Tensor computing for big data analytic - Ong, Jenn Bing (Nanyang Technological University, 2021)
Tensors have been around since the end of nineteenth century with the development of differential calculus. Tensor research and applications have spanned many areas ranging from mathematics and physics in the early days to psychometrics and linguistics later in around 1960s, and more recently to signal processing and machine learning in the 1990s. Tensor is multi-dimensional extension of matrix, it emerges as important mathematical tool because measurements from experimental studies usually come from more than two dimensions (e.g., space, time, sensors data, and locations), treating these arrays as matrices might lose important structural information such as multi-dimensional correlation structure during data analysis. Tensor decomposition is an established technique for multi-way data analysis such as blind source separation, feature extraction, higher-order statistical analyses, etc. In general, matrix and tensor decomposition have different properties (e.g., uniqueness and interpretability) despite their similarity in concept. Tensor network decomposes higher-order tensors into sparsely-interconnected low-order core tensors, which captures the complex correlation structure in parsimonious manner. Tensor network has been used mostly for data imputation and compressed computation due to the lack of physical interpretability, however, it is promising for big data processing and high-dimensional numerical computing due to their natural support for parallel distributed and compressed computation.