TGDA@OSU NSF TRIPODS Center

Information

TGDA@OSU: Discovering Structure, Shape, and Dynamics in Data

This project will advance the methodological and theoretical foundations of data analytics by considering the geometric and topological aspects of complex data from mathematical, statistical and algorithmic perspectives, thus enhancing the synergy between the Computer Science, Mathematics, and Statistics communities.

Furthermore, this project will benefit a range of impactful scientific areas including medicine, neuronanatomy, machine learning, geographic information systems, mechanical engineering designs, and political science. The research products will be implemented and disseminated through software packages and tutorials, allowing widespread application by industrial and academic practitioners.

Through this project, the PIs will develop curricula for cross-disciplinary, undergraduate and graduate education. Additionally, this project aims to develop partnerships with the Translational Data Analytics and the Mathematical Biosciences Institutes at OSU, as well as other internal and external research and education centers.

The TGDA@OSU TRIPODS team is composed of Tamal DeyMatthew KahleSebastian KurtekFacundo MémoliDavid Sivakoff and Yusu Wang.

Areas of Expertise

Tamal Dey (CSE): algorithms, computational geometry and topology, topological data analysis, surface reconstruction, mesh generation, geometric modeling.

Matthew Kahle (Math): stochastic topology, topological statistical mechanics, combinatorics.

Sebastian Kurtek (Stats): statistical shape analysis, functional data analysis, statistics on manifolds, computational statistics.

Facundo Memoli (Math and CSE ): shape analysis, topological data analysis, applied metric geometry, networks.

David Sivakoff (Stats and Math): probability theory, stochastic processes on large finite graphs,  percolation models and particle systems.

Yusu Wang (CSE): discrete and computational geometry, computational and applied topology, geometric algorithms, and topological data analysis.

Dey, Tamal K and Xin, Cheng. “Computing Bottleneck Distance for 2-D Interval Decomposable Modules,” j34th International Symposium on Computational Geometry (SoCG 2018), v.99, 2018. Citation details

Bharath, Karthik and Kurtek, Sebastian and Rao, Arvind and Baladandayuthapani, Veerabhadran. “Radiologic image-based statistical shape analysis of brain tumours,” Journal of the Royal Statistical Society: Series C (Applied Statistics), v.67, 2018. doi:10.1111/rssc.12272  Citation details

Strait, Justin and Kurtek, Sebastian and MacEachern, Steven N. “Locally-Weighted Elastic Comparison of Planar Shapes,” IEEE Workshop on Differential Geometry in Computer Vision and Machine Learning, 2018. Citation details

Strait, Justin and Kurtek, Sebastian. “A novel algorithm for optimal matching of elastic shapes with landmark constraints,” International Conference on Image Processing Theory, Tools and Applications, 2017. doi:10.1109/IPTA.2017.8310079  Citation details

Chen, Chao and Ni, Xiuyan and Bai, Qinxun and Wang, Yusu. “A Topological Regularizer for Classifiers via Persistent Homology,” Proceedings of Machine Learning Research, v.89, 2019. Citation details

Bharath, Karthik and Kurtek, Sebastian. “Distribution on Warp Maps for Alignment of Open and Closed Curves,” Journal of the American Statistical Association, 2019. doi:10.1080/01621459.2019.1632066  Citation details

Strait, Justin and Chkrebtii, Oksana and Kurtek, Sebastian. “Automatic Detection and Uncertainty Quantification of Landmarks on Elastic Curves,” Journal of the American Statistical Association, 2018. doi:10.1080/01621459.2018.1527224  Citation details

Dey, Tamal K and Wang, Jiayuan and Wang, Yusu. “Graph Reconstruction by Discrete Morse Theory,” Leibniz international proceedings in informatics, v.99, 2018. Citation details

Saha, Abhijoy and Kurtek, Sebastian. “Geometric Sensitivity Measures for Bayesian Nonparametric Density Estimation Models,” Sankhya A, v.81, 2019. doi:10.1007/s13171-018-0145-7  Citation details

Cho, Min Ho and Asiaee, Amir and Kurtek, Sebastian. “Elastic Statistical Shape Analysis of Biological Structures with Case Studies: A Tutorial,” Bulletin of Mathematical Biology, v.81, 2019. doi:10.1007/s11538-019-00609-w  Citation details

Lyu, Hanbaek and Sivakoff, David. “Persistence of sums of correlated increments and clustering in cellular automata,” Stochastic Processes and their Applications, 2018. doi:10.1016/j.spa.2018.04.012  Citation details

Saha, Abhijoy and Bharath, Karthik and Kurtek, Sebastian. “A Geometric Variational Approach to Bayesian Inference,” Journal of the American Statistical Association, 2019. doi:10.1080/01621459.2019.1585253  Citation details

Tucker, J. Derek and Lewis, John R. and King, Caleb and Kurtek, Sebastian. “A geometric approach for computing tolerance bounds for elastic functional data,” Journal of Applied Statistics, 2019. doi:10.1080/02664763.2019.1645818  Citation details

Facundo Memoli, Zane Smith. “The Wasserstein Transform,” Proceedings of the 36th International Conference on Machine Learning,, v.97, 2019. Citation details

Xie, Weiyi and Chkrebtii, Oksana and Kurtek, Sebastian. “Visualization and Outlier Detection for Multivariate Elastic Curve Data,” IEEE Transactions on Visualization and Computer Graphics, 2019. doi:10.1109/TVCG.2019.2921541  Citation details

  1. Wang, X. Li, P. Mitra and Y. Wang, “Topological Skeletonization and Tree-Summarization of

Neurons Using Discrete Morse Theory” arXiv:1805.04997 <https://arxiv.org/abs/1805.04997>.

Facundo Mémoli, Anastasios Sidiropoulos, Kritika Singhal “Sketching and Clustering Metric Measure Spaces” https://arxiv.org/abs/1801.00551.

  1. Chowdhury and F. Memoli “A functorial Dowker theorem and persistent homology of asymmetric networks” J Appl. and Comput. Topology 2, 115–175 (2018) doi:10.1007/s41468-018-0020-6.

Elchesen, A. & Mémoli, F. The reflection distance between zigzag persistence modules.  J Appl. and Comput. Topology (2019) 3: 185. https://doi.org/10.1007/s41468-019-00031-0

Mémoli, F. & Okutan, O.B. Quantitative Simplification of Filtered Simplicial Complexes.  Discrete Comput Geom (2019). https://doi.org/10.1007/s00454-019-00104-y

  1. Gravner and D. Sivakoff. “Bootstrap percolation on the product of the two-dimensional lattice with a Hamming square”. Annals of Applied Probability (2020).
  1. K. Dey and C. Xin (2019). /Generalized Persistence Algorithm for Decomposing Multi-parameter Persistence Modules/. Axiv publication: arxiv: https://arxiv.org/abs/1904.03766

Zhao, Qi and Wang, Yusu (2019). /Learning metrics for persistence-based summaries and applications for graph classification/.  available at arXiv: arXiv:1904.12189 . URL: https://arxiv.org/abs/1904.12189.

  • 2019 Ohio Day of Topological Data Analysis: July 29th 2019 together with colleagues from Wayne State University and the Air Force Research Labs in Dayton Ohio we co-organized the first Ohio Day of TDA. The event took place in Dayton Ohio and counted with several talks by PhD students from Ohio State, Wayne State, as well as project presentations by undergraduate students participating in the 2019 Summer of TDA organized by AFRL-Dayton. https://tgda.osu.edu/ohio-tda-day-2019/
  • Special session at the AMS Fall Central Sectional Meeting on Recent Trends in the Mathematics of Data: The session takes place on September 14-15, 2019, at the University of Wisconsin-Madison. co-PI Sivakoff co-organized with Sebastien Roch (U. Wisc-Madison) and Joseph Watkins (U. Arizona), who are members TRIPODS centers at their institutions. The session features researchers at all career stages with connections to TRIPODS centers around the country.
  • Three-part Mini-Symposium at ICIAM 2019 on Geometry and Topology in Data Analysis: The MS took place during ICIAM-2019 in Valencia-Spain and it was coorganized by co-PI Memoli togher with W. Mio (FSU) and Y. Hiraoka (Kyoto). The MS featured talks by researchers in different areas of data analysis and at various career stages. ICIAM is one of the largest international conferences on industrial and applied mathematics.
  • Co-sponsorship of the Invitations to Industry seminar hosted by the Erdos Institute at Ohio State
  • Workshop on Microstructures and TGDA* This workshop co-organized with TDAI and MBI at OSU focused on application topological and geometric data analysis to microstructures arising in material science, neuroscience, medical science and the like. The workshop was held during May 28–May 31, 2019. We had 11 invited speakers whose expertise spanned both foundations of TGDA and domain science/applications. The workshop was attended by ~70 attendees including ~40 students. The details can be found at: https://tdai.osu.edu/tripods-workshop/
  • A Graduate Student Conference on Geometry and Topology in Data Analysis and Machine Learning. *TDAML 2019 was be held at The Ohio State University on June 1st and June 2nd, 2019 (Saturday and Sunday). The goal of the conference was to gather graduate students in order to share their research work in applications of Geometry and Topology to Data Analysis and Machine Learning. Around 85 students registered/participated in the conference which included ~25 student talks: https://tgda.osu.edu/gtdaml2019/
  • The TRIPODS team has been working with the MBI directorate to design an online course on TGDA methods in Neuroscience as part of the TRIPODS+X initiative. The MBI recently hosted a course design workshop and the course will be offered during Spring 2020 with a follow-up research experience for the associated students in early Summer 2020.
  • Invitations to Industry seminar hosted by the Erdos Institute at Ohio State.
  • Outreach activity at local Olentangy Liberty High School. Co-PI Kurtek spent a day at the high school giving a presentation to the Statistics students on the topic of Data Analytics.
  • “Graph reconstruction with discrete Morse theory”, T. K. Dey, J. Wang, Y. Wang was presented and appeared in the premier conference on Computational Geometry, SoCG 2018.
  • “Computing bottleneck distance for 2-D interval decomposable modules”, T. K. Dey, C. Xin was presented and appeared in SoCG 2018.
  • “A Novel Algorithm for Optimal Matching of Elastic Shapes with Landmark Constraints,” J. Strait and S. Kurtek was presented and appeared in IPTA 2017.
  • “Locally-Weighted Elastic Comparison of Planar Shapes,” J. Strait, S. Kurtek and S.N. MacEachern was presented and appeared in DIFF-CVML 2018.
  • Tamal Dey, “Computational topology and data analysis,” Inspiring Lectures on Applications of Computational Geometry, Intensive Research Program in Discrete, Combinatorial, Computational Geometry, UPC, Barcelona, Spain, April 2018.
  • Tamal Dey, “Nerves can only kill,” 7th Mini-Symposium on Computational Topology, CG Week, Budapest, Hungary, June 2018.
  • Yusu Wang, “Geometric and topological data analysis for graphs,” School on Low-Dimensional Geometry and Topology, Institute Henri Poincare (IHP), Paris, France, June 2018.
  • Yusu Wang, “Computing Gromov-Hausdorff and Interleaving distances for trees,” 7th Mini-Symposium on Computational Topology, CG Week, Budapest, Hungary, June 2018.
  • Sebastian Kurtek, “Radiologic image-based statistical shape analysis of brain tumors,” ENAR Spring Meeting, Atlanta, GA, March 2018.
  • Sebastian Kurtek, “Statistical shape analysis of surfaces using square root normal fields,” Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, April 2018.
  • David Sivakoff, “Polluted bootstrap percolation in three dimensions”, Department of Mathematics, Duke University, Durham, NC, November 2017.
  • David Sivakoff, “Stochastic modeling with graphs,” Mathematics Colloquium, Iowa State University, Ames, IA, February 2018.
  • Facundo Memoli, “Stable signatures for dynamic graphs and dynamic metric spaces via zigzag persistence,” Abel Symposium, Geiranger, Norway, June 2018.
  • Facundo Memoli, “Stable signatures for dynamic graphs and dynamic metric spaces via zigzag persistence,” Algebraic Topology: Methods, Computation and Science (ATMCS), Vienna, Austria, June 2018.
  • Tamal Dey, “Generalised persistence algorithm for multiparameter persistence module,” Workshop on Computational Topology, CGweek, Portland, June, 2019.
  • Tamal Dey, “Multiparameter persistent homology” BIRS-CMO, Mexico, August, 2018.
  • Sebastian Kurtek, “Geometric Methods for Image-based Statistical Analysis of Brain Tumors,” Department of Biostatistics, Columbia University, New York, NY, April, 2019.
  • Sebastian Kurtek, “A Geometric Approach to Pairwise Bayesian Alignment of Functional Data Using Importance Sampling,” Joint Statistical Meetings, Denver, CO, July, 2019.
  • David Sivakoff, “Polluted bootstrap percolation in three dimensions”, Department of Mathematics, University of Virginia, Charlottesville, VA, October 2018.
  • David Sivakoff, “The contact process with avoidance,” MBI Workshop on Modeling and Analysis of Dynamic Social Networks, Columbus, OH, November 2018.
  • David Sivakoff, “The contact process with avoidance,” Scaling Limits of Dynamical Processes on Random Graphs, BIRS-CMO, Mexico, May 2019.
  • David Sivakoff, “Bootstrap percolation on products of lattices and complete graphs,” Special Session on Bootstrap Percolation at Canadian Discrete and Algorithmic Mathematics Conference (CanaDAM), June 2019.
  • Facundo Memoli, “Stable invariants for Dynamic Metric Spaces.” Conference on Geometric Data Analysis. University of Chicago. May 2019.
  • Facundo Memoli, “The Gromov-Wasserstein distance and distributional invariants of datasets.” Oberwolfach workshop on “ Statistical and Computational Aspects of Learning”. May 2019.
  • Facundo Memoli. “Time Dependent Data, Persistence, and Stability”. Worshop on “Topological Data Analysis, with Applications”. University of Western Ontario. May 2019.
  • Facundo Memoli. “Metrics on the collection of dynamic shapes. “Workshop on Shape Analysis, Stochastic Mechanics and Optimal Transport. BIRS-Banff. December 2018.
  • Facundo Memoli, “Stable Signatures for Dynamic Graphs and Dynamic Metric Spaces via Zigzag Persistence.” Brazilian Topology Meeting. Niteroi. August 2018.
  • Matuk, O. Chkrebtii, S. Kurtek, “Estimation of Sparsely Observed Signals with an Empirical Bayesian Model,” Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, November, 2019.
  • Farahbakhsh Touli, Elena and Wang, Yusu. ” FPT-algorithms for computing Gromov-Hausdorff and interleaving distances between trees”. In 27th Annual European Sympos. Algorithms (ESA), to appear, 2019.
  • “A topological regularizer for classifiers via persistent homology”, C. Chen, X. Ni, Q. Bai and Y. Wang, appeared in 22nd Intl. Conf. Artificial Intellience and Stats (AISTATS), PMLR 89:2573-2582, 2019.
  • “Computing height persistence and homology generators in R^3 efficiently”, T. K. Dey appeared in Proc. 30th ACM-SIAM Symposium on Discrete Algorithms (SODA 19), pages 2649–2662.
  • “FPT-algorithms for computing Gromov-Hausdorff and interleaving distances between trees”, E. Farahbakhsh Touli and Y. Wang., accepted to 27th Annl. European Sympos. Alg. (ESA), 2019.
  • Learning metrics for persistence-based summaries and applications for graph classification”, Zhao and Wang., arXiv:1904:12189, 2019. [URL: https://arxiv.org/abs/1904.12189]
  • The paper, “Geometric Sensitivity Measures for Bayesian Nonparametric Density Estimation Models,” A. Saha and S. Kurtek, Sankhya A, 2018.
  • The paper, “Automatic Detection and Uncertainty Quantication of Landmarks on Elastic Curves,” J. Strait, O. Chkrebtii, S. Kurtek,Journal of the American Statistical Association, 2018.
  • The paper, “A Geometric Variational Approach to Bayesian Inference,” A. Saha, K. Bharath, S. Kurtek, Journal of the American Statistical Association, 2019.
  • The paper, “Distribution on Warp Maps for Alignment of Open and Closed Curves,” K. Bharath, S. Kurtek, Journal of the American Statistical Association, 2019.
  • The paper, “Elastic Statistical Shape Analysis of Biological Structures with Case Studies: A Tutorial,” M.H. Cho, A. Asiaee, S. Kurtek, Bulletin of Mathematical Biology, 2019.
  • The paper, “Visualization and Outlier Detection for Multivariate Elastic Curve Data,” W. Xie, O. Chkrebtii, S. Kurtek, IEEE Trans. On Visulization and Computer Graphics, 2019.
  • The paper, “A Geometric Approach for Computing Tolerance Bounds for Elastic Functional Data,” J.D. Tucker, J.R. Lewis, C. King, S. Kurtek, Journal of Applied Statistics, 2019.
  • The paper, “Estimation of Sparsely Observed Signals with an Empirical Bayesian Model” was accepted for presentation at the Asilomar Conference on Signals, Systems, and Computers, 2019.
  • The paper, “Parking on transitive unimodular graphs,” M. Damron, J. Gravner, M. Junge, H. Lyu and D. Sivakoff, Annals of Applied Probability, 2019.
  • The paper, “Bootstrap percolation on the product of the two-dimensional lattice with a Hamming square,” J. Gravner and D. Sivakoff will appear in Annals of Applied Probability.
  • Multiple papers currently under submission by co-PI Sivakoff and colleagues are on the arXiv: arXiv:1706.07338, arXiv:1811.00627, arXiv:1908.03218.
  • The paper “The Wasserstein Transform”, F. Memoli, Z. Smith, and Z. Wan,was accepted and presented at the 2019 International Conference for Machine Learning.
  • The paper “A primer on Persistent Homology of Finite Metric Spaces”, F. Memoli and K. Singhal, was published in the Bulletin of Mathematical Biology, 2019.
  • The paper “The Reflection distance for persistence modules”, A. Elchesen and F. Memoli was published in the Journal of Applied and Computational Topology 2019.
  • The paper “A topological study of Frechet functions on metric measure spaces”, H. Hang. W. Mio, and F. Memoli was published in the Journal of Applied and Computational Topology 2019.
  • The paper “Stable Persistent Homology Features of Dynamic Metric Spaces”, W. Kim and F. Memoli, https://arxiv.org/abs/1812.00949.
  • The paper “Metric Graph Approximations of Geodesic Spaces”, F. Memoli and O. B. Okutan, https://arxiv.org/abs/1809.05566.
  • The paper “Generalized Persistence Diagrams for Persistence Modules over Posets”, W. Kim and F. Memoli, https://arxiv.org/abs/1810.11517
  • The paper “The Distortion of the Reeb Quotient Map on Riemannian Manifolds”, F. Mémoli and O. B. Okutan, https://arxiv.org/abs/1801.01562.

Justin Eldridge, Mikhail Belkin, and Yusu Wang. “Graphons, mergeons, and so on!” Conference on Neural Information Processing Systems, 2016. Barcelona, Spain https://papers.nips.cc/paper/6089-graphons-mergeons-and-so-on.pdf

Justin Eldridge, Mikhail Belkin, and Yusu Wang. “Unperturbed: spectral analysis beyond Davis-Kahan,” Algorithmic Learning Theory (ALT), 2018. Cornell University, Ithaca, NY http://www.cs.cornell.edu/conferences/alt2018/A/Eldridge18Paper.pdf

  1. K. Dey, A. Rossi, A, Sidiropoulos. “Temporal hierarchical clustering,” Proc. 28th International Symposium and Computation (ISAAC), 2017. Phuket, Thailand https://drops.dagstuhl.de/opus/volltexte/2017/8251/pdf/LIPIcs-ISAAC-2017-28.pdf
  1. K. Dey and R. Slechta. “Edge contraction in persistence-generated discrete Morse vector fields,” Computers & Graphics, v.74, 2018. doi:https://doi.org/10.1016/j.cag.2018.05.002

Matthew Kahle, Frank Lutz, Andrew Newman, Kyle Parsons. “Cohen-Lenstra heuristics for torsion in homology of random complexes,” Experimental Mathematics. DOI: 10.1080/10586458.2018.1473821.

  1. K. Dey and R. Slechta. “Filtration simplification for persistent homology via edge contraction,” Proc. Discrete Geometry and Computer Imagery (DGCI 2019), 2019. In: Couprie M., Cousty J., Kenmochi Y., Mustafa N. (eds) Discrete Geometry for Computer Imagery. DGCI 2019. Lecture Notes in Computer Science, vol 11414. Springer, Cham DOI: https://doi.org/10.1007/978-3-030-14085-4_8
  1. K. Dey and C. Xin. “Computing Bottleneck Distance for 2-D Interval Decomposable Modules,” Proc. 34th Internat. Sympos. Comput. Geoem. (SoCG 2018), v.32, 2018.
  1. K. Dey. “Computing height persistence and homology generators in R^3 efficiently,” Proc. 30th ACM-SIAM Sympos. Discrete Algorithms, 2019 (SODA 19), 2019.
  1. K. Dey, T. Hou, and S. Mandal. Computing Minimal Persistent Cycles: Polynomial and Hard Cases. Proceedings ACM-SIAM Sympos. Discrete Algorithms (SODA 20), to appear. July 2019, arxiv: https://arxiv.org/abs/1907.04889
  1. Adamaszek, H. Adams, E. Gasparovic, M. Gommel, E. Purvine, R. Sazdanovic, B. Wang, Y. Wang and L. Ziegelmeier. “Vietoris-Rips and Cech Complexes of Metric Gluings,” Proc. 34th Internat. Sympos. Comput. Geom., 2018.

U. of Texas MD Anderson Cancer Center

U. of Nottingham (UK)

Sandia National Laboratories

U. of Clermont (Fr)

Duke

UC Davis

Georgia Tech

U. Virginia

U. Cambridge (UK)

CUNY

KAUST

FSU

UCLA

Activities

2018 TRIPODS Summer School. When: May 14 to 18, 2018. Details.

2018 TRIPODS Workshop. When: May 21 to 25, 2018. Details

2018 CMBS conference on ‘Elastic functional and shape data analysis”. When: July 16-20, 2018. Details.

TGDA seminar talk, Gunnar Carlsson. When: February 27th, 2018. Details.

Invitations to industry talk, Gunnar Carlsson. When: February 28th, 2018. Details.

New course on Applied Algebraic Topology: Math 4570: Spring 2018.

TGDA mini-course by Yasu Hiraoka: November 13 to 15, 2017.