Algorithms for Tensor-Based Modeling of Large-Scale Structured Data
Most approaches to Big Data do not exploit all of their structure. Specifically, Big Data tasks such as denoising, imputation of missing data and classification can greatly benefit from the information contained in the structure of the data. Typically, arrays of dimension $3$ or higher are flattened in order to apply conventional linear algebra methods. In doing so, one loses the rich tensor structure.
The Canonical Polyadic (CP) decomposition is a powerful tool for analyzing tensor data. CP decompositions have been applied in many areas such as psychometrics, chemometrics, signal and image processing, computer vision, neuroscience and finance. Unfortunately, CP decompositions are computationally inefficient and numerically unstable. The lack of scalable algorithms to apply tensor-based methods is a major obstacle in utilizing the structural information.
In this proposal, the PIs develop novel theoretical foundations and scalable algorithms for tensor decomposition and apply them to some major Big Data tasks such as noise removal, data imputation, information integration and dimension reduction. To evaluate the performance of the proposed tensor methods, they will be applied to early detection of sepsis, which represents a spectrum of complex problems in medicine and science.