报告人：夏志明教授

报告时间：2023-11-14（星期二）9：30-10：30

报告地点：数学楼2-1

 #腾讯会议：790-578-592

题目：Multiview PCA: A methodology of feature extraction and dimension reduction for high-order data

摘要：In this talk, we focus on a new PCA methodology for tensor data. Facing with rapidly-increasing demands for analyzing high-order data or multiway data, feature-extracting methods become imperative for analysis and processing. The traditional feature-extracting methods, however, either need to overly vectorize the data and smash the original structure hidden in data, such as PCA and PCA-like methods, which is unfavourable to the data recovery, or can not eliminate the redundant information very well, such as Tucker Decomposition (TD) and TD-like methods. To overcome these limitations, we propose a more flexible and more powerful tool, called the Multiview Principal Components Analysis (Multiview-PCA) in this paper. By segmenting a random tensor into equal-sized subarrays named sections and maximizing variations caused by orthogonal projections of these sections, the Multiview-PCA finds principal components in a parsimonious and flexible way. In so doing, two new operations on tensors, the direction inner/outer product, are introduced to formulate tensor projection and recovery. With different segmentation ways characterized by section depth and direction, the Multiview-PCA can be implemented many times in different ways, which defines the sequential and global Multiview-PCA respectively. These multiple Multiview-PCA take the PCA and PCA-like, Tucker Decomposition and the TD-like as the special cases, which corresponds to the deepest section-depth and the shallowest section depth respectively. We propose an adaptive depth and direction selection algorithm for implementation of Multiview-PCA. The Multiview-PCA is then tested in terms of subspace recovery ability, compression ability and feature extraction performance when applied to a set of artificial data, surveillance videos and hyperspectral imaging data. All the tests support the flexibility, effectiveness and usefulness of Multiview-PCA.

个人简介：夏志明，教授，博士生导师，西北大学数学学院副院长，主要致力于张量数据分析、大数据异质性结构推断、分布式统计推断与计算、生物统计学等数据科学理论与应用研究。在“Biometrika”, “Technometrics”、“IEEE Transaction on Cybernetics”、“Journal of Machine Learning Research”、“Statistics in Medicine”等国际统计与机器学习期刊以及“中国科学”等国内期刊发表论文40余篇；主持国家自然科学基金项目4项，主持省部级项目3项, 作为骨干成员获得“陕西省科学技术进步奖”二、三等奖共2项，“陕西省高校科学技术奖”一等奖共2项；先后赴香港科技大学、佛罗里达大学等科研机构进行专业访问与学术交流。