演講者：林澤佑教授 ( 國立臺灣大學資料科學學位學程 )

日   期：2025 年 11 月 19 日（星期三）13:30

地   點：國立高雄大學理學院 408 室

講   題：Manifold Reconstruction with Deep Residual Networks and Modeling Complex

摘   要：

In this talk, we briefly introduce our two recent works in manifold learning.

In the first part, we consider the manifold approximation algorithm of a dataset $X$ in $\mathbb{R}^n$ by a low dimensional submanifold $M$ proposed in [1]. Our work is to rephrase this manifold reconstruction algorithm as a learning process of some residual neural networks. This connection bridges the theory of Differential Geometry and Deep Learning.

In the second part, we will explore hyperbolic metric learning in e-commerce,focusing on modeling complex user behavior. By transforming users' clickstream datainto a graph and converting it to a spanning tree, we embed this structure into the Poincaré disk model. This hyperbolic embedding captures hierarchical and sequential patterns with low distortion, allowing us to represent user interactions efficiently in a lower-dimensional space. This approach leverages hyperbolic geometry to improve action prediction and provide insights into behavior patterns, offering valuable applications for recommendation systems and user engagement analysis.

[1] Fefferman, C., Ivanov, S., Kurylev, Y., Lassas, M., & Narayanan, H. (2019). Reconstruction and Interpolation of Manifolds. I: The Geometric Whitney Problem. Foundations of Computational Mathematics, 1-99.