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 Dey, Matthew Kahle, Sebastian Kurtek, Facundo Mémoli, David 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
- 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.
- 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
- Gravner and D. Sivakoff. “Bootstrap percolation on the product of the two-dimensional lattice with a Hamming square”. Annals of Applied Probability (2020).
- 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.