应002全讯白菜网数学系的邀请，挪威卑尔根大学和香港浸会大学台雪成教授将于近期来访数学系并做一系列学术报告。欢迎感兴趣的老师和同学参加。

报告时间和地点：2018年7月5日（星期四）上午 8:30开始格物楼 503

报告题目1：Fast Algorithms for Euler´s Elastica energy minimization and applications

报告摘要1：In the talk, we consider an Euler's elastica based image segmentation model. An interesting feature of this model lies in its preference of convex segmentation contour. However, due to the high order and non-differentiable term, it is often nontrivial to minimize theassociated functional. In this work, we propose using augmented Lagrangianmethod to tackle the minimization problem. Especially, we design a novel augmentedLagrangian functional that deals with the mean curvature term differently as those ones in theprevious works. The new treatment reduces the number of Lagrange multipliers employed, and more importantly, it helps represent the curvature more effectively and faithfully. Numerical experiments validate the efficiency of the proposed augmented Lagrangian methodand also demonstrate new features of this particular segmentation model, such as shapedriven and data driven properties.

报告题目2：Nonlocal graph TV for variational  semi-supervised learning and clustering and fast algorithms

报告摘要2：In this talk, we first show the essential ideas to use graph cut for data clustering. Then we present some recent developed continuous max-flow model and algorithms. Afterwards, we show the application of these models and algorithms for machine learning and data clustering. One essential ingradient is to use nonlocal total variation and Laplacian to formulate a the problem as a graph cut.  We propose an algorithm for semi-supervised clustering of high-dimensional data. The data points are modeled as vertices of a weighted graph, and the labeling function defined on each vertex takes values from the unit simplex, which can be interpreted as the probability of belonging to each class.  The algorithm is proposed as a minimization of a convex functional of the labeling function. There are two versions of the models. The first one combines the Rayleigh quotient for the graph Laplacian and a region-force term, and the second one only replaces the Rayleigh quotient with the total variation of the labeling function. The region-force term is calculated by the affinity between each vertex and the training samples, characterizing the conditional probability of each vertex belonging to each class. The numerical methods for solving these two versions of the proposed algorithm are presented, and both are tested on several benchmark data sets such as handwritten digits (MNIST) and moons data. Experiments indicate that the correction rates and the computational speed are competitive with the state-of-the-art in multi-class semi-supervised clustering algorithms. Especially, the new models produce substantial improvements of the classification accuracy in comparison with the corresponding models without the regional force in cases that the sampling rate is relatively low.

报告人简介：台雪成，挪威卑尔根大学教授和香港浸会大学教授，第8届“冯康”计算数学奖获得者。台雪成教授的研究领域主要包括数值PDE、优化技术、计算机视觉以及图像处理等，在SIAM J. Sci. Comput.、International Journal of Computer Vision、IEEE Transactions on Image Processing、IEEE Transactions on Visualization and Computer Graphics、SIAM J. Numer. Anal.等国际顶级杂志以及CVPR、ECCV等国际顶级会议共发表论文100多篇。担任多个国际会议的大会主席，并多次应邀做大会报告，目前担任Inverse Problems and Imaging，International Journal of Numerical analysis and modelling，Numerical Mathematics: Theory, Methods and Applications，Advances in Numerical Analysis, SIAM Journal on Imaging Sciences, Journal of Mathematical Imaging and Vision等多个国际知名期刊的编辑及执行编辑。