Title: Tensor Analysis and Neuroimaging Applications
Data in the form of multidimensional array, or tensor, are fast emerging in a wide variety of scientific and business applications. Simply turning an array into a vector would both induce extremely high dimensionality and destroy the inherent structure of the array. In this talk, we discuss two tensor analysis problems, one about regression with a tensor-valued response, and the other about dynamic tensor clustering. We introduce two low-dimensional structures: sparsity and low-rankness, which helps bring the ultrahigh dimensionality to a manageable level. We develop fast estimation algorithms, and derive the associated asymptotic properties. We illustrate with two applications in brain imaging analysis.