报告人：王东（香港中文大学深圳分校）

时  间：4月9日下午2:00

地  点：厦大海韵园实验楼105报告厅

内容摘要:

Archetypal analysis is an unsupervised learning method that uses a convex polytope to summarize multivariate data. For fixed k, the method finds a convex polytope with k vertices, called archetype points, such that the polytope is contained in the convex hull of the data and the mean squared distance between the data and the polytope is minimal. In this talk, we prove a consistency result that shows if the data is independently sampled from a probability measure with bounded support, then the archetype points converge to a solution of the continuum version of the problem, of which we identify and establish several properties. We also obtain the convergence rate of the optimal objective values under appropriate assumptions on the distribution. If the data is independently sampled from a distribution with unbounded support, we also prove a consistency result for a modified method that penalizes the dispersion of the archetype points. Our analysis is supported by detailed computational experiments of the archetype points for data sampled from the uniform distribution in a disk, the normal distribution, an annular distribution, and a Gaussian mixture model.

个人简介：

王东博士现为香港中文大学（深圳）理工学院助理教授，2013年本科毕业于四川大学数学学院，2017年博士毕业于香港科技大学数学系。在加入香港中文大学（深圳）前，王东博士曾在美国犹他大学数学系任助理教授讲师。王东博士的主要科研方向为计算材料，计算机视觉，机器学习及其交叉研究领域相关问题的理论与科学计算方法。

联系人：陈黄鑫