Similarity search over a bipartite graph aims to retrieve from the graph the nodes that are similar to each other, which finds applications in various fields such as online advertising, recommender systems etc. Existing similarity measures either (i) overlook the unique properties of bipartite graphs, or (ii) fail to capture high-order information between nodes accurately, leading to suboptimal result quality. Recently, Hidden Personalized PageRank (HPP) is applied to this problem and found to be more effective compared with prior similarity measures. However, existing solutions for HPP computation incur significant computational costs, rendering it inefficient especially on large graphs. In this paper, we first identify an inherent drawback of HPP and overcome it by proposing bidirectional HPP (BHPP). Then, we formulate similarity search over bipartite graphs as the problem of approximate BHPP computation, and present an efficient solution Approx-BHPP. Specifically, Approx-BHPP offers rigorous theoretical accuracy guarantees with optimal computational complexity by combining deterministic graph traversal with matrix operations in an optimized and non-trivial way. Moreover, our solution achieves significant gain in practical efficiency due to several carefully-designed optimizations. Extensive experiments, comparing BHPP against 8 existing similarity measures over 7 real bipartite graphs, demonstrate the effectiveness of BHPP on query rewriting and item recommendation. Moreover, Approx-BHPP outperforms baseline solutions often by up to orders of magnitude in terms of computational time on both small and large datasets.

翻译：二分图上的相似性搜索旨在从图中检索彼此相似的节点，这在在线广告、推荐系统等众多领域具有广泛应用。现有相似性度量方法要么（i）忽略了二分图的独特属性，要么（ii）未能准确捕捉节点间的高阶信息，导致结果质量次优。最近，隐式个性化PageRank（HPP）被应用于该问题，并发现其效果优于先前的相似性度量方法。然而，现有HPP计算方法计算成本高昂，尤其在大型图上效率低下。本文首先指出HPP的固有缺陷，并提出双向HPP（BHPP）加以克服。随后，我们将二分图相似性搜索问题建模为近似BHPP计算问题，并提出高效解决方案Approx-BHPP。具体而言，Approx-BHPP通过以优化且非平凡的方式结合确定性图遍历与矩阵运算，实现了严格的理论精度保证与最优计算复杂度。此外，由于多项精心设计的优化策略，我们的解决方案在实际效率上取得了显著提升。通过在7个真实二分图上将BHPP与8种现有相似性度量方法进行广泛对比实验，验证了BHPP在查询重写与物品推荐中的有效性。同时，Approx-BHPP在小规模与大规模数据集上相比基准方案的计算时间往往提升数个数量级。