演講者：林澤佑教授
              國立臺灣大學資料科學學位學程

日   期：2024 年 11 月 27 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 Data in Hyperbolic Space

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 ecommerce, focusing on modeling complex user behavior. By transforming users' clickstream data into 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.