EAGER: Fast and Accurate Nonnegative Tensor Decompositions: Algorithms and Software

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EAGER: Fast and Accurate Nonnegative Tensor Decompositions: Algorithms and Software During the past decades, numerous efficient and effective data analysis algorithms have been designed where data sets are represented as two dimensional arrays, i.e., matrices. However, matrix based methods have limitations since modern data sets are multi-scale and multi-dimensional. In numerous applications, data sets are more naturally represented as tensors than matrices including image analysis, climate modeling, chemometrics, genome signal analysis, and biometric recognition. In this project, the mathematical characteristics of tensor decompositions will be studied. Algorithms will be designed for large scale data analysis that can reveal complex relationships among many dimensions which matrix based methods often cannot. Computations on tensors are expected to extend many of the advantages that the matrix based data analysis methods have offered. Tensor-based methods can be utilized for data compression, modeling, regression, and fusing of information obtained from different sources and scales. Tensor based methods are relatively new in many application areas and theoretical and algorithmic developments, especially for large scale problems, have been slow even in the areas where they have been heavily utilized. The key goals of the project include extension of the matrix decomposition techniques such as the SVD to higher order tensors and develop efficient algorithms for large scale analysis of multi-dimensional data and design their higher-order extensions, development of algorithms for the computation of various nonnegative matrix factorizations (NMF) and nonnegative tensor factorizations (NTF) and study of the mathematical properties of the algorithms, such as robustness, efficiency and accuracy, and implement them in publicly available software. This research will substantially improve the possibility of detailed study of larger scale multi dimensional data sets in numerous application areas including text mining, biological network analysis, and medical examination and diagnosis.