Preprints

S.Bhatia, Y.Cao, P.Lezeau, A.Monod, Tropical Expressivity of Neural Networks. [URL],[PDF]
R.Talbut, D.Tramontano, Y.Cao, M.Drton, A.Monod, Probability Metrics for Tropical Spaces of Different Dimensions. [URL],[PDF]
Y.Cao, A.Monod, A Geometric Condition for Uniqueness of Fréchet Means of Persistence Diagrams. [URL], [PDF]
Y.Cao, A.Monod, Approximating Persistent Homology for Large Datasets. [URL], [PDF]

Publications

Y.Cao, P.Leung, A.Monod, k-Means Clustering for Persistent Homology.Advances in Data Analysis and Classification, 2024. [URL],[PDF]
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. [URL], [PDF]
Y.Cao, D.Li, H.Sun, A.H.Assadi, S.Zhang, Efficient Weingarten Map and Curvature Estimation on Manifolds. Machine Learning Journal, 2021. [URL], [PDF]
F.Sun, Y.Cao, S.Zhang, H.Sun, The Bayesian Inference of Pareto Models Based on Information Geometry. Entropy, 2021. [URL], [PDF]
J.Yi, S.Zhang, Y.Cao, E.Zhang, H.Sun, Rigid Shape Registration Based on Extended Hamiltonian Learning. Entropy, 2020. [URL], [PDF]
Y.Wang, H.Sun, Y.Cao, S.Zhang, Torsion Discriminance for Stability of Linear Time-Invariant Systems. Mathematics, 2020. [URL], [PDF]

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]
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. [URL]
S.Zhang, Y.Cao, W.Li, F.Yan, Y.Luo, H.Sun, A New Riemannian Structure in SPD(n). 2019 IEEE International Conference on Signal, Information and Data Processing (ICSIDP), Chongqing, 2019. [URL]
A.Xiong, A.Assadi, Y.Cao, Calculating Persistence Homology of Attractors in High-Dimensional Chaotic Systems, 2017 International Conference on Computational Science and Computational Intelligence (CSCI), Las Vegas, 2017. [URL]

Imperial MLDS, Unstructured Data Analysis, Sep 2022 – Jan 2023; Sep 2023 – Jan 2024. [website]
Aalto-Imperial-TUM workshops on Algebraic Methods in Data Science, An introduction to Topological Data Analysis, joint work with Anna Song, Jan 2022. [Slides]