A Taxonomy of Collab based recommender syster Predictability Paths Aggarwal et al. 9 proposed a graph-based recommendation algorithm in which the users are represented as nodes of a graph and the edges between the nodes indicate the degree of similarity between the users. The recommendations for a user were computed by traversing nearby nodes in this graph. The graph repre- entation has the ability to capture transitive relations which cannot be captured by nearest neighborhood algorithms. Authors reported better performance than the user -based schemes The approach is based on the concepts of horting and predictability. The horting condition states whether there is enough overlap between each pair of users(k, i )to decide whether the behavior of one user could predict the behavior of the other or not. By definition, user k horts user l if the following equation is card(Rk∩R)2min(F·card(Rk),G) where F< l and G is some predefined threshold. The predictability condition establishes that user I predicts behavior of user k if there exists a linear rating transformation k1,k,·k=8·7y+t carries ratings rL,] of user l into ratings Tk,j of user k with an acceptable The(s, t) pair of real numbers is chosen so that the transformation 8 keeps at least one value in the rating domain(see 9 for further details on s-t value pair restrictions). More formally, user I predicts user k if user k horts user I(eq 7)and if there exists a linear rating transformation Ts, t such that the expression 9 is satisfied, with B a positive real number. ∑/∈RnR1n-xk) Each arc between users k and l indicates that user l predicts user k and therefore it has associated a linear transformation TskltkI. Using an appropriate graph search algorithm a set of optimal directed paths between user k and any user that selected item j can be constructed. Each directed path allows a rating prediction computation based on the composition of transformations(eq. 8) For instance, given the directed graph k→l1→….→ In with predictor values (sk. 1, tk, 1), ($12, t1.2),.(sn-1,n, tn-1n)the predicted rating of item j will be SkA,tL o(Tsa,ty o(.oTsn-lntn-(rn.).). Since different paths may exist the average of these predicted ratings is computed as the final prediction. a top- N recommendation is constructed by aggregating the n items with the highest predicted ratings Item-Based The item-based algorithm is an analogous alternative to the user-based approach that was proposed by Sarwar et al. 53 to address the scalability problems ofA Taxonomy of Collaborative-Based Recommender Systems 87 Predictability Paths Aggarwal et al. [9] proposed a graph-based recommendation algorithm in which the users are represented as nodes of a graph and the edges between the nodes indicate the degree of similarity between the users. The recommendations for a user were computed by traversing nearby nodes in this graph. The graph repre￾sentation has the ability to capture transitive relations which cannot be captured by nearest neighborhood algorithms. Authors reported better performance than the user-based schemes. The approach is based on the concepts of horting and predictability. The horting condition states whether there is enough overlap between each pair of users (k,l) to decide whether the behavior of one user could predict the behavior of the other or not. By definition, user k horts user l if the following equation is satisfied: card(Rk ∩ Rl) ≥ min(F · card(Rk), G) (7) where F ≤ 1 and G is some predefined threshold. The predictability condition establishes that user l predicts behavior of user k if there exists a linear rating transformation Tsk,l,tk,l : xk,j = s · rl,j + t (8) that carries ratings rl,j of user l into ratings xk,j of user k with an acceptable error. The (s, t) pair of real numbers is chosen so that the transformation 8 keeps at least one value in the rating domain (see [9] for further details on s-t value pair restrictions). More formally, user l predicts user k if user k horts user l (eq. 7) and if there exists a linear rating transformation Ts,t such that the expression 9 is satisfied, with β a positive real number. j∈Rk∩Rl |rk,j − xk,j )| card(Rk ∩ Rl) < β (9) Each arc between users k and l indicates that user l predicts user k and therefore it has associated a linear transformation Tsk,l,tk,l . Using an appropriate graph search algorithm a set of optimal directed paths between user k and any user l that selected item j can be constructed. Each directed path allows a rating prediction computation based on the composition of transformations (eq. 8). For instance, given the directed graph k → l1 → ... → ln with predictor values (sk,1, tk,1),(s1,2, t1,2), ...,(sn−1,n, tn−1,n) the predicted rating of item j will be Tsk,1,tk,1 ◦ (Ts1,2,t1,2 ◦ (... ◦Tsn−1,n,tn−1,n (rn,j )...)). Since different paths may exist, the average of these predicted ratings is computed as the final prediction. A top￾N recommendation is constructed by aggregating the N items with the highest predicted ratings. Item-Based The item-based algorithm is an analogous alternative to the user-based approach that was proposed by Sarwar et al. [53] to address the scalability problems of