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About Me

About Me
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Curriculum Vitae

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Publications

Leveraging Topology and Geometry in Machine Learning

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Presentations

Teaching

MSc in Applied Mathematics

Published: September 01, 2013

• Dissertation: “Analysis of the Source Trajectory in Cone Beam Micro CT.” Advisor: Prof. Bill Lionheart.

Dissertation Award

Published: May 01, 2014

• Awarded GBP 3000 in funding to carry out dissertation research with industrial collaborators.

PhD in Computing

Published: August 05, 2015

• Thesis: “Utilizing Topological Structures of Data for Machine Learning.” Advisor: Dr. Bei Wang-Phillips.

Graduate Research Assistant

Published: May 16, 2016

• Collaborated with neuroscientists, applying advanced data science techniques in autism research.
  - Developed and implemented novel machine learning and data analysis methods for brain networks.
  - Developed and implemented spectral algorithms for simplicial complexes and hypergraphs.
  - Helped design a visualization tool for DNN interpretability: TopoAct

Foundations of Data Science

Published: August 01, 2018

• Invited to participate as a visiting graduate researcher in the Fall semester program on mathematical foundations of data science.

Postdoctoral Research Associate

Published: October 12, 2020

• Led interdisciplinary collaborative projects consisting of mathematicians, computer scientists and biologists.
  - Developed image analysis techniques for 3D X-Ray scans and 2D RGB images for applications in plant biology.
  - Developed exploratory visual analytics tools to study gene expression data across plant evolution.
  - Guided undergrad and grad student research projects in computational biology.
  - Helped design and publish a novel interactive book introducing python programming to biology students: Plants & Python

Models and Methods for (Hyper) Network Science

Published: June 05, 2022

• Invited to participate in Mathematical Research Communities (MRC)
  - Established continued research collaborations to identify and solve open problems in hyper network science.

Data Scientist II

Published: August 21, 2023

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Kernel partial least squares regression for relating functional brain network topology to clinical measures of behavior

Published in 2016 IEEE 13th International Symposium on Biomedical Imaging (ISBI), 2016

We use topological features to analyze the relationship between functional brain networks and behavioral phenotypes.
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Topological data analysis of functional MRI connectivity in time and space domains

Published in Connectomics in NeuroImaging: Second International Workshop, CNI 2018, 2018

We use TDA to compare fMRI preprocessing strategies, and to analyze spatial vs temporal functional connectivity.
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Revisiting Abnormalities in Brain Network Architecture Underlying Autism Using Topology-Inspired Statistical Inference

Published in Brain Connectivity, 2019

We apply TDA in conjunction with scMRI to study structural and functional brain network abnormalities in ASD.
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Autism classification using topological features and deep learning: A cautionary tale

Published in International Conference on Medical Image Computing and Computer-Assisted Intervention, 2019

We present a cautionary tale about the limited discriminative power of topological features derived from fMRI data in ASD classification.
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Spectral sparsification of simplicial complexes for clustering and label propagation

Published in Journal of Computational Geometry (JoCG), 2020

We show that the theory of Spielman and Srivastava for the sparsification of graphs extends to simplicial complexes via the up Laplacian. We also introduce higher-order generalizations of spectral clustering and label propagation for simplicial complexes
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Utilizing Topological Structures of Data for Machine Learning

Published in The University of Utah ProQuest Dissertations Publishing, 2020

We describe ways to integrate ideas from TDA into different stages of a machine learning pipeline. First we present unsupervised and semisupervised learning algorithms that leverage the topological structure of the data. Then, we describe ways to extract topological features from data and ways to utilize them in classical machine learning models. Lastly, we present methods to compare complex objects such as graphs and their ensembles.
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TopoAct: Visually exploring the shape of activations in deep learning

Published in Computer Graphics Forum, 2021

Applying tools from TDA, we present TopoAct, a visual exploration system to study topological summaries of activation vectors.
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Plants & Python: A series of lessons in coding, plant biology, computation, and bioinformatics

Published in The Plant Cell, 2022

An introductory python programming course for plant biologists published as a JupyterBook.
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Uncertainty Visualization for Graph Coarsening

Published in 2022 IEEE International Conference on Big Data (Big Data)., 2022

We present a framework to quantify and visualize the uncertainty associated with randomized graph reduction techniques.
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Sketching merge trees for scientific data visualization

Published in 2023 Topological Data Analysis and Visualization (TopoInVis), 2023

We develop a framework for sketching a set of merge trees that combines the Gromov-Wasserstein probabilistic matching with techniques from matrix sketching.
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Topological data analysis reveals a core gene expression backbone that defines form and function across flowering plants

Published in PLoS Biology, 2023

We apply mapper to a novel data set of gene expression from diverse species spanning the evolution of flowering plants.
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G-Mapper: Learning a Cover in the Mapper Construction

Published in ArXiv preprint [cs.LG], 2024

We present a G-means clustering-based algorithm that optimizes the cover of a Mapper graph by iteratively splitting it using the Anderson-Darling test of normality.
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Any Graph is a Mapper Graph

Published in ArXiv preprint [cs.CG], 2024

We demonstrate that it is possible to engineer parameters to fit any desired graph to any given dataset.
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Expression-based machine learning models for predicting plant tissue identity

Published in Applications in Plant Sciences, 2024

We examine the ability of models based on Arabidopsis gene expression data to predict tissue identity in other flowering plants.
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Kernel partial least squares regression for relating functional brain network topology to clinical measures of behavior

Published: May 20, 2016

Using topological features to analyze the relationship between functional brain networks and behavioral phenotypes.
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Autism classification using topological features and deep learning: A cautionary tale

Published: October 13, 2019

We present a cautionary tale about the discriminative power of topological features derived from fMRI data in ASD classification.
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TDA + ML: Utilizing Topological Structures of Data for Machine Learning

Published: October 26, 2020

Describing ways to integrate TDA into different stages of a machine learning pipeline.
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The topological shape of gene expression across the evolution of flowering plants

Published: September 30, 2022

Applying mapper to a novel data set of gene expression from diverse species spanning the evolution of flowering plants.
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Leveraging Topological Structure in Data Analysis, Machine Learning, and Visualization

Published: March 24, 2023

Presenting various methods to leverage topological structure in data analysis, machine learning, and visualization.
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Advanced Scientific Computing

, School of Computing, University of Utah, 2016

This was a graduate level course intended to give students exposure to the algorithms and implementations often used in scientific computing. In this course, we touched upon topics such as: computational linear algebra, eigenvalues and singular values, nonlinear systems and optimization, interpolation and approximation, numerical integration and differentiation.
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Computational Topology

, School of Computing, University of Utah, 2017

This was a graduate level course intended to familiarize students with Topological Data Analysis (TDA). In this course we covered basic comcepts, data structures and algorithms commonly used in TDA, Including homology, persistent homology, and mapper. Students learned about the various tools and their applications in machine learning, statistical analysis, and visualization.
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Plants and Python

, Michigan State University, 2020

This is a graduate level course that introduces students to data analysis, algorithmic thinking, model building, bioinformatics, and molecular biology using coding and computational resources. It selects specific examples in which mathematical, modeling, and bioinformatic approaches intersect with the biology of plants. Students apply learned objectives to a course research project.
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