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2018 NCTS Summer Course: Diffusion Learning Theory and Medical Applications – the first step
10:30 - 11:45 and 13:00 - 14:15, Every Tuesday, July 31 - August 21, 2018
Room 201, Astronomy-Mathematics Building, NTU

Gi-Ren Liu (National Cheng Kung University)

Yuan-Chung Sheu (National Chiao Tung University)
Hau-Tieng Wu (Duke University)

Nonlinearity and nonstationarity are common features of modern datasets. To quantify these natures and hence carry out statistical analyses, new techniques are needed to model the underlying structure, and develop the algorithms. The purpose of this course is introducing the frontier research field, diffusion learning theory, which helps organize modern complicated data in an unsupervised fashion. In this introductory short course, we provide the first step toward this field by introducing the main algorithm, diffusion maps and related topics, and showing its application in the medical field. 
Students with background in calculus and linear algebra are encouraged to participate in this first step course. Depending on students’ interest, we will provide further advanced course in the near future.
2. 課程講者:Gi-Ren Liu (National Cheng Kung University)
3. 課程之大綱:
The lecture is based on the upcoming text book “Ten lectures in diffusion map” by Amit Singer and Hau-tieng Wu. 
Here is a tentative course plan for this short course: 
Graph Laplacian (GL) and spectral graph theory. Random walk on a graph and Diffusion maps (DM). Relationship with locally linear embedding, eigenmap, etc. Natural metrics on an affinity graph – Diffusion distance (DD) and commute time. Bochner theorem.

Poster: events_3_1481806013647176677.pdf

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 (C) 2018 National Center for Theoretical Sciences