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, SPD (symmetric positive-definite) data, and shape data.

Papers

*: corresponding author

·Jongmin Lee and Victor-Emmanuel Brunel. (2025). Finite-sample bounds for M-estimators in metric spaces. In preparation.

· Soyoung Park and Jongmin Lee* (2025). Influence function of the Huber mean and its application (in Korean), submitted to Journal of the Korean Data & Information Science Society.

· Jongmin Lee and Sungkyu Jung. (2025). On the Kolmogorov-Feller weak law of large numbers for Fréchet mean on non-compact symmetric spaces, Submitted to Electronic Journal of Probability. (arXiv)

· Jongmin Lee and Sungkyu Jung. (2025). General M-estimators of location on Riemannian manifolds: existence and uniqueness. Submitted to Electronic Journal of Statistics. (arXiv)

· Jongmin Lee and Sungkyu Jung. (2025). Huber means on Riemannian manifolds. Journal of the Royal Statistical Society, Series B (Statistical Methodology). In press. (arXiv) (Journal)

· Soyoung Park and Jongmin Lee* (2025). A robust location estimator for circular data and its uniqueness condition (in Korean), Journal of the Korean Data & Information Science Society, 36, 677-684. (Journal)

· 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. (Journal)

· Jongmin Lee and Hee-Seok Oh. (2023). Robust spherical principal curves. Pattern Recognition, 138, 109380. (Journal)

· 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. (Journal)

· Jongmin Lee, Jang-Hyun Kim and Hee-Seok Oh. (2021). Spherical principal curves. IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI), 43, 2165–2171. (arXiv) (Journal)

Collaborators: Hee-Seok Oh(4), Sungkyu Jung(3), Jang-Hyun Kim(2), Soyoung Park(2), Victor-Emmanuel Brunel(1), Kyoungjae Lee(1), Joonpyo Kim(1), Junho Shin(1), Sungjin Cho(1), Sungmin Kim(1),

Ph.D. Thesis

Ph.D. in Statistics (2022), Seoul National University

– Thesis: “Nonparametric dimension reductions on Riemannian manifolds” (Link)

Advisor: Hee-Seok Oh (Link)

Thesis.pdf

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