12 research outputs found
rTensor: An R Package for Multidimensional Array (Tensor) Unfolding, Multiplication, and Decomposition
rTensor is an R package designed to provide a common set of operations and decompositions for multidimensional arrays (tensors). We provide an S4 class that wraps around the base 'array' class and overloads familiar operations to users of 'array', and we provide additional functionality for tensor operations that are becoming more relevant in recent literature. We also provide a general unfolding operation, for which the k-mode unfolding and the matrix vectorization are special cases of. Finally, package rTensor implements common tensor decompositions such as canonical polyadic decomposition, Tucker decomposition, multilinear principal component analysis, t-singular value decomposition, as well as related matrix-based algorithms such as generalized low rank approximation of matrices and popular value decomposition
Tensor Factor Model Estimation by Iterative Projection
Tensor time series, which is a time series consisting of tensorial
observations, has become ubiquitous. It typically exhibits high dimensionality.
One approach for dimension reduction is to use a factor model structure, in a
form similar to Tucker tensor decomposition, except that the time dimension is
treated as a dynamic process with a time dependent structure. In this paper we
introduce two approaches to estimate such a tensor factor model by using
iterative orthogonal projections of the original tensor time series. The
approaches extend the existing estimation procedures and our theoretical
investigation shows that they improve the estimation accuracy and convergence
rate significantly. The developed approaches are similar to higher order
orthogonal projection methods for tensor decomposition, but with significant
differences and theoretical properties. Simulation study is conducted to
further illustrate the statistical properties of these estimators