Network Data Analysis

Gülen, A. B., Mémoli, F. and Wan, Z. Orthogonal Mobius Inversion and Grassmannian Persistence Diagrams, arXiv preprint: arXiv:2311:06870 (2023). [arXiv link]

Arya, S., Auddy, A., Edmonds, R., Lim, S., Mémoli, F. and Packer, D. The Gromov-Wasserstein distance between spheres, arXiv preprint: arXiv:2306:10586 (2023). [arXiv link]

Gülen, A. B., Mémoli, F., Wan, Z. and Wang, Y. A Generalization of the Persistent Laplacian to Simplicial Maps, Proceedings of the 39th International Symposium on Computational Geometry (SoCG 2023). [ Publisher Link]

Zhou, L. and Mémoli, F. Ephemeral Persistence Features and the Stability of Filtered Chain Complexes, Proceedings of the 39th International Symposium on Computational Geometry (SoCG 2023). [ Publisher Link]

Clause, N., Dey, T. K., Mémoli, F. and Wang, B. Meta-Diagrams for 2-Parameter Persistence, Proceedings of the 39th International Symposium on Computational Geometry (SoCG 2023). [ Publisher Link]

Katz, M., Mémoli, F. and Wang, Q. Extremal Spherical Polytopes and Borsuk's Conjecture, arXiv preprint: arXiv:2301.13076 (2023). [arXiv link]

Lyu, H., Mémoli, F. and Sivakoff, D. Sampling random graph homomorphisms and applications to network data analysis, Journal of Machine Learning Research 24 (2023). [ Publisher Link]

Mémoli, F., Stefanou, A. and Zhou, L. Persistent Cup Product Structures and Related Invariants, arXiv preprint arxiv:2211.16642 (2022). [arXiv link]

Chambers, E., Duchin, M., Edmonds, R., Edwards, P., Matthews, J., Pizzimenti, A., Richardson, C., Rule, P. and Stern, A. Aggregating community maps, Proceedings of the 30th International Conference on Advances in Geographic Information Systems. [ Publisher Link]

Eastwood, P., Ellison, A., Goméz, M. and Mémoli, F. Homology groups of the curvature sets of S¹, arXiv preprint arXiv:2209.04674 (2022). [arXiv link]

Mémoli, F. and Zhou, L. Stability of Filtered Chain Complexes, arXiv preprint arXiv:2208.11770 (2022). [arXiv link]

Clause, N., Kim, W. and Mémoli, F.The discriminating power of the generalized rank invariant, arXiv preprint arXiv:2207.11591 (2022). [arXiv link]

Chen, S., Lim, S., Mémoli, F., Wan, Z. and Wang, Y. Weisfeiler-Lehman meets Gromov-Wasserstein, arXiv preprint arXiv:2202.02495 (2022). [arXiv link]

Lim, S. and Mémoli, F. Classical MDS on Metric Measure Spaces, arXiv preprint arXiv:2201.09385 (2021). [arXiv link]

Gülen, A. B. and McCleary, A. Galois Connections in Persistent Homology, arXiv preprint arXiv:2201.06650 (2022). [arXiv link]

Dey, T. K., Kim, W. and Mémoli, F. Computing Generalized Rank Invariant for 2-Parameter Persistence Modules via Zigzag Persistence and its Applications, arXiv preprint arXiv:2111.15058 (2021). [arXiv link]

Lim, S., Mémoli, F., Wan, Z., Wang, Q. and Zhou, L. Some results about the Tight Span of spheres, arXiv preprint arXiv:2112.12646 (2021). [arXiv link]

Gómez, M. and Mémoli, F. The Four Point Condition: An Elementary Tropicalization of Ptolemy's Inequality, arXiv preprint arXiv:2111.10328 (2021). [arXiv link]

Mémoli, F., Smith, Z., and Wan, Z. The Gromov-Hausdorff distance between ultrametric spaces: its structure and computation, arXiv preprint arXiv:2110.03136 (2021). [arXiv link]

Adams, H., Mémoli, F., Moy, M. and Wang, Q. The Persistent Topology of Optimal Transport Based Metric Thickenings, arXiv preprint arXiv:2109.15061 (2021). [arXiv link]

Carlsson, G., Mémoli, F. and Segarra S. Robust Hierarchical Clustering for Directed Networks: An Axiomatic Approach, arXiv preprint arXiv:2108.07247 (2021). [Accepted to SIAGA, 2021]

Kim, W. and Mémoli, F. Generalized persistence diagrams for persistent modules over posets, Journal of Applied and Computational Topology (2021). [Publisher link]

Contessoto, M., Mémoli, F., Stefanou, A. and Zhou, L. Persistent cup-length, arXiv preprint arXiv:2107.01553 (2021). [arXiv link]

Mémoli, F. and Wan, Z. Characterization of Gromov-type geodesics, arXiv preprint arXiv:2105.05369 (2021). [arXiv link]

Lim, S. and Mémoli, F., Smith, Z. The Gromov-Hausdorff distance between spheres, arXiv preprint arXiv:2105.00611 (2021). [arXiv link]

Gómez, M. and Mémoli, F. Curvature Sets Over Persistence Diagrams, arXiv preprint arXiv:2103.04470 (2021). [arXiv link]

Mémoli, F., Munk, A., Wan, Z. and Weitkamp, C. The ultrametric Gromov-Wasserstein distance , arXiv preprint arXiv:2101.05756 (2021). [arXiv link]

Mémoli, F., Wan, Z. and Wang, Y. Persistent Laplacians: properties, algorithms and implications , arXiv preprint arXiv:2012.02808 (2020). [arXiv link]

Wan, Z. A novel construction of Urysohn universal ultrametric space via the Gromov-Hausdorff ultrametric , Topology and its Applications (2021). [Publisher link]

Jin, K., Mémoli, F. and Wan, Z. The Gaussian Transform, arXiv preprint arXiv:2006.11698 (2020). [arXiv link]

Chowdhury, S., Clause, N., Mémoli, F., Sánchez, J. Á., & Wellner, Z. New families of stable simplicial filtration functors, Topology and its Applications. [Publisher link]

Cai, C., Kim, W., Mémoli, F., and Wang, Y. Elder-rule-Staircodes for Augmented Metric Spaces, To appear in SIAM Journal on Applied Algebra and Geometry. [ arXiv link] Short version has been published in the Proceedings of the 36th International Symposium on Computational Geometry (SoCG 2020). [Publisher link]

Lim, S. and Mémoli, F., Okutan, O. B. Vietoris-Rips Persistent Homology, Injective Metric Spaces, and The Filling Radius , arXiv preprint arXiv:2001.07588 (2020). [arXiv link]

Mémoli, F., and Zhou, L. Persistent Homotopy Groups of Metric Spaces, arXiv preprint arXiv:1912.12399 (2019). [arXiv link]

Mémoli, F., Smith, Z. and Wan, Z. Gromov-Hausdorff distances on p-metric spaces and ultrametric spaces , arXiv preprint arXiv:1912.00564 (2019). [arXiv link]

Stefanou, A. Tree decomposition of Reeb graphs, parametrized complexity, and applications to phylogenetics, Journal of Applied and Computational Topology. [Publisher link]

Kim, W., Mémoli, F., and Stefanou, A. Interleaving by Parts for Persistence In a Poset, arXiv preprint arXiv:1912.04366 (2019). [arXiv link]

Kim, W. and Mémoli, F. Spatiotemporal Persistent Homology for Dynamic Metric Spaces, Discrete & Computational Geometry. [ Publisher Link]

Kim, W. and Mémoli, F. Generalized Persistence Diagrams for Persistence Modules over Posets, arXiv preprint arXiv:1810.11517 (2018). [arXiv link]

Mémoli, F. and Needham, T. Gromov-Monge Quasi-metrics and Distance Distributions, arXiv preprint arXiv:1810.07793 (2018). [arXiv link]

Mémoli, F., Smith, Z., Wan, Z. The Wasserstein Transform, arXiv preprint arXiv:1810.07793 (2018). [arXiv link]

Mémoli, F. and Okutan, O. Metric Graph Approximations of Geodesic Spaces, arXiv preprint arXiv:1809.05566 (2018). [arXiv link]

Chowdhury, S. and Mémoli, F., The Gromov-Wasserstein distance between networks and stable network invariants, arXiv preprint arXiv:1808.04337 (2018). [arXiv link]

Kim, W. and Mémoli, F., Formigrams: Clustering Summaries of Dynamic Data. In the 30th Canadian Conference on Computational Geometry (2018). [Conference link]

Chowdhury, S., Dai, B. and Mémoli, F., The Importance of Forgetting: Limiting Memory Improves Recovery of Topological Characteristics from Neural Data. PLoS ONE (2018). [Journal link]

Chowdhury, S. and Mémoli, F., The Metric Space of Networks, arXiv preprint arXiv:1804.02820 (2018). [arXiv link]

Chowdhury, S. and Mémoli, F., Explicit Geodesics in Gromov-Hausdorff Space. Electronic Research Announcements in Mathematical Sciences, 2018, 25: 48-59. [arXiv]

Kim, W. and Mémoli, F. Stable Signatures for Dynamic Metric Spaces via Zigzag Persistent Homology. ArXiv preprint (2017). [arXiv link][Website with experiments and more details.]

Chowdhury, S. and Mémoli, F., Convergence of Hierarchical Clustering and Persistent Homology Methods on Directed Networks, arXiv preprint arXiv:1711.04211 (2017). [arXiv link]

Chowdhury, S. and Mémoli, F., Distances and Isomorphism between Networks and the Stability of Network Invariants, arXiv preprint arXiv:1708.04727 (2017). [arXiv link]

Chowdhury, S., Dai, B., and Mémoli, F., Topology of Stimulus Space via Directed Network Persistent Homology, COSYNE 2017. [conference link] [poster]

Chowdhury, S. and Mémoli, F., Persistent Path Homology of Directed Networks, In the Proceedings of the 29th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2018). [ SODA version ] [ Slides ] [ Code ] [arXiv v1]

Chowdhury, S. and Mémoli, F., A functorial Dowker theorem and persistent homology of asymmetric networks. In the Journal of Applied and Computational Topology. [journal link] arXiv preprint arXiv:1608.05432 (2018). [arXiv] [old version with supplementary experiments]

Chowdhury, S., Mémoli, F., and Smith, Z., Improved Error Bounds for Tree Representations of Metric Spaces, In the Proceedings of the 30th annual conference on Neural Information Processing Systems (NIPS 2016). [conference link]

Smith, Z., Chowdhury, S., and Mémoli, F., Hierarchical Representations of Network Data with Optimal Distortion Bounds, In the 50th Asilomar Conference on Signals, Systems, and Computers. IEEE, 2016. [conference] [supplementary material]

Chowdhury, S., and Mémoli, F., Persistent Homology of Directed Networks, In the 50th Asilomar Conference on Signals, Systems, and Computers. IEEE, 2016.

Chowdhury, S., and Mémoli, F., Distances between Directed Networks and Applications, In the 41st IEEE Conference on Acoustics, Speech and Signal Processing. IEEE, 2016.

Chowdhury, S., and Mémoli, F., Metric Structures on Networks and Applications, In the 2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton). IEEE, 2015.