Methods are disclosed for performing proper word alignment that satisfy constraints of coverage and transitive closure. Initially, a translation matrix which defines word association measures between source and target words of a corpus of bilingual translations of source and target sentences is computed. Subsequently, in a first method, the association measures in the translation matrix are factorized and orthogonalized to produce cepts for the source and target words, which resulting matrix factors may then be, optionally, multiplied to produce an alignment matrix. In a second method, the association measures in the translation matrix are thresholded, and then closed by transitivity, to produce an alignment matrix, which may then be, optionally, factorized to produce cepts. The resulting cepts or alignment matrices may then be used by any number of natural language applications for identifying words that are properly aligned.