What is Tensor

The last decade has witnessed exponential growth of data particularly in the fields of biomedicine, unstructured text processing and signal processing. There exist instances of data depicting simultaneous interactions amongst more than two types of entities. Such data are not readily amenable to matrix representation as matrices can show interactions between only two types of entities at a time. Tensors are multimodal extensions of matrices (a matrix can be thought of as 2-mode tensor), and tensor factorizations (decompositions) are multiway generalizations of matrix factorizations. This chapter provides an overview of tensor factorization methods as well as a literature review of selected applications in areas that are currently experiencing exponential data growth and likely of interest to a broad audience.