Mining structured tensor data

挖掘结构化张量数据

• 批准号: 1207771
• 负责人: Xiaotong Shen
• 金额: $ 20.02万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-07-01 至 2016-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1207771&HistoricalAwards=false
• 关键词: Mining; structured; tensor; data

Structured modeling situations, with multivariate data involving tensors, are treated using constrained likelihood approaches, as an efficient means to exploit lower-dimensional structure for high-order analysis. In gene network analysis, for example, a constrained approach helps reveal gene-gene relations in a context of multiple graphical models. Special attention is devoted to the appropriate choice of the constraints for adaptation to a variety of structures. The general theme of the proposed project is the development of statistical methods of practical utility, both in prediction and estimation. In particular, the proposed project develops methods for (a) multiple graphical models for structure extraction, and for (b) high-order analysis of tensor data. The proposed research is primarily motivated by challenging problems that arise in gene network analysis and collaborative filtering, where one central issue is how to leverage and utilize lower-dimensional structure to battle high statistical uncertainty in a discovery process. New techniques are proposed and investigated, both computationally and statistically, which target biomedical and engineering problems. In (a) and (b), our effort will be on classification and regression, and on structure adaptation through tensor decomposition and factorization, with most effort focused towards condition specific extraction of lower-dimensional structure.Modern scientific and engineering investigation, as in biomedical research and computer vision, now produces enormous data that aim to simultaneously explore relations among hundreds and thousands interacting units. This project proposes methods for treating the new scientific environment. The project develops technology that is directly applicable to applied research, particularly in automatic machine processing and data mining, biomedical research, advertisement, and economics. Plans for technology transfer are described, in addition to an educational program that will train students in statistical learning and data mining. Educational activities include developing a course, and attracting undergraduate students to research.

结构化建模的情况下，涉及张量的多变量数据，被视为使用约束似然方法，作为一种有效的手段，利用低维结构的高阶分析。 例如，在基因网络分析中，约束方法有助于在多个图形模型的上下文中揭示基因-基因关系。特别注意的是适当选择的约束，以适应各种结构。拟议项目的总主题是发展预测和估计方面的实用统计方法。特别是，拟议的项目开发方法（a）多个图形模型的结构提取，和（B）高阶分析张量数据。这项研究的主要动机是基因网络分析和协同过滤中出现的挑战性问题，其中一个核心问题是如何利用和利用低维结构来对抗发现过程中的高统计不确定性。 新技术的提出和调查，计算和统计，目标生物医学和工程问题。在（a）和（B）中，我们将致力于分类和回归，以及通过张量分解和因子分解进行结构自适应，其中大部分工作集中在低维结构的特定条件提取上。现代科学和工程研究，如生物医学研究和计算机视觉，现在产生大量数据，旨在同时探索数百和数千个相互作用的单元之间的关系。 该项目提出了处理新的科学环境的方法。该项目开发直接适用于应用研究的技术，特别是自动机器处理和数据挖掘，生物医学研究，广告和经济学。技术转让计划的描述，除了教育计划，将培训学生在统计学习和数据挖掘。教育活动包括开发一门课程，吸引本科生进行研究。