Research

My overall research goal is to develop fast, effective, theoretically-grounded algorithms to power data science applications. At the moment, my focus is on improving algorithms for dynamic clustering and similarity search.

All Publications

ICML 2026

Fully Dynamic Coreset Spectral Clustering

Ben Jourdan, Peter Macgregor, Gregory Schwartzman

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ICML 2025

Dynamic Similarity Graph Construction with Kernel Density Estimation

Steinar Laenen, Peter Macgregor, and He Sun

@inproceedings{laenen2025dynamic,
  title = {{Dynamic Similarity Graph Construction with Kernel Density Estimation}},
  booktitle = {42nd {{International Conference on Machine Learning}} ({{ICML}}'25)},
  author = {Steinar Laenen and Peter Macgregor and He Sun},
  year = {2025}
}

arXiv code

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ICLR 2025

Coreset Spectral Clustering

Ben Jourdan, Gregory Schwartzman, Peter Macgregor, and He Sun

@inproceedings{jourdan2025coreset,
  title = {{Coreset Spectral Clustering}},
  booktitle = {13th {{International Conference on Learning Representations}} ({{ICLR}}'25)},
  author = {Ben Jourdan and Gregory Schwartzman and Peter Macgregor and He Sun},
  year = {2025}
}

arXiv conference code

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AISTATS 2025

Dynamic DBSCAN with Euler Tour Sequences

Seiyun Shin, Ilan Shomorony, and Peter Macgregor

@inproceedings{shin2025dynamic,
  title = {Dynamic DBSCAN with Euler Tour Sequences},
  booktitle = {28th {{International Conference on Artificial Intelligence and Statistics}} ({{AISTATS}}'25)},
  author = {Seiyun Shin and Ilan Shomorony and Peter Macgregor},
  year = {2025}
}

arXiv conference code

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Tech. Report

Spectral Toolkit of Algorithms for Graphs: Technical Report (2)

Peter Macgregor and He Sun

@article{stag_report_2,
  author       = {Peter Macgregor and He Sun},
  title        = {Spectral Toolkit of Algorithms for Graphs: Technical Report {(2)}},
  journal      = {CoRR},
  volume       = {abs/2407.07096},
  year         = {2024},
  doi          = {10.48550/arXiv.2407.07096},
  eprinttype    = {arXiv},
  eprint       = {2407.07096},
}  

arXiv PDF code

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Preprint

Polynomial-Time Algorithms for Weaver's Discrepancy Problem in a Dense Regime

Ben Jourdan, Peter Macgregor, and He Sun

@misc{jourdan2024polynomialtime,
  title={Polynomial-Time Algorithms for Weaver's Discrepancy Problem in a Dense Regime}, 
  author={Ben Jourdan and Peter Macgregor and He Sun},
  year={2024},
  eprint={2402.08545},
  archivePrefix={arXiv},
  primaryClass={cs.DS}
}

arXiv

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NeurIPS 2023 Spotlight

Fast Approximation of Similarity Graphs with Kernel Density Estimation

Peter Macgregor and He Sun

@inproceedings{macgregorKDESimilarityGraph2023,
  title = {Fast Approximation of Similarity Graphs with Kernel Density Estimation},
  booktitle = {36th {{Advances}} in {{Neural Information Processing Systems}} ({{NeurIPS}}'23)},
  author = {Peter Macgregor and He Sun},
  year = {2023}
}

arXiv conference talk code

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NeurIPS 2023

Fast and Simple Spectral Clustering in Theory and Practice

Peter Macgregor

@inproceedings{macgregorFastSpectralClustering2023,
  title = {Fast and Simple Spectral Clustering in Theory and Practice},
  booktitle = {36th {{Advances}} in {{Neural Information Processing Systems}} ({{NeurIPS}}'23)},
  author = {Macgregor, Peter},
  year = {2023}
}

arXiv conference talk code

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ISAAC 2023

Is the Algorithmic Kadison-Singer Problem Hard?

Ben Jourdan, Peter Macgregor, and He Sun

@InProceedings{jourdan_et_al:LIPIcs.ISAAC.2023.43,
  author =	{Jourdan, Ben and Macgregor, Peter and Sun, He},
  title =	{{Is the Algorithmic Kadison-Singer Problem Hard?}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{43:1--43:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-289-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{283},
  editor =	{Iwata, Satoru and Kakimura, Naonori},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.43},
  URN =		{urn:nbn:de:0030-drops-193457},
  doi =		{10.4230/LIPIcs.ISAAC.2023.43},
  annote =	{Keywords: Kadison-Singer problem, spectral sparsification}
}

arXiv conference

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Tech. Report

Spectral Toolkit of Algorithms for Graphs: Technical Report (1)

Peter Macgregor and He Sun

@article{stag_report_1,
  author       = {Peter Macgregor and He Sun},
  title        = {Spectral Toolkit of Algorithms for Graphs: Technical Report {(1)}},
  journal      = {CoRR},
  volume       = {abs/2304.03170},
  year         = {2023},
  doi          = {10.48550/arXiv.2304.03170},
  eprinttype    = {arXiv},
  eprint       = {2304.03170},
}  

arXiv PDF code

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ICML 2022

A Tighter Analysis of Spectral Clustering, and Beyond

Peter Macgregor and He Sun

@inproceedings{macgregorTighterAnalysisSpectral2022,
  title = {A Tighter Analysis of Spectral Clustering, and Beyond},
  booktitle = {39th {{International Conference}} on {{Machine Learning}} ({{ICML}}'22)},
  author = {Macgregor, Peter and Sun, He},
  year = {2022},
  pages = {14717--14742}
}

arXiv conference talk code

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NeurIPS 2021

Finding Bipartite Components in Hypergraphs

Peter Macgregor and He Sun

@inproceedings{macgregorFindingBipartiteComponents2021,
  title = {Finding Bipartite Components in Hypergraphs},
  booktitle = {34th {{Advances}} in {{Neural Information Processing Systems}} ({{NeurIPS}}'21)},
  author = {Macgregor, Peter and Sun, He},
  year = {2021},
  pages = {7912--7923}
}

arXiv conference talk code

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ICML 2021 Oral

Local Algorithms for Finding Densely Connected Clusters

Peter Macgregor and He Sun

@inproceedings{macgregorLocalAlgorithmsFinding2021,
  title = {Local Algorithms for Finding Densely Connected Clusters},
  booktitle = {38th {{International Conference}} on {{Machine Learning}} ({{ICML}}'21)},
  author = {Macgregor, Peter and Sun, He},
  year = {2021},
  pages = {7268--7278}
}

arXiv conference talk code demo

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PhD Thesis

On Learning the Structure of Clusters in Graphs

Peter Macgregor, University of Edinburgh, 2022

@phdthesis{macgregorLearningStructureClusters2022,
  title = {On Learning the Structure of Clusters in Graphs},
  author = {Macgregor, Peter},
  year = {2022},
  school = {University of Edinburgh}
}

arXiv University version

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