The SAN activation process is iterative. Let A; (p) denotes the activation value of ode j at iteration p. All the original term nodes corresponding to the tuples in a user profile t, take their term weights wj as their initial activation value Ai (0)=wj. The activation value of all the other nodes are initalized to 0. In each iteration Every node propagates its activation to its neighbours he propagated value is a function of the nodes current activation value and weight of the edge(see [15])that connects them(denoted as O,(p)) After a certain number of iterations when the termination condition is reached. the highest activation value among the nodes that are associated with each of the original term node is retrieved into a set ACT=acti, act2, .,actn+m).The the these activation values can be mapped to the similarity between the profiles under the intuition that the nodes with higher activation values are typically the ones that have alue contributions from both the profiles and hence should contribute more to similarity to a value between 0 and 1. The SAN-based similarity between two profiles u1 and u2 where mar(ACT)is the highest activation value is siman(u1, u2 5.3 Similarity Computation by Matching Bipartite Graph A key insight here is that by omitting the intermediate related nodes and considering only the path length between the nodes representing the original profile terms, the semantic network can be converted to a bipartite graph(shown on the left side of Figure 2b). The nodes of the first profile and second profile are the two vertex sets of the bipartite graph where the edge denotes the length between the original term nodes as obtained from the emantic network. Once the bipartite graph is derived, we are able to apply standard algorithms for optimal matching of the bipartite graph. Our similarity measures based on optimal bipartite matching operates under the simple notion that the nodes with higher weights and that are closely located contribute more to the similarity of the entities and viceversa Each node u" in the semantic network is a pair(ti, wi) where u= l or 2 dentin hich user's profile term the node represents. The path(ul, va)denotes the set of edges between two nodes ui and u, in the semantic network. All the edges between ny two nodes with different terms in the semantic network have uniform weight Ve e path (ui, US)set wt(e)=l where wt (e)denotes the weight of the edge e For any two vertices uI and v2 the distance between the them is len(ui, UA if ti =t, wt(ek), otherwise Definition 2(Bipartite Representation). The bipartite graph representation G of the profiles u1 and u2 is a pair G=(V, E)where V=VUV2 where V denotes the vertices from the first profile u1 and v2 denotes the vertices from the second profile u2 E={e1,e12,…,ei} where i={1,2,…,n},j={1,2,…,m} andlen(t} denotes the path length between then vertices u; and ugThe SAN activation process is iterative. Let Aj (p) denotes the activation value of node j at iteration p. All the original term nodes corresponding to the tuples in a user profile tj take their term weights wj as their initial activation value Aj (0) = wj . The activation value of all the other nodes are initalized to 0. In each iteration, – Every node propagates its activation to its neighbours. – The propagated value is a function of the nodes current activation value and weight of the edge (see [15]) that connects them (denoted as Oj (p)). After a certain number of iterations when the termination condition is reached, the highest activation value among the nodes that are associated with each of the original term node is retrieved into a set ACT = {act1, act2, ..., actn+m} 3 . The aggregate of the these activation values can be mapped to the similarity between the profiles under the intuition that the nodes with higher activation values are typically the ones that have value contributions from both the profiles and hence should contribute more to similarity and vice versa. Therefore, the similarity value is the sum of the set ACT normalized to a value between 0 and 1. The SAN-based similarity between two profiles u1 and u2 where max(ACT) is the highest activation value is (2) simsan(u1, u2) = P ∀acti∈ACT acti |ACT| × max(ACT) 5.3 Similarity Computation by Matching Bipartite Graph A key insight here is that by omitting the intermediate related nodes and considering only the path length between the nodes representing the original profile terms, the semantic network can be converted to a bipartite graph (shown on the left side of Figure 2b). The nodes of the first profile and second profile are the two vertex sets of the bipartite graph where the edge denotes the length between the original term nodes as obtained from the semantic network. Once the bipartite graph is derived, we are able to apply standard algorithms for optimal matching of the bipartite graph. Our similarity measures based on optimal bipartite matching operates under the simple notion that the nodes with higher weights and that are closely located contribute more to the similarity of the entities and viceversa. Each node v u i in the semantic network is a pair hti , wii where u = 1 or 2 denoting which user’s profile term the node represents. The path(v 1 i , v2 j ) denotes the set of edges between two nodes v 1 i and v 2 j in the semantic network. All the edges between any two nodes with different terms in the semantic network have uniform weights ∀e ∈ path(v 1 i , v2 j ) set wt(e) = 1 where wt(e) denotes the weight of the edge e. For any two vertices v 1 i and v 2 j the distance between the them is len(v 1 i , v 2 j ) = ( 0 P , if ti = tj ∀ek∈path(v 1 i ,v2 j ) wt(ek), otherwise Definition 2 (Bipartite Representation). The bipartite graph representation G of the profiles u1 and u2 is a pair G = hV, Ei where – V = V 1 ∪V 2 where V 1 denotes the vertices from the first profile u1 and V 2 denotes the vertices from the second profile u2 – V 1 = {v 1 1 , v1 2 , . . . , v1 n} and V 2 = {v 2 1 , v2 2 , . . . , v2 m} where n ≤ m and v k i = ht k i , wk i i is a term. – E = {e11, e12, . . . , eij} where i = {1, 2, . . . , n}, j = {1, 2, . . . , m} and len(v 1 i , v2 j ) denotes the path length between then vertices v 1 i and v 2 j . 3 n and m are the number of terms in the first and second profile respectively