Dissertation: Manifold Embedding with Deep ResNet and A Study of the Continuity of HodgeRank
I have two main research topics:
a) HodgeRank and its real-world applications;
b) Manifold reconstruction using Neural Network.
For the first topic, I mainly deal with HodgeRank method and its generalization. A sufficient condition of continuity of HodgeRank was studied.
For the second topic, I reformulate a manifold interpolation algorithm as a learning process of deep residual network (ResNet) using the characterization property of affine orthogonal projections.
Studied on manifold interpolation/reconstruction based on composition of local affine projections
Thesis: Stochastic Portfolio Optimization Models for the Stable Growth Benchmark Tracking
I focused on the combination between portfolio optimization problem and scenario trees. Moment matching method was introduced to provide a user-defined scenario tree which fits the first few moments of past data.
Major in Judo (2nd Dan), double major in Karate (brown belt), minor in Slavic languages and applied mathematics. Besides, I am one of the co-founders of speciality coffee club in NCCU.
HodgeRank is a pairwise comparison method for recommendation system.
The theory of HodgeRank is based on the theory of cohomology group and Hodge/Helmholtz Decomposition.
The figure is referred from the paper by Jiang, X., Lim, L. H., Yao, Y., & Ye, Y.
I am recently focus on how to use neural network in medical image analysis. I am working with master students in NTU with Prof. Weichung Wang. We are now trying to duplicate some existence models and then improve it in any sense.
This figure is the MRI image of my left shoulder.