校庆讲座之三十五:美国德州大学阿灵顿分校Prof. Ren-Cang Li教授应邀来我校讲学

编辑: | 来源:数学学院 | 发布日期:2019-07-08

题目:Learning Low-dimensional Latent Graph Structures
       Prof. Ren-Cang Li,  1995年毕业于美国加州伯克利分校,获应用数学博士学位。现为美国德州大学阿灵顿分校(www.3522.com)教授、博导,厦门大学“闽江学者”讲座教授。长期从事数值代数、科学计算、微分方程数值解法等领域的研究。曾担任“SIAM J. Matrix Anal. Appl.”、“Mathematical Communications”、“Numerical Algebra, Control and Optimization”副主编、“Operators and Matrices”、“Linear and Multilinear Algebra”等刊物的编委。主持过含美国国家自然科学基金在内的各类项目十几项。在SIAM J SCI COMPUT,  Math. Comp., SIAM J. Matrix Anal. Appl., Numerische Mathematik, Numerical Linear Algebra with Applications, BIT Numerical Mathematics 等国际著名期刊上发表学 术论文100多篇。

We aim to automatically learn a latent graph structure in a low-dimensional space from high-dimensional, unsupervised data based on a unified density estimation framework for both feature extraction and feature selection, where the latent structure is considered as a compact and informative representation of the high-dimensional data. Based on this framework, two novel methods are proposed with very different but intuitive learning criteria from existing methods. The proposed feature extraction method can learn a set of embedded points in a low-dimensional space by naturally integrating the discriminative information of the input data with structure learning so that multiple disconnected embedding structures of data can be uncovered.The proposed feature selection method preserves the pairwise distances only on the optimal set of features and selects these features simultaneously. It not only obtains the optimal set of features, but also learns both the structure and embeddings for visualization.Extensive experiments demonstrate that our proposed methods can achieve competitive quantitative (often better) results in terms of discriminant evaluation performance, and are able to obtain the embeddings of smooth skeleton structures and select optimal features to unveil the correct graph structures of high-dimensional datasets.

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