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.