Tensor methods and Algebra
DACS Research - Applied Mathematics
Methods to analyse multilinear structure in multivariate data and for numerically solving systems of multivariate polynomial equations. Tensor decompositions aim to reveal and exploit low rank structure in high dimensional data arrays. This admits the generalisation of principal component analysis and singular value decomposition to multivariate problems, with applications in multivariate signal processing and efficiency gains in neural network training. Global optimization of multivariate polynomial criteria is addressed with a combination of algebraic and numerical linear algebraic methods