局部聚类中热核PageRank的有效估计
Efficient Estimation of Heat Kernel PageRank for Local Clustering
摘要：
给定一个无向图G和一个种子节点s，局部聚类问题的目标是识别一个高质量的簇，该簇包含的s在时间上与簇的大小大致成比例，而不管G的大小。这个问题在大规模图上有许多应用。最近，热核PageRank（HKPR），这是一个衡量节点在图中的接近程度，被应用到这个问题，并发现是更有效的比以前的方法。然而，现有的解决方案计算HKPR要么是昂贵的，或提供不满意的误差近似HKPR值，使他们不切实际，特别是在十亿边图。在本文中，我们提出了TEA和TEA+，两个新的局部图聚类算法的基础上HKPR，以解决上述限制。具体地说，这些算法在HKPR值的相对误差和时间复杂度方面提供了非平凡的理论保证。其基本思想是利用确定性图遍历产生精确HKPR向量的粗略估计，然后利用Monte-Carlo随机游走以优化和非平凡的方式改进结果。特别是，由于非平凡的优化，TEA+提供了实际的效率和有效性。在真实世界数据集上进行的大量实验表明，TEA+在大多数基准数据集上的计算时间方面比最先进的算法高出四倍以上，当实现相同的聚类质量时，特别是在大型图上，包括广泛研究的Twitter和Monster数据集。
英文摘要：
Given an undirected graph G and a seed node s, the local clustering problem aims to identify a high-quality cluster containing s in time roughly proportional to the size of the cluster, regardless of the size of G. This problem finds numerous applications on large-scale graphs. Recently, heat kernel PageRank (HKPR), which is a measure of the proximity of nodes in graphs, is applied to this problem and found to be more efficient compared with prior methods. However, existing solutions for computing HKPR either are prohibitively expensive or provide unsatisfactory error approximation on HKPR values, rendering them impractical especially on billion-edge graphs. In this paper, we present TEA and TEA+, two novel local graph clustering algorithms based on HKPR, to address the aforementioned limitations. Specifically, these algorithms provide non-trivial theoretical guarantees in relative error of HKPR values and the time complexity. The basic idea is to utilize deterministic graph traversal to produce a rough estimation of exact HKPR vector, and then exploit Monte-Carlo random walks to refine the results in an optimized and non-trivial way. In particular, TEA+ offers practical efficiency and effectiveness due to non-trivial optimizations. Extensive experiments on real-world datasets demonstrate that TEA+ outperforms the state-of-the-art algorithm by more than four times on most benchmark datasets in terms of computational time when achieving the same clustering quality, and in particular, is an order of magnitude faster on large graphs including the widely studied Twitter and Friendster datasets.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
