Geometric Specification for Deep Perception Models

Abraham Smith, Michael Catanzaro, Gabrielle Angeloro, Nirav Patel, and Paul Bendich

In Advances in Neural Information Processing Systems , 2023

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Topological Data Analysis Captures Task-Driven fMRI Profiles in Individual Participants: A Classification Pipeline Based on Persistence

Michael J. Catanzaro, Sam Rizzo, John Kopchick, Asadur Chowdury, David R Rosenberg, Peter Bubenik, and Vaibhav A Diwadkar

Neuroinformatics, Nov 2023

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BOLD-based fMRI is the most widely used method for studying brain function. The BOLD signal while valuable, is beset with unique vulnerabilities. The most notable of these is the modest signal to noise ratio, and the relatively low temporal and spatial resolution. However, the high dimensional complexity of the BOLD signal also presents unique opportunities for functional discovery. Topological Data Analyses (TDA), a branch of mathematics optimized to search for specific classes of structure within high dimensional data may provide particularly valuable applications. In this investigation, we acquired fMRI data in the anterior cingulate cortex (ACC) using a basic motor control paradigm. Then, for each participant and each of three task conditions, fMRI signals in the ACC were summarized using two methods: a) TDA based methods of persistent homology and persistence landscapes and b) non-TDA based methods using a standard vectorization scheme. Finally, using machine learning (with support vector classifiers), classification accuracy of TDA and non-TDA vectorized data was tested across participants. In each participant, TDA-based classification out-performed the non-TDA based counterpart, suggesting that our TDA analytic pipeline better characterized task- and condition-induced structure in fMRI data in the ACC. Our results emphasize the value of TDA in characterizing task- and condition-induced structure in regional fMRI signals. In addition to providing our analytical tools for other users to emulate, we also discuss the unique role that TDA-based methods can play in the study of individual differences in the structure of functional brain signals in the healthy and the clinical brain.