Diversity-Aware k-Maximum Inner Product Search Revisited

The k-Maximum Inner Product Search (kMIPS) serves as a foundational component in recommender systems and various data mining tasks. However, while most existing kMIPS approaches prioritize the efficient retrieval of highly relevant items for users, they often neglect an equally pivotal facet of search results: diversity. To bridge this gap, we revisit and refine the diversity-aware kMIPS (DkMIPS) problem by incorporating two well-known diversity objectives – minimizing the average and maximum pairwise item similarities within the results – into the original relevance objective. This enhancement, inspired by Maximal Marginal Relevance (MMR), offers users a controllable trade-off between relevance and diversity. We introduce Greedy and DualGreedy, two linear scan-based algorithms tailored for DkMIPS. They both achieve data-dependent approximations and, when aiming to minimize the average pairwise similarity, DualGreedy attains an approximation ratio of 1/4 with an additive term for regularization. To further improve query efficiency, we integrate a lightweight Ball-Cone Tree (BC-Tree) index with the two algorithms. Finally, comprehensive experiments on ten real-world data sets demonstrate the efficacy of our proposed methods, showcasing their capability to efficiently deliver diverse and relevant search results to users.