Research

Recent research news:

Archived news:

Mathematics Faculty Develops Algorithms with Predictive Capabilities interviewed by LMU Newsroom

My research lies at the intersection of computational graph theory, network analysis, machine learning, and data science. I focus on developing interdisciplinary mathematical and computational methods for broad applications to biology and social networks, often collaborating with domain scientists. My work is both theoretical and applied, frequently data-driven, and can be broadly classified into the following areas.

SELECTED PUBLICATIONS: (see full list on my Google Scholar Page)

Scientific Computing:

Faster Hodgerank Approximation Algorithm for Statistical Ranking and User Recommendation Problems

Shelby Ferrier, Junyuan Lin, and Guangpeng Ren.

Advances in Data Science. Association for Women in Mathematics Series, vol 37. Springer, Cham.

https://doi.org/10.1007/978-3-031-87804-6_7. 2025

Proposed method with pseudo-nodes

Proposed methods' CPU computational performances on Erdos-Renyi graph

Implementation of 1/2-Approximation Path Cover Algorithm and Its Empirical Analysis

Junyuan Lin and Guangpeng Ren

2024 Hawaii University International Conferences on STEM/STEAM and Education Conference Preceedings , Article 14, 2024. Online Publication

Solving Graph Laplacians via Multilevel Sparsifiers

Xiaozhe Hu, Junyuan Lin*

*Corresponding Author

SIAM J. Sci. Comput., S378-S400 (2023)

Full Text: https://epubs.siam.org/doi/abs/10.1137/22M1503932

An example of spanning positive subgraph preconditioner

kNN Graph Construction: the Overlap Method

Random-Walk Based Approximate k-Nearest Neighbors Algorithm for Diffusion State Distance

Lenore J. Cowen, Xiaozhe Hu, Junyuan Lin, Yue Shen, Kaiyi Wu

International Conference on Large-Scale Scientific Computing, Volume 13127, pp 3-15 (2021)

Full Text: https://link.springer.com/chapter/10.1007/978-3-030-97549-4_1

Invited paper

cover.mp4

Finding 1/2-approximated path cover

An Adaptive Algebraic Multigrid Method Based on Path Cover

Xiaozhe Hu, Junyuan Lin*, Ludmil Zikatanov

*Corresponding Author

SIAM J. Sci. Comput., 41(5), S220–S241. (2019)

Full Text: https://epubs.siam.org/doi/abs/10.1137/18M1194493

Awarded Best Student Paper at the 15th Copper Mountain Conference on Iterative Methods

Histograms of pairwise distance distributions using shortest path metric (left) vs. using the diffusion state distance metric (right)

Computing the Diffusion State Distance on Graphs via Algebraic Multigrid and Random Projections

Junyuan Lin, Lenore J. Cowen, Ben Hescott, Xiaozhe Hu

Numer Linear Algebra Appl. 2018; e2156.

Full Text: doi.org/10.1002/nla.2156 (PDF)

Potential Voter Proﬁle

Algebraic Multigrid for Least Squares Problems on Graphs with Applications to HodgeRank

Charles Colley, Junyuan Lin, Xiaozhe Hu, Shuchin Aeron

2017 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW)

Full Text: doi: 10.1109/IPDPSW.2017.163 (PDF)

Graph-based Machine Learning and Network Analysis:

Structure-Aware Content Classication on Social Networks via Diffusion Graph Learning and LLMs

Cameron Hajaliloo, Cameron Scolari, Sophie Kadifa, Lanyu Shang, Junyuan Lin

2025 IEEE International Conference on Big Data, pp. 8237-8241. Online Publication.

Overview of DSD-enhanced analysis pipeline

GraphRAG Knowledge Graph of the Serial Podcast

Narrative Analysis of True Crime Podcasts With Knowledge Graph-Augmented Large Language Models

James Chapman, Xinyi Leng, Jason Liang, Jack Mauro, Xu Wang, Andrea Bertozzi, Junyuan Lin, Bohan Chen, Chenchen Ye, Temple Daniel and P. Jerey Brantingham

The 33rd ACM International Conference on Information and Knowledge Management, 2024

Hate speech and hate crimes: a data-driven study of evolving discourse around marginalized groups

Malvina Bozhidarova, Jonathn Chang, Aaishah Ale-Rasool, Yuxiang Liu, Chongyao Ma, Andrea L Bertozzi, P Jeffrey Brantingham, Junyuan Lin, Sanjukta Krishnagopal

2023 IEEE International Conference on Big Data

Full Text: https://ieeexplore.ieee.org/abstract/document/10386312/

The knowledge graph ontology for hate speech and hate crime datasets

Hierarchical clustering of QAnon-related topics from BERTopic

Knowledge Graphs of the QAnon Twitter Network

Clay Adams, Malvina Bozhidarova, James Chen, Andrew Gao, Zhengtong Liu, J. Hunter Priniski, Junyuan Lin, Rishi Sonthalia, Andrea L. Bertozzi, P. Jeffrey Brantingham

2022 IEEE International Conference on Big Data

Full Text: https://ieeexplore.ieee.org/abstract/document/10021128

An Analysis of COVID-19 Knowledge Graph Construction and Applications

Dominic Flocco, Bryce Palmer-Toy, Ruixiao Wang, Hongyu Zhu, Rishi Sonthalia, Junyuan Lin, Andrea L. Bertozzi, P. Jeffrey Brantingham

2021 IEEE International Conference on Big Data

Full Text: https://ieeexplore.ieee.org/abstract/document/9671479

General structure of knowledge graph with an underlying social network of tweets at the center and external information and tweet attributes surrounding the network

Assessment of network module identification across complex diseases

Sarvenaz Choobdar, Mehmet E Ahsen, Jake Crawford, Mattia Tomasoni, David Lamparter, Junyuan Lin, Ben Hescott, Xiaozhe Hu, Johnathan Mercer, Ted Natoli, Rajiv Narayan, The DREAM Module Identification Challenge Consortium, Aravind Subramanian, Jitao D. Zhang, Gustavo Stolovitzky, Zoltan Kutalik, Kasper Lage, Donna K Slonim, Julio Saez-Rodriguez, Lenore J. Cowen, Sven Bergmann, Daniel Marbach

Nature Methods, volume 16, pages 843–852 (2019)

Full Text: https://www.nature.com/articles/s41592-019-0509-5

A Double Spectral Approach to DREAM 11 Subchallenge 3

Jake Crawford, Junyuan Lin, Xiaozhe Hu, Ben Hescott, Donna Slonim, Lenore J. Cowen

2017 Sage Bionetworks, 7 Oct. 2016 Published. Web.

Full Text: syn7349492

Awarded Best Performer in 2016 Disease Module Identification DREAM Challenge

Team Tusk (Jake Crawford, Junyuan Lin, Xiaozhe Hu, Ben Hescott, Donna Slonim, Lenore J. Cowen) ranked No.1 in 2016 Disease Module Identification DREAM Challenge

Mathematical Modelling:

Proposed process changes and software implementation framework

Impact of Telehealth on Health Disparities Associated With Travel Time to Hospital for Patients With Recurrent Admissions: 4-Year Panel Data Analysis,

Youyou Tao, Ace Vo, Dezhi Wu, Junyuan Lin, Kala Seal, Abhay Mishra, Arindam Brahma.

Journal of Medical Internet Research, 26(1), Article e63661, 2024.

Full Text: https://doi.org/10.2196/63661

plane_emo20s.mp4

Plane Evacuation Simulation with Emotion Factor

A Particle Swarm Optimization Model of Emergency Airplane Evacuations with Emotion

Junyuan Lin, Timothy Lucas

Applied Math Journal Networks and Heterogeneous Media, Volume 10, Issue 3, (2015): 631-646.

Full Text: doi: 10.3934/nhm.2015.10.631 (PDF)

SOFTWARE PACKAGE:

Path Cover Adaptive Algebraic Multigrid Solver for Graph Laplacians

Authors: Xiaozhe Hu, Junyuan Lin and Ludmil Zikantonov

Link: https://github.com/XiaozheHu/Multilevel_Subgraph_Preconditioner

Reference: An Adaptive Algebraic Multigrid Method Based on Path Cover

1/2 approximation path cover algorithm

Authors: Guangpeng Ren and Junyuan Lin

Link: https://github.com/George-the-Ren/12_Optimization/tree/main

Reference: Implementation of 1/2-Approximation Path Cover Algorithm and Its Empirical Analysis

Knowledge Graph for COVID-19 Twitter Network

Authors: Dominic Flocco, Bryce Palmer-Toy, Ruixiao Wang, Hongyu Zhu, Rishi Sonthalia, Junyuan Lin, Andrea L. Bertozzi, P. Jeffrey Brantingham

Link: https://github.com/dominicflocco/Twitter-COVID-19-Knowledge-Graph

Reference: An Analysis of COVID-19 Knowledge Graph Construction and Applications

Knowledge Graph for QAnon Twitter Network

Authors: Clay Adams, Malvina Bozhidarova, James Chen, Andrew Gao, Zhengtong Liu, J. Hunter Priniski, Junyuan Lin, Rishi Sonthalia, Andrea L. Bertozzi, P. Jeffrey Brantingham

Link: https://github.com/rsonthal/kg-twitter-reu

Reference: Knowledge Graphs of the QAnon Twitter Network

Knowledge Graph for hate speech and hate crimes data sets

Authors: Malvina Bozhidarova, Jonathn Chang, Aaishah Ale-Rasool, Yuxiang Liu, Chongyao Ma, Andrea L Bertozzi, P Jeffrey Brantingham, Junyuan Lin, Sanjukta Krishnagopal

Link: https://github.com/jimliu01/kg-twitter-hate-crimes

Reference: Hate speech and hate crimes: a data-driven study of evolving discourse around marginalized groups

POSTERS:

Predictive Models for Sports Readiness: A Data-Driven Analysis of Collegiate Female Soccer Players

Presented at:

2024 Southern California Applied Mathematics Symposium, University of San Diego (Poster prize winner)

An AMG Approach in Solving Graph Laplacians of Protein Networks based on DSD Metrics

Presented at:

2019 Joint Mathematics Meetings (JMM), Baltimore, MD.

2018 MAA MATHFEST, Denver, CO.

2017 SIAM Annual Meeting, AWM workshop, Pittsburgh, PA.

2017 Computational Aspects of Biological Information, Microsoft Research, Cambridge, MA.

Data Intensive Studies Center Fall 2017 Symposium, Tufts University, Medford, MA.

Applied Math Days 2017, Rensselaer Polytechnic Institute, Troy, NY.

Graduate Student Research Symposium, Tufts University, Medford, MA.

A Contagion Model of Emergency Airplane Evacuations

Presented at MAA Undergraduate Poster Session, 2014 Joint Mathematics Meetings, Baltimore, MD. (Outstanding Poster Winner)

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