Given the bipartite representation G, the optimal matching EC E between two vertex sets is computed using the Hungarian Algorithm [27]. The optimal bipartite graph(shown on the right side of Figure 2b)isG=(V, E)where ES E such that H12EE, len(u1, ui) is optimal. Given the weights of vertices in the representation Wwl,.,w,wi,..., w2, these are normalized(value [0-1))to I }whey时 a'ew12 wi= Aggregate Path Distances: Abiding by our notion that the closer nodes with higher weights contribute more to the similarity value, we present three(slightly different) path length aggregation measures for empirical evaluation. The path distance of an edge e, in the optimal bipartite graph is defined as if len(ui, U))is 0 path(ei)=lo, n(v2,v)is∞ The Euler path distance of an edge eii in the optimal bipartite graph is defined as if len(vi, Ui)is 0 en("2, otherwise The Euler half path distance of an edge eii in the optimal graph is defined as 0 if len(ui, u2)is euhalf(eij) The aggregate distance of all the matching edges of the bipartite graph is given by the sum of their path distances. them using aggregate path distances in the optimal bipartite graph are defined as foll ( sympath(u1, u2) ∑ve∈ E, path(ey) min(size(terms(u1), size(terms(u2)))x mar(path(eii)) ∑ VEneER empath(ei) (4)simeupath(u1, u2)= min(size(terms(un)), size(terms(u2)))x mar(eupath(ein)) (5)simeuhalf(u1, u2 vse∈ gy((e) min(size(terms(un)), size(terms(u2)))x mar(euhalf(eij)) 5.4 Compound Similarity Measures While the term vector similarity technique considers only intersecting terms while computing similarity, when two profiles actually intersect this measure is quite accurate Therefore, we propose compound similarity measures where the similarity between tersecting profile terms are computed using cosine similarity(Equation 1), and theGiven the bipartite representation G, the optimal matching E0 ⊆ E between two vertex sets is computed using the Hungarian Algorithm [27]. The optimal bipartite graph (shown on the right side of Figure 2b) is G0 = hV, E0 P i where E0 ⊆ E such that ∀eij∈E0 len(v 1 i , v2 j ) is optimal. Given the weights of vertices in the representation W12 = {w 1 1 , . . . , w1 i , w2 1 , . . . , w2 j }, these are normalized (value [0-1]) to W120 = {w 1 0 1 , . . . , w1 0 i , w2 0 1 , . . . , w2 0 j } where ∀wk0 l ∈W120 is w k 0 l = w k P l wk l . Aggregate Path Distances: Abiding by our notion that the closer nodes with higher weights contribute more to the similarity value, we present three (slightly different) path length aggregation measures for empirical evaluation. The path distance of an edge eij in the optimal bipartite graph is defined as path(eij ) = 8 >>< >>: 1, if len(v 1 i , v2 j ) is 0 0, if len(v 1 i , v2 j ) is ∞ w1 0 i ×w2 0 j len(v 1 i ,v2 j ) , otherwise The Euler path distance of an edge eij in the optimal bipartite graph is defined as eupath(eij ) = 8 >>< >>: 1, if len(v 1 i , v2 j ) is 0 0, if len(v 1 i , v2 j ) is ∞ w1 0 i ×w2 0 j e len(v1 i ,v2 j ) , otherwise The Euler half path distance of an edge eij in the optimal bipartite graph is defined as euhalf(eij ) = 8 >>>>< >>>>: 1, if len(v 1 i , v2 j ) is 0 0, if len(v 1 i , v2 j ) is ∞ w1 0 i ×w2 0 j e 0 @ len(v1 i ,v2 j ) 2 1 A , otherwise The aggregate distance of all the matching edges of the bipartite graph is given by the sum of their path distances. Similarity Measures: Given two user profiles u1 and u2, the similarity between them using aggregate path distances in the optimal bipartite graph are defined as follows. (3) simpath(u1, u2) = P ∀eij∈E0 path(eij ) min(size(terms(u1)), size(terms(u2))) × max(path(eij )) (4) simeupath(u1, u2) = P ∀eij∈E0 eupath(eij ) min(size(terms(u1)), size(terms(u2))) × max(eupath(eij )) (5) simeuhalf (u1, u2) = P ∀eij∈E0 euhalf(eij ) min(size(terms(u1)), size(terms(u2))) × max(euhalf(eij )) 5.4 Compound Similarity Measures While the term vector similarity technique considers only intersecting terms while computing similarity, when two profiles actually intersect this measure is quite accurate. Therefore, we propose compound similarity measures where the similarity between intersecting profile terms are computed using cosine similarity (Equation 1), and the