EXPLANATION IN RECOMMENDER SYSTEMS recommendation dialogue in inn are closely linked to the attribut selection strategy that characterises the approach 3. 2. Identifying dominated cases In INN, an important role in the recommendation process is played by the concept of case dominance that we now define Definition 1: A given case C2 is dominated by another case CI with respect to a query o if sim( C2, 0)< sim(C1, @)and sim(C2, 0*)< sim(Cl, Q")for all extensions Q"of Q One reason for the importance of case dominance in product rec- ommendation is that if a given case C2 is dominated by another case CI then the product represented by C2 can be eliminated. Of course, the number of ways in which a given query can be extended may be very large. So given an incomplete query Q and cases Cl, C2 such that sim(C2, 0)<sim(C1, 0), how can we tell if C2 is dominated by CI without resorting to exhaustive search? One situation in which C2 is clearly dominated by Ci is when both es have the same values for all the remaining attributes. Another is when sim(C1, Q)-sim(C2, Q)is greater than the sum of the impor- tance weights of all the remaining attributes. In situations where dom- inance is less obvious, account must be taken of the similarity between the two cases as well as their similarities to the current query(MeSh erry, 2003a). The criterion used to identify dominated cases in iNN is presented in the following theorem Theorem 1: A given case C2 is dominated respect to a query e if and only if: sim(C2,2)+>wa(l-sima(C1, C2)<sim(C1,Q) a∈A-AQ Proof: See Appendix A 3.3. Attribute selection strategy The attribute selected by inN on each cycle of the recommendation process is the one that is most useful for confirming the case selected as the target case. The target first selected at random from the cases that are maximally similar to an initial query entered by theEXPLANATION IN RECOMMENDER SYSTEMS 185 recommendation dialogue in iNN are closely linked to the attribute￾selection strategy that characterises the approach. 3.2. Identifying dominated cases In iNN, an important role in the recommendation process is played by the concept of case dominance that we now define. Definition 1: A given case C2 is dominated by another case C1 with respect to a query Q if sim(C2, Q) < sim(C1, Q) and sim(C2, Q∗) < sim(C1, Q∗) for all extensions Q∗ of Q. One reason for the importance of case dominance in product rec￾ommendation is that if a given case C2 is dominated by another case C1 then the product represented by C2 can be eliminated. Of course, the number of ways in which a given query can be extended may be very large. So given an incomplete query Q and cases C1, C2 such that sim(C2, Q) < sim(C1, Q), how can we tell if C2 is dominated by C1 without resorting to exhaustive search? One situation in which C2 is clearly dominated by C1 is when both cases have the same values for all the remaining attributes. Another is when sim(C1, Q)−sim(C2, Q) is greater than the sum of the impor￾tance weights of all the remaining attributes. In situations where dom￾inance is less obvious, account must be taken of the similarity between the two cases as well as their similarities to the current query (McSh￾erry, 2003a). The criterion used to identify dominated cases in iNN is presented in the following theorem. Theorem 1: A given case C2 is dominated by another case C1 with respect to a query Q if and only if: sim(C2, Q)+
a∈A−AQ wa(1−sima(C1, C2)) <sim(C1, Q). Proof: See Appendix A. 3.3. Attribute selection strategy The attribute selected by iNN on each cycle of the recommendation process is the one that is most useful for confirming the case selected as the target case. The target case is first selected at random from the cases that are maximally similar to an initial query entered by the