Network Data Analysis

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

Kim, W. and Mémoli, F., Stefanou, A. The metric structure of the formigram interleaving distance , arXiv preprint arXiv:1912.04366 (2019). [arXiv link]

Kim, W. and Mémoli, F. Spatio-temporal persistent homology for dynamic metric spaces , arXiv preprint arXiv:1812.00949 (2018). [arXiv 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.