Then Kernelized Sort-ing formulates Π as the solution of the following optimization problem (Gretton et al., 2005): In our supervised version of Kernelized Sorting, we fix the permutation matrix (to sayΠ) and modify the kernel matrices K x and K y so that the objective function is maximized for the given permutation.
we find a mapping for each language, such that when the documents are projected into their common subspaces they are more likely to respect the alignment given byΠ.