Extension of PCA to Higher Order Data Structures: An Introduction to Tensors, Tensor Decompositions, and Tensor PCA.

The widespread use of multisensor technology and the emergence of big data sets have brought the necessity to develop more versatile tools to represent higher order data with multiple aspects and high dimensionality. Data in the form of multidimensional arrays, also referred to as tensors, arise in a variety of applications including chemometrics, hyperspectral imaging, high-resolution videos, neu...