Tensors, polynomials and models for directional data

Abstract

In this chapter we describe tensorial tools for the study of directional data. We first make explicit different tensor representations. We then use this to compare models, as one of the tensor representations is polynomial. Thus a multivariate Taylor expansion uses Higher Order Tensors, and models will use an expansion in higher order polynomials. We show provide formulas for different model-to-model conversions.