Vincent Grande

Computational Network Science@RWTH Aachen University

ProfilePic11.jpeg

I am a second-year PhD Candidate in the Computational Network Science Group of Michael Schaub and a member of the RTG UnRAVeL (Research Training Group for Uncertainty and Randomness in Algorithms, Verification, and Logic).

My research deals with the analysis of networks and data sets with higher-order information. A central motive is to use a blend of techniques from algebra, topology, homotopy theory, and network science to explore the relationship between small scale connectivity data and other localised information, and large-scale behaviour and global properties of data sets.

If you are interested in my research and have questions, new ideas, or suggestions, feel free to get in touch! :)

Short CV

Before moving to Aachen, I obtained a Master of Science in Pure Mathematics at the University of Bonn and a Master of Advanced Study at the University of Cambridge, UK, both times focussing on homotopy theory, algebraic topology, and discrete mathematics. Prior to that, I did a Bachelor of Science in Pure Mathematics and a Two-Subjects Bachelor of Arts in Philosophy/Mathematics at the University of Göttingen focussing on algebra and Wittgenstein’s philosophy of language.

I wrote my Master’s thesis on G-global homotopy theory supervised by Stefan Schwede, my Cambridge Part III essay on Bott periodicity and the J-homomorphism supervised by Oscar Randal-Williams, and my Bachelor’s thesis on exact modules over Manuel Köhler’s ring supervised by Ralf Meyer.

news

Dec 20, 2023 “Disentangling the Spectral Properties of the Hodge Laplacian: Not All Small Eigenvalues Are Equal” has just been accepted at ICASSP 2024, the International Conference on Acoustics, Speech and Signal Processing. In the joint article with Michael Schaub we attempt to “track” eigenvectors of the Hodge Laplacian through the filtration of a simplicial complex, bridging TDA and Topological Signal Processing. And we have many pictures! :tada:
Nov 28, 2023 How to make sense of the vast spectral information of the Hodge Laplacian? “Disentangling the Spectral Properties of the Hodge Laplacian: Not All Small Eigenvalues Are Equal”, a new preprint of my joint article with Michael Schaub is now available on arXiv. :blush:
Nov 24, 2023 My article with Michael Schaub on Non-isotropic Homology just got accepted to the 2nd Learning on Graph Conference! :tada: Feel free to drop by my poster at the poster session!
Oct 26, 2023 Is there one ‘correct’ metric for Persistent Homology, or should we rather analyse and compare multiple metrics on point clouds at once? We change the metric, track the effects on the persistence diagrams and extract new information on orientation and orientational variance and strength of point clouds! A preprint of my joint article with Michael Schaub on Non-isotropic Homology is now available on arXiv. :blush:
Jul 26, 2023 I just uploaded the new extended abstract on Non-Isotropic Persistent Homology, which I will be presenting on Friday at the TAG-ML Workshop @ ICML2023. Check it out here!
Jun 20, 2023 The code for both Topological Point Cloud Clustering and Restarting Strategies on Markov Chains is now publicly available.
Jun 18, 2023 Our extended abstract on Non-Isotropic Persistent Homology together with Michael Schaub has been accepted for a poster presentation at the workshop on Topology, Algebra, and Geometry in ML @ICML 2023. See you in Hawaii. :blush:
Apr 25, 2023 Topological Point Cloud Clustering, my favourite paper I wrote so far, got accepted at ICML 2023! :blush: :tada:
Apr 24, 2023 Two articles got accepted for publication! :tada: The paper on paper Restarting Strategies on Partially Observable Markov Chains got accepted at ICALP 2023, and Signal Processing on Product Spaces got accepted for ICASSP 2023.
Apr 10, 2023 A preprint of my joint article with Michael Schaub on Topological Point Cloud Clustering is now available on arXiv. Very many colourful pictures, figures, and some cool new ideas! :blush:
Mar 21, 2023 A preprint of my joint paper with Mitch Roddenberry, Florian Frantzen, Michael Schaub, and Santiago Segarra on Signal Processing on Product Spaces is now on arxiv! :whale: (There is a connection to oceans!)
Mar 7, 2023 A preprint of my paper on Restarting Strategies on Partially Observable Markov Chains together with Javier Esparza is now available on arXiv. :blush:
Feb 22, 2023 Launch of the new website. I still don’t have much to show here, but anyway, a website is a website. :tada:
Nov 9, 2022 Gave a talk at the UnRAVeL bi-weekly seminar on restart strategies on partially observable Markov chains.
Nov 4, 2022 Co-organised the joint workshops of the research training groups UnRAVeL and LogiCS a TU Vienna. Wonderful opportunity to visit Vienna! :blush:
Jul 22, 2022 I had a great time visiting the research group of Javier Esparza at TU Munich for a week, working on restart strategies for partially observable Markov chains.
Jun 1, 2022 Workshop of my Research Training Group in Vaals. I somehow managed to come out on top at the beer tasting challenge. I always knew that doing a PhD uncovers hidden abilities…
Apr 1, 2022 I just started my PhD and I am a Computer Scientist now. How exciting! :blush:

selected publications

  1. TPCCTeaser.png
    Topological Point Cloud Clustering
    Vincent P. Grande, and Michael T. Schaub
    ICML 2023. Proceedings of the 40th International Conference on Machine Learning, 2023
  2. RestartingTeaser.png
    Black-box Testing Liveness Properties of Partially Observable Stochastic Systems
    Javier Esparza, and Vincent P. Grande
    ICALP 2023. 50th EATS International Colloquium on Automata, Languages and Programming, 2023
    Authors in alphabetical ordering.
  3. ChangingPhi.gif
    Non-isotropic Persistent Homology: Leveraging the Metric Dependency of PH
    Vincent P. Grande, and Michael T. Schaub
    LoG 2023. Proceedings of the 2nd Annual Learning on Graphs Conference, 2023
  4. HOSCpreview.png
    Disentangling the Spectral Properties of the Hodge Laplacian: Not All Small Eigenvalues Are Equal
    Vincent P. Grande, and Michael T. Schaub
    In ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2024
    To appear.