Tensors

Tensors are mathematical objects that have recently gained great popularity due to their ability to model multiway data dependencies. Tensor factorization into latent factors is very important for numerous tasks, such as feature selection, dimensionality reduction, compression, data visualization and interpretation. The problem of tensor completion, where we are called upon to "predict" the missing values of tensors, is extremely important in applications such as recommendation systems. In recent years, several software packages (n-way Toolbox, Tensorlab, Tensor Toolbox) have been developed for tensor processing, which highlights their growing importance. In many important applications, the tensors we are called upon to handle have billions of data, which makes it extremely difficult to process them on conventional computers. The available software packages are mainly serial implementations based on MATLAB, so the are not suitable for processing very large tensors. We estimate that the only viable way to process very large tensors is through parallel supercomputers.