About

Jose Perea is an associate professor in the Khoury College of Computer Sciences and the College of Science at Northeastern University, based in Boston. He holds a PhD in Mathematics from Stanford University and a BS in Mathematics from Universidad del Valle in Colombia. Perea is the inaugural 2022–24 lecturer for the Mathematical Association of America and the National Association of Mathematics. His research interests include data science, machine learning, algorithms, and theory, with a focus on using nonstandard ideas from mathematics to solve problems in these fields. Prior to joining Northeastern, he was an assistant professor at Michigan State University with joint appointments in the departments of computational mathematics, science and engineering, and mathematics. He is passionate about applying mathematical concepts to advance data science and machine learning.

Research topics

• Computer Science
• Artificial Intelligence
• Mathematics
• Algorithm
• Machine Learning
• Pure mathematics
• Physics
• Combinatorics
• Theoretical computer science

Selected publications

• Discrete Approximate Circle Bundles

  arXiv (Cornell University) · 2025-08-18

  preprintOpen accessSenior author

  In this paper, we introduce discrete approximate circle bundles, a class of objects designed to serve as the data science analog of circle bundles from algebraic topology. We show that, under appropriate conditions, one can meaningfully and stably identify a discrete approximate circle bundle with an isomorphism class of true circle bundles. We also describe two cohomology invariants which uniquely determine the isomorphism class of a circle bundle, and provide algorithms to compute them given a discrete approximate representative. Finally, we propose a novel methodology for coordinatization and dimensionality reduction of circle bundle data. To illustrate the practical utility and viability of our algorithms, we present applications to both real and synthetic datasets from computer vision (e.g., modeling optical flow). The paper is accompanied by an open-source software package, with full documentation and tutorials, enabling reproducible implementation of the proposed algorithms and experiments, including those used to generate the figures in this paper.

  PublisherOA PDFDOI

• Revealing brain network dynamics during the emotional state of suspense using TDA

  Network Neuroscience · 2025-01-01

  articleOpen access

  Suspense is an affective state that is ubiquitous in human life, from art to quotidian events. However, little is known about the behavior of large-scale brain networks during suspenseful experiences. To address this question, we examined the continuous brain responses of participants watching a suspenseful movie, along with reported levels of suspense from an independent set of viewers. We employ sliding window analysis and Pearson correlation to measure functional connectivity states over time. Then, we use Mapper, a topological data analysis tool, to obtain a graphical representation that captures the dynamical transitions of the brain across states; this representation enables the anchoring of the topological characteristics of the combinatorial object with the measured suspense. Our analysis revealed changes in functional connectivity within and between the salience, fronto-parietal, and default networks associated with suspense. In particular, the functional connectivity between the salience and fronto-parietal networks increased with the level of suspense. In contrast, the connections of both networks with the default network decreased. Together, our findings reveal specific dynamical changes in functional connectivity at the network level associated with variation in suspense, and suggest topological data analysis as a potentially powerful tool for studying dynamic brain networks.

  PublisherOA PDFDOI

• Topological Data Analysis Based Characteristics of Electroencephalogram Signals in Children With Sleep Apnea

  Journal of Sleep Research · 2025-03-11 · 1 citations

  articleOpen accessSenior author

  ABSTRACT This study aims to identify differences in the functional neural connectivity of the brain of paediatric patients with obstructive sleep apnea. Using EEG signals from 3673 paediatric patients, we grouped subjects into OSA or control groups based on sleep oxygen desaturation levels and apnea‐hypopnea index (AHI), and applied topological data analysis (TDA) techniques. We evaluated our approach through statistical testing of TDA‐based EEG features, which indicate fundamental differences in the functional neural connectivity of subjects with sleep apnea as compared to controls. There were statistically significant differences () between EEG signals taken during apnea and hypopnea events as compared to those taken from healthy controls. No significance was found between the latent EEG signals within the same groups. We observed significant differences between EEG signals collected during oxygen desaturation as compared to the EEG signals of the controls. We additionally identified significant differences between the latent EEG signals (i.e., no oxygen desaturation event occurring) of subjects as compared with the EEGs from controls. Lastly, significant differences were additionally found in the awake before sleep portion of the polysomnograms when grouping subjects based on minimum oxygen saturation experienced during sleep. TDA techniques allow us to identify statistically significant differences between the EEG signals of subjects with OSA and healthy controls, including during awake periods. Our results provide novel insights on the effects of OSA on the central nervous system, and insights into potential novel methods for identification of sleep apnea.

  PublisherOA PDFDOI

• Automated Quantification of Stereotypical Motor Movements in Autism Using Persistent Homology

  bioRxiv (Cold Spring Harbor Laboratory) · 2025-09-05

  preprintOpen access

  Stereotypical motor movements (SMM) are a core diagnostic feature of autism that remain difficult to quantify efficiently and validly across individuals and developmental stages. The current paper presents a novel pipeline that leverages Topological Data Analysis to quantify and characterize recurrent movement patterns. Specifically, we use persistent homology to construct low-dimensional, interpretable feature vectors that capture geometric properties associated with autistic SMM by extracting periodic structure from time series derived from pose estimation landmarks in video data and accelerometer signals from wearable sensors. We demonstrate that these features, combined with simple classifiers, enable accurate automated quantification of autistic SMM. Visualization of the learned feature space reveals that extracted features generalize across individuals and are not dominated by person-specific SMM. Our results highlight the potential of using mathematically principled features to support more scalable, interpretable, and person-agnostic characterization of autistic SMM in naturalistic settings.

  PublisherOA PDFDOI

• \({O({k})}\)-Equivariant Dimensionality Reduction on Stiefel Manifolds

  SIAM Journal on Mathematics of Data Science · 2025-04-09

  articleOpen access
  PublisherDOI

• Move schedules: fast persistence computations in coarse dynamic settings

  Journal of Applied and Computational Topology · 2024-01-20

  articleOpen accessSenior author

  Abstract Matrix reduction is the standard procedure for computing the persistent homology of a filtered simplicial complex with m simplices. Its output is a particular decomposition of the total boundary matrix, from which the persistence diagrams and generating cycles are derived. Persistence diagrams are known to vary continuously with respect to their input, motivating the study of their computation for time-varying filtered complexes. Computing persistence dynamically can be reduced to maintaining a valid decomposition under adjacent transpositions in the filtration order. Since there are $$O(m^2)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mi>m</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math> such transpositions, this maintenance procedure exhibits limited scalability and is often too fine for many applications. We propose a coarser strategy for maintaining the decomposition over a 1-parameter family of filtrations. By reduction to a particular longest common subsequence problem, we show that the minimal number of decomposition updates d can be found in $$O(m \log \log m)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>log</mml:mo><mml:mo>log</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> time and O ( m ) space, and that the corresponding sequence of permutations—which we call a schedule —can be constructed in $$O(d m \log m)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mi>d</mml:mi><mml:mi>m</mml:mi><mml:mo>log</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> time. We also show that, in expectation, the storage needed to employ this strategy is actually sublinear in m . Exploiting this connection, we show experimentally that the decrease in operations to compute diagrams across a family of filtrations is proportional to the difference between the expected quadratic number of states and the proposed sublinear coarsening. Applications to video data, dynamic metric space data, and multiparameter persistence are also presented.

  PublisherOA PDFDOI

• Revealing brain network dynamics during the emotional state of suspense using topological data analysis

  bioRxiv (Cold Spring Harbor Laboratory) · 2024-01-30

  preprintOpen access

  A bstract Suspense is an affective state ubiquitous in human life, from art to quotidian events. However, little is known about the behavior of large-scale brain networks during suspenseful experiences. To address this question, we examined the continuous brain responses of participants watching a suspenseful movie, along with reported levels of suspense from an independent set of viewers. We employ sliding window analysis and Pearson correlation to measure functional connectivity states over time. Then, we use Mapper, a topological data analysis tool, to obtain a graphical representation that captures the dynamical transitions of the brain across states; this representation enables the anchoring of the topological characteristics of the combinatorial object with the measured suspense. Our analysis revealed changes in functional connectivity within and between the salience, fronto-parietal, and default networks associated with suspense. In particular, the functional connectivity between the salience and fronto-parietal networks increased with the level of suspense. In contrast, the connections of both networks with the default network decreased. Together, our findings reveal specific dynamical changes in functional connectivity at the network level associated with variation in suspense, and suggest topological data analysis as a potentially powerful tool for studying dynamic brain networks.

  PublisherOA PDFDOI

• Topological Data Analysis of Electroencephalogram Signals for Pediatric Obstructive Sleep Apnea

  2023-07-24 · 2 citations

  article

  Topological data analysis (TDA) is an emerging technique for biological signal processing. TDA leverages the invariant topological features of signals in a metric space for robust analysis of signals even in the presence of noise. In this paper, we leverage TDA on brain connectivity networks derived from electroencephalogram (EEG) signals to identify statistical differences between pediatric patients with obstructive sleep apnea (OSA) and pediatric patients without OSA. We leverage a large corpus of data, and show that TDA enables us to see a statistical difference between the brain dynamics of the two groups.Clinical relevance- This establishes the potential of topological data analysis as a tool to identify obstructive sleep apnea without requiring a full polysomnogram study, and provides an initial investigation towards easier and more scalable obstructive sleep apnea diagnosis.

  PublisherDOI

• Sliding window persistence of quasiperiodic functions

  Journal of Applied and Computational Topology · 2023-09-05 · 10 citations

  articleSenior author
  PublisherDOI

• Topological Data Analysis of Electroencephalogram Signals for Pediatric Obstructive Sleep Apnea

  arXiv (Cornell University) · 2023-04-28

  preprintOpen access

  Topological data analysis (TDA) is an emerging technique for biological signal processing. TDA leverages the invariant topological features of signals in a metric space for robust analysis of signals even in the presence of noise. In this paper, we leverage TDA on brain connectivity networks derived from electroencephalogram (EEG) signals to identify statistical differences between pediatric patients with obstructive sleep apnea (OSA) and pediatric patients without OSA. We leverage a large corpus of data, and show that TDA enables us to see a statistical difference between the brain dynamics of the two groups.

  PublisherOA PDFDOI

Recent grants

• CDS&E: Collaborative Research: Machine Learning on Dynamical Systems via Topological Features

  NSF · $105k · 2016–2019

Frequent coauthors

• John Harer

  6 shared

• Christopher J. Tralie

  6 shared

• Luis Polanco

  6 shared

• Luis Scoccola

  University of Oxford

  5 shared

• Aarti Sathyanarayana

  Northeastern University

  5 shared

• Steven B. Haase

  Duke University

  4 shared

• Hitesh Gakhar

  University of Oklahoma

  4 shared

• S. Manjunath

  Karnataka Veterinary Animal and Fisheries Sciences University

  3 shared

Education

• PhD, Mathematics

  Stanford University

  2011

Awards & honors

• 2020 NSF CAREER award
• 2020 honoree of Lathisms
• 2018 honoree of Mathematically Gifted and Black
• Inaugural 2022–24 lecturer for the Mathematical Association…