Clustering is a fundamental problem in unsupervised learning. In this talk, we will introduce a convex clustering model, which can be regarded as a convex relaxation to the K-means with some favorable properties. We will establish sufficient conditions for the perfect recovery guarantee of the general weighted convex clustering model, which also improves existing theoretical results of the convex clustering model with uniform weights. In addition, we will introduce a highly efficient algorithm and a dimension reduction technique for solving the convex clustering model. Extensive numerical results will also demonstrate the superior performance of the convex clustering model and the proposed algorithms.

Papers related to the talk:
Yancheng Yuan, Tsung-Hui Chang, Defeng Sun, and Kim-Chuan Toh, A Dimension Reduction Technique for Structured Sparse Optimization Problems with Application to Convex Clustering, SIAM Journal on Optimization, 32: 3 (2022) 2294–2318. https://epubs.siam.org/doi/10.1137/21M1441080

Defeng Sun, Kim-Chuan Toh, and Yancheng Yuan, Convex clustering: model, theoretical guarantee and efficient algorithm, Journal of Machine Learning Research, 22(9):1−32, (2021). ]
https://www.jmlr.org/papers/volume22/18-694/18-694.pdf

Yancheng Yuan is a research assistant Professor of the Department of Applied Mathematics, The Hong Kong Polytechnic University. He received his Ph.D in mathematics from NUS in 2020. His research focuses on optimization theory, algorithm design and software development, the mathematical foundation of data science, and data-driven applications. He has published papers in prestigious journals and leading conferences, including SIOPT, JMLR, IJAA, OMS, ICML, WWW. His research has been featured in some prestigious academic conferences, such as the Best Paper Award Finalist (WWW 2021) and the Best 10% Paper Award (ICIP 2014).

For more information about the ESD Seminar, please email esd_invite@sutd.edu.sg