Similarity Component Analysis: Supplementary Material

k=1 q1−s k r s k log θk (S1) where p(s) = Pr(s1, . . . , sK|u,v, s) = ∏K k=1 Pr(sk|u,v, s). pk = P (sk = 1|u,v) is given by eq. (2). qk = P (sk = 1|u,v, s = 0) and rk = P (sk = 1|u,v, s = 1) are given by eq. (7). Note that the last equation uses the fact that Ep(s)(sk) = q 1−s k r s k. The third term Ep(s)[s log(1− ∏K k=1 θ 1(sk=1) k )] is not tractable; variational methods can be used, as described in [1].