Exploiting Social Network Structure for Person-to-Person Sentiment Analysis (Supplementary Material to [WPLP14])

Our definition of a triangle t = {e1,e2,e3} for an undirected signed graph G = (V,E,x) expresses each triangle as an unordered set of edges. However, we implicitly impose an ordering on the edges of t when we form xt = (xe1 ,xe2 ,xe3) because the vector xt is an ordered object. As this ordering is arbitrary, d : {0,1}3→ R+ must be invariant to the order of its arguments, i.e., for any permutation matrix π, d(xt) = d(xtπ). This requirement implies that there are only 4 possible values that d can take on: d(0,0,0),d(1,0,0) = d(0,1,0) = d(0,0,1),d(0,1,1) = d(1,0,1) = d(1,1,0), and d(1,1,1). We always use this restriction when learning or specifying d.