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Preprints

• S. Bhatia, Y. Cao, P. Lezeau, A. Monod. Tropical Expressivity of Neural Networks. arXiv:2405.20174.
• R. Talbut, D. Tramontano, Y. Cao, M. Drton, A. Monod. Probability Metrics for Tropical Spaces of Different Dimensions. arXiv:2307.02846.
• Y. Cao, A. Monod. A Geometric Condition for Uniqueness of Fréchet Means of Persistence Diagrams. arXiv:2207.03943.
• Y. Cao, A. Monod. Approximating Persistent Homology for Large Datasets. arXiv:2204.09155.

Selected Publications

• Y. Cao, P. Leung, A. Monod, k-Means Clustering for Persistent Homology. Advances in Data Analysis and Classification, 2024.
• Y. Cao, A. Vlontzos, L. Schmidtke, B. Kainz, A. Monod. Topological Information Retrieval with Dilation-Invariant Bottleneck Comparative Measures. Information and Inference: A Journal of IMA, 2023.
• Y. Cao, D. Li, H. Sun, A. Assadi, S. Zhang. Efficient Weingarten Map and Curvature Estimation on Manifolds. Machine Learning, 2021.
• F. Sun, Y. Cao, S. Zhang, H. Sun. The Bayesian Inference of Pareto Models Based on Information Geometry. Entropy, 2021.
• Y. Cao, S. Zhang, F. Yan, W. Li, F. Sun, H. Sun. Unsupervised Environmental Sound Classification Based On Topological Persistence. 2019 IEEE International Conference on Signal, Information and Data Processing (ICSIDP), Chongqing, 2019.

Talks & Posters

• Y. Cao, A. Monod. Computational tropical Abel-Jacobi map for metric graphs, Applied Algebra and Geometry, 19th meeting, Edinburgh, Edinburgh, 2024. [Invited Talk]
• S. Bhatia, Y. Cao, P. Lezeau, A. Monod. A Tropical Geometric Perspective on Deep Learning, Geometric Deep Learning workshop, Cambridge, 2024. [Poster]
• Y. Cao, A. Monod. A Condition for the Uniqueness of Fréchet Means of Persistence Diagrams, Minisymposium on Applied Algebraic Topology: Theory and Implementation, SIAM Conference on Applied Algebraic Geometry, Eindhoven, 2023. [Invited Talk]
• Y. Cao, A. Monod. A Condition for the Uniqueness of Fréchet Means of Persistence Diagrams, Algebraic Topology: Methods, Computation and Science (ATMCS10), Oxford, 2022. [Poster]