2433fec2144ccf5fea1c9c5ebdbc3924-Supplemental-Conference.pdf

A Proof of the object in Equation 3 is convex, when α is sufficiently small. To validate this statement, we first prove two factors in the object are convex (Lemma A.1 and Lemma A.2) and the combination of them keeps the convex property (Lemma A.3). Lemma A.1. P and Q are positive semidefinite indicates that i [ [1..N ] ], 0 λ Thus, P α Q is positive semidefinite. Combining Lemma A.1, Lemma A.2 and Lemma A.3, the objective of Equation 3 is convex when In addition, to avoid replacement clash, we do not allow any word to appear in more than word set. Eventually, top 50 semantically matching pairs are retained for CA TER.