(2005a) define the Hilbert-Schmidt independence criterion (HSIC) to be the squared Hilbert-Schmidt norm ||C XY || 2 HS of (2) and derive an expression for it in terms of kernels K and L They also show the empirical estimate of it to be where T is the centering matrix and (j) ), i, j = 1:D are the kernel (Gram) matrices of observations.
crucially, the kernel evaluations for K take place between and not between the individual word embeddings x (i) and x (j) , and similarly for L. both K and L are square matrices of dimension D × D .