Collaborative Research: Matrix-Model Machine Learning: Unifying Machine Learning and Scientific Computing

协作研究：矩阵模型机器学习：统一机器学习和科学计算要分析日益增长的海量数据以进行模式识别和知识发现，有效的机器学习模型和高效的计算算法是必不可少的工具。这项研究的目的是利用近几十年来科学计算的成功-包括成熟的算法和成熟的免费软件-为利用矩阵/张量计算方法解决具有挑战性的机器学习问题奠定理论基础。本研究始于机器学习和科学计算之间的关键联系：基于奇异值分解(SVD)的主成分分析为K-Means聚类算法提供了有效的全局解决方案。这种基本关系将系统地扩展到矩阵、张量和多关系数据，以处理越来越高的维度、多个索引和数据类型。本研究的主要目标是建立可以直接用于模式发现的著名科学计算技术，如奇异值分解、矩阵和张量分解，并进一步发展这些计算方法用于半监督学习、聚类和分类。重点将放在多索引数据(张量，如天气图序列或网络上的交通序列)和多关系数据(多个成对关系，如蛋白质结构域？蛋白质？小路还是文字？文件？作者)。将研究在基因组学、文本挖掘和计算机视觉中的应用。

Collaborative Research: Matrix-Model Machine Learning: unifying machine learning and scientific computingTo analyze the ever-growing massive quantities of data for pattern recognition and knowledge discovery, effective machine learning models and efficient computational algorithms are essential tools. The goal of this research is to establish a theoretical foundation for solve challenging machine learning problems utilizing matrix/tensor computational methodologies, leveraging over the success of scientific computing over recent decades - including well-developed algorithms and mature, freely-available software.This research begins with a critical connection between machine learning and scientific computing: an effective global solution to K-means clustering algorithm is provided by the principal component analysis which is based on singular value decomposition (SVD). This fundamental relationship will be systematically extended to matrices, tensors and multi-relational data, to deal with increasingly higher dimensions, multiple indexes and data types. The key goal of this research is to establish that well-known scientific computing techniques such as SVD, matrix and tensor decompositions can be directly utilized for pattern discovery, and further develop these computational methodologies for semi-supervised learning, clustering and classification. The focus will be on multi-index data (tensors, such as a sequence of weather maps or a sequence of traffics over a network) and multi-relational data (multiple pairwise relations, such as protein domains ? proteins ? pathways or words ? documents ? authors). Applications in genomics, text mining, and computer vision will be investigated.