Mathematical Research at FSU
Research in data science at the FSU Mathematics Department covers a wide spectrum of topics in mathematical modeling, foundations, optimization and computation. Methods based on Riemannian geometry, in both finite and infinite dimensions, are employed in shape analysis and studies of manifold-valued data arising in multiple scientific domains. Several data analysis projects employ topology and geometry in the construction of informative data summaries used in such problems as uncovering and analyzing genotype-to-phenotype associations and mapping phenotypic plasticity. Research on random graph theory and stochastic optimization target applications such as development of social network models. Machine learning is being applied to forecasting high frequency financial price data, studying market behavior, and exploiting market inefficiencies. In biological and medical imaging, machine learning has been applied to such problems as segmentation and classification of lung nodules in CT-scans as malignant or benign, and analysis of the morphology of pollen grains, the richest fossil record on planet Earth.
M. Bauer, M. Bruveris, P. Harms and J. Møller-Andersen.
A numerical framework for Sobolev metrics on the space of curves.
SIAM J. Imaging Sci., 10(1), 47-73.(2017)
M. Bauer, S. Joshi and K. Modin. Diffeomorphic density matching by optimal information transport. SIAM J. Imaging Sci. 8(3):1718-1751, 2015.
D. H. Díaz Martínez, F. Mémoli, W. Mio The Shape of Data and Probability Measures Appl. Comput. Harmon. Anal. (2018)
- X. Gaou, M. Gürbüzbalaban and L. Zhu Global Convergence of Stochastic Gradient Hamiltonian Monte Carlo for Non-Convex Stochastic Optimization: Non-Asymptotic Performance Bounds and Momentum-Based Acceleration. arXiv:1809.04618
Matthew C. Hancock, Jerry F. Magnan. Lung nodule malignancy classification using only radiologist-quantified image features as inputs to statistical learning algorithms: probing the Lung Image Database Consortium dataset with two statistical learning methods. SPIE J. of Medical Imaging , 3(4), 044504 (2016)
A. Kercheval and Y. Zhang Modeling high frequency limit order book dynamics with support vector machines. Quantitative Finance, 15 (8), 1315-1329. (2015)
- A. Kercheval and Y. Liu Risk forecasting with GARCH, skewed t distributions, and multiple time scales. Wiley Handbook of Modeling High-Frequency Data in Finance, Wiley, 2012, ISBN: 978-0-470-87688-6, 163-218.
M. Li, M. H. Frank, V. Coneva, W. Mio, D. Chitwood, C. Topp The Persistent Homology Mathematical Framework Provides Enhanced Genotype-to-Phenotype Associations for Plant Morphology Plant Physiol. (2018)
- A. Mele and L. Zhu. Approximate Variational Estimation for a Model of Network Formation. arXiv:1702.00308
A. Srivastava and E. Klassen. Functional and Shape Data Analysis. Springer Series in Statistics
Z. Su, E. Klassen, and M. Bauer Comparing curves in homogeneous spaces. Differential Geometry and Its Applications , 60 (2018), 9-32.