Yong-Do Lim
Sungkyunkwan University · 数学
研究室紹介
Professor Yong-Do Lim's research lab specializes in geometric analysis, matrix analysis, and operator theory, with a strong focus on positive definite matrices, Riemannian and Hadamard manifolds, and their applications in optimization and differential equations. The lab investigates advanced matrix means—such as the Karcher mean, geometric mean, and golden mean—applying them to Riccati equations, matrix inequalities, and symplectic structures. It also explores novel frameworks in machine learning and deep learning for cybersecurity, particularly in detecting web-based threats like XSS attacks through hybrid ensemble models. The integration of differential geometry with functional analysis and computational methods defines the lab’s interdisciplinary approach.
Research Overview
Research Output Trend
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Selected Papers
15We show that the Karcher mean of n points in any Hadamard space can be approximated by a natural explicitly constructed sequence. In the special case when the Hadamard space is the Riemannian manifold of positive definite matrices, this has been recently proved by J. Holbrook. A general version, in which the n points are assigned different weights, is established.
Existing web-based security applications have failed in many situations due to the great intelligence of attackers. Among web applications, Cross-Site Scripting (XSS) is one of the dangerous assaults experienced while modifying an organization's or user's information. To avoid these security challenges, this article proposes a novel, all-encompassing combination of machine learning (NB, SVM, k-NN) and deep learning (RNN, CNN, LSTM) frameworks for detecting and defending against XSS attacks with