Title: Symmetric tensor rank and projection pursuit
Authors: Nicola Loperfido - University of Urbino (Italy) [presenting]
Abstract: A tensor is a multi-way array representing a multilinear operator, up to a choice of bases. It is symmetric if it is invariant under permuting indices. A symmetric tensor is decomposable if its elements may be represented as products of a fixed number of elements belonging to the same vector. The symmetric rank of a symmetric tensor (also known as the symmetric tensor rank) is the minimum number of symmetric, decomposable tensors which need to be added together to get the tensor itself. Symmetric tensor rank plays a relevant role in projection pursuit, as for example in skewness-based projection pursuit, kurtosis-based projection pursuit, projection pursuit regression and projection pursuit density estimation.