Mathieu Carrière

Books and Lecture Notes

Analyse topologique de données M.C., Vincent Humilière and Steve Oudot To appear in the Journées Mathématiques X-UPS, Éditions de l'École Polytechnique, 2024 Draft

Computational Topology

Sparsification of the generalized persistence diagrams for scalability through gradient descent M.C., Seunghyun Kim and Woojin Kim Preprint, 2024 arXiv, HAL, code

Fast, stable and efficient approximation of multi-parameter persistence modules with MMA David Loiseaux, M.C. and Andrew Blumberg Preprint, 2022 arXiv, HAL, code

On the metric distortion of embedding persistence diagrams into separable Hilbert spaces M.C. and Ulrich Bauer Proceedings of the International Symposium on Computational Geometry (SoCG), 2019 arXiv

Local equivalence and intrinsic metrics between Reeb graphs M.C. and Steve Oudot Proceedings of the International Symposium on Computational Geometry (SoCG), 2017 arXiv, HAL

Structure and stability of the 1-dimensional Mapper M.C. and Steve Oudot Foundations of Computational Mathematics (FoCM), 2017 Proceedings of the International Symposium on Computational Geometry (SoCG), 2016 arXiv, HAL (proceedings), HAL (journal)

Machine Learning

Resampling and averaging coordinates on data Andrew Blumberg, M.C., Jun Hou Fung and Michael Mandell Preprint, 2024 arXiv, HAL, code

Stable vectorization of multiparameter persistent homology using signed barcodes as measures David Loiseaux, Luis Scoccola, M.C., Magnus Botnan and Steve Oudot Proceedings of the Conference on Neural Information Processing Systems (NeurIPS), 2023 arXiv, HAL, code

A framework for fast and stable representations of multiparameter persistent homology decompositions David Loiseaux, M.C. and Andrew Blumberg Proceedings of the Conference on Neural Information Processing Systems (NeurIPS), 2023 arXiv, HAL, code

Multiparameter persistence image for topological machine learning M.C. and Andrew Blumberg Proceedings of the Conference on Neural Information Processing Systems (NeurIPS), 2020 HAL, code

Sliced Wasserstein kernel for persistence diagrams M.C., Marco Cuturi and Steve Oudot Proceedings of the International Conference on Machine Learning (ICML), 2017 arXiv, HAL, code

Deep Learning

MAGDiff: covariate data set shift detection via activation graphs of neural networks Felix Hensel, Charles Arnal, M.C., Théo Lacombe, Hiroaki Kurihara, Yuichi Ike and Frédéric Chazal Transactions on Machine Learning Research (TMLR), 2024 arXiv, HAL, code

RipsNet: a general architecture for fast and robust estimation of the persistent homology of point clouds Thibault de Surrel, Felix Hensel, M.C., Théo Lacombe, Yuichi Ike, Hiroaki Kurihara, Marc Glisse and Frédéric Chazal Proceedings of Topological, Algebraic, and Geometric Learning Workshops, 2022 arXiv, HAL, code

Topological Uncertainty: monitoring trained neural networks through persistence of activation graphs Théo Lacombe, Yuichi Ike, M.C., Frédéric Chazal, Marc Glisse and Yuhei Umeda Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI), 2021 arXiv, HAL, code

PersLay: a neural network layer for persistence diagrams and new graph topological signatures M.C., Frédéric Chazal, Yuichi Ike, Théo Lacombe, Martin Royer and Yuhei Umeda Proceedings of the International Conference on Artificial Intelligence and Statistics (AISTATS), 2020 arXiv, HAL, code, legacy code

Statistics

Statistical analysis of Mapper for stochastic and multivariate filters M.C. and Bertrand Michel Journal of Applied and Computational Topology (JACT), 2022 arXiv, HAL, code

Statistical analysis and parameter selection for Mapper M.C., Bertrand Michel and Steve Oudot Journal of Machine Learning Research (JMLR), 2018 arXiv, HAL, code

Optimization

Diffeomorphic interpolation for efficient persistence-based topological optimization M.C., Marc Theveneau and Théo Lacombe To appear in the Proceedings of the Conference on Neural Information Processing Systems (NeurIPS), 2024 arXiv, HAL

Differentiability and optimization of multiparameter persistent homology Siddharth Setlur, Luis Scoccola, David Loiseaux, M.C. and Steve Oudot Proceedings of the International Conference on Machine Learning (ICML), 2024 arXiv, HAL, code

Differentiable Mapper for topological optimization of data representation Ziyad Oulhaj, M.C. and Bertrand Michel Proceedings of the International Conference on Machine Learning (ICML), 2024, oral presentation (top ~6%) arXiv, HAL, code

A gradient sampling algorithm for stratified maps with applications to topological data analysis Jacob Leygonie, M.C., Théo Lacombe and Steve Oudot Mathematical Programming, 2023 arXiv, HAL, code

Optimizing persistent homology based functions M.C., Frédéric Chazal, Marc Glisse, Yuichi Ike and Hariprasad Kannan Proceedings of the International Conference on Machine Learning (ICML), 2021, oral presentation (top ~3%) arXiv, HAL, code (layer 1, layer 2, layer 3), legacy code

Computational Biology

Statistical estimation of sparsity and efficiency for molecular codes Jun Hou Fung, M.C. and Andrew Blumberg Preprint, 2024 biorXiv, HAL, code

Topological Data Analysis and its usefulness for precision medicine studies Raquel Iniesta, Ewan Carr, M. C., Naya Yerolemou, Bertrand Michel and Frédéric Chazal Statistics and Operations Research Transactions (SORT), 2022 HAL, code

Identifying homogeneous subgroups of patients and important features: a topological machine learning approach Ewan Carr, M.C., Bertrand Michel, Frédéric Chazal and Raquel Iniesta BMC Bioinformatics, 2021 HAL, code

Topology identifies emerging adaptive mutations in SARS-CoV-2 Michael Bleher, Lukas Hahn, Juan Ángel Patiño-Galindo, M.C., Ulrich Bauer, Raúl Rabadán and Andreas Ott Preprint, 2021 medrXiv, arXiv, HAL

MREC: a fast and versatile framework for aligning and matching point clouds with applications to single cell molecular data Andrew Blumberg, M.C., Michael Mandell, Raúl Rabadán and Soledad Villar Preprint, 2020 arXiv, code

Persistent homology based characterization of the breast cancer immune microenvironment: a feasibility study Andrew Aukerman, M.C., Chao Chen, Kevin Gardner, Raúl Rabadán and Rami Vanguri Journal of Computational Geometry (JoCG), 2022 Proceedings of the International Symposium on Computational Geometry (SoCG), 2020 HAL

Two-Tier Mapper: a user-independent clustering method for global gene expression analysis based on topology Rachel Jeitziner, M.C., Jacques Rougemont, Steve Oudot, Kathryn Hess and Cathrin Brisken Bioinformatics, 2019 arXiv, code

Topological data analysis of single-cell Hi-C contact maps M.C. and Raúl Rabadán Proceedings of the Abel Symposium, 2018 arXiv

Computer Graphics

Stable topological signatures for points on 3D shapes M.C., Steve Oudot and Maks Ovsjanikov Proceedings of the Eurographics Symposium on Geometry Processing (SGP), 2015 HAL, code, technical report

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