Research
As a researcher, my primary research areas include (but not limited to) geometric data analysis. It contains not only the statistical methodologies for analyzing non-standard data taking values in manifolds, probability distribution, and general metric spaces but also the theoretical guarantees of such methodologies through the lens of statistical learning theory, leading to more reliable and usable methodologies.
In the contemporary era of data science, non-standard data have frequently emerged in vast areas including natural science (e.g. statistics, geology, astronomy, and physics, etc.) and engineering fields (e.g. computer science and neuroscience). The (possibly) most typical space on which the non-standard data lie is manifold. Topologically, it is a second-countable and Hausdorff topological space locally homeomorphic to a Euclidean space. Roughly speaking, it is a curved space like a surface, sphere, torus, or matrix group. Examples of manifold-valued data are astronomical data, seismic data, and climate data physically observed on the globe and any Euclidean-vector data under geometric constraints such as directional data, compositional data, diffusion tensor imaging (DTI) data, motion data, and shape data.
Publications
- Peer-Reviewed International Journals
· Jongmin Lee, Jang-Hyun Kim and Hee-Seok Oh. (2021). Spherical principal curves. IEEE Transactions on Pattern Analysis and Machine Intelligence, 43, 2165–2171. (arXiv) (Link) (Top 1% SCIE Journal in CS/AI Catergory, Impact factor = 20.33, JCR2023)
· Jongmin Lee, Jang-Hyun Kim and Hee-Seok Oh (2022). spherepc: An R package for dimension reductions on a sphere. The R Journal, 14, 167–181. (Link)
· Jongmin Lee and Hee-Seok Oh. (2023). Robust spherical principal curves. Pattern Recognition, 138, 109380. (Link)
· Jongmin Lee, Joonpyo Kim, Joonho Shin, Sungil Cho, Sungmin Kim, and Kyoungjae Lee. (2023). Analysis of wildfires and their extremes via spatial quantile autoregressive model. Extremes, 26, 353-379. (Link)
· Jongmin Lee and Sungkyu Jung. (2024). Huber means on Riemannian manifolds. Submitted to Annals of Statistics. (arXiv)
- Domestic Journals
· Hojin Yang, Jongmin Lee, and Donghyuk Lee. (2023). An effect of the misspecified technical inefficiency on the maximum likelihood estimation of the stochastic frontier model. Journal of the Korean Data Analysis Society, 25, 1759-1771.
· Jongmin Lee and Minwoo Kim. (2023). Exploratory association analysis between coverages using exact inference on Ising model., Submitted.
- Papers in Preparation
· Jongmin Lee and Sungkyu Jung. (2024+). Two-sample test on Riemannian manifolds by means of M-estimators of location.
· Jongmin Lee and Hee-Seok Oh. (2024+). Local principal curves on Riemannian manifolds.
· Jongmin Lee and Seoncheol Park. (2024+). Exploratory data analysis on complex constrained domains using extrinsic principal curves.
Collaborators: Hee-Seok Oh(4), Jang-Hyun Kim(2), Sungkyu Jung(2), Hojin Yang(1), Donghyuk Lee(1), Kyoungjae Lee(1), Minwoo Kim(1), Seoncheol Park(1), Joonpyo Kim(1), Junho Shin(1), Sungjin Cho(1), Sungmin Kim(1),
