Disparity-Aware Group Formation for Recommendation

Group recommendation has attracted significant research efforts for its importance in benefiting a group of users, however, seldom investigation has been put into the essential problem of how the groups should be formed. This paper investigates the disparity-aware group formation problem in group recommendation. In this work, we present a formulation of the disparity-aware group formation problem, and further show its NP-Hardness. For the case when group satisfaction is maximized, we propose a cutting plane algorithm based on bilinear program that achieves a ε approximation to the optimum. For the general case, we design an efficient optimization algorithm based on Projected Gradient Descent and further propose a simplified swapping alike algorithm that accommodates to large datasets. We conduct extensive experiments on both simulated and real-world datasets. Experimental results verify that the performance of our algorithm is close to the optima. More importantly, our work reveals that proper group formation can lead to better performances of group recommendation in different scenarios. To our knowledge, we are the first to study the group formation problem with disparity awareness for recommendation, and more promising works are expected. 1. DISPARITY-AWARE GROUP FORMATION In this section, we formulate the Disparity-Aware Group Formation (DAGF) problem. We first give some introductions about the semantics adopted in group recommendation problems from [1]. We assume the individual preference of an individual user i on item j is depicted as a number Rij ∈ [Rmin, Rmax]. DEFINITION 1. Group Satisfaction: Given an item j and a Appears in: Proceedings of the 16th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2017), Das, Durfee, Larson, Winikoff (eds.), May 8–12, 2017, São Paulo, Brazil. Copyright c ⃝ 2017, International Foundation for Autonomous Agents and Multiagent Systems (www.ifaamas.org). All rights reserved. group of users U , the satisfaction score Sc(U, j) of the group given the item recommended to them is defined as a function in [Rmin, Rmax]: Sc(U, j) = ∑ i∈U 1 |U|Rij . DEFINITION 2. Group Disparity: Given an item j and a group of users U , the disparity D(U, j) of the group on item j is defined as a function in [Rmin, Rmax]: D(U, j) = 1 |U| ∑ i∈U |Rij− ∑ i∈U 1 |U|Rij |. Since most recommender systems follow the Top-K recommendation, the Top-K items with high satisfaction and low disparity are recommended to each group in our work. We set variablesXig and Yjg as indicator variables deciding whether user i is in group g and item j is recommended to group g respectively. Based on this, the Disparity-Aware Group Formation (DAGF) problem is rewritten into an integer programming: