TPA: Fast, Scalable, and Accurate Method for Approximate Random Walk with Restart on Billion Scale Graphs

Abstract

Given a large graph, how can we determine similarity between nodes in a fast and accurate way? Random walk with restart (RWR) is a popular measure for this purpose and has been exploited in numerous data mining applications including ranking, anomaly detection, link prediction, and community detection. However, previous methods for computing exact RWR require prohibitive storage sizes and computational costs, and alternative methods which avoid such costs by computing approximate RWR have limited accuracy.In this paper, we propose TPA, a fast, scalable, and highly accurate method for computing approximate RWR on large graphs. TPA exploits two important properties in RWR: 1) nodes close to a seed node are likely to be revisited in following steps due to block-wise structure of many real-world graphs, and 2) RWR scores of nodes which reside far from the seed node are proportional to their PageRank scores. Based on these two properties, TPA divides approximate RWR problem into two subproblems called neighbor approximation and stranger approximation. In the neighbor approximation, TPA estimates RWR scores of nodes close to the seed based on scores of few early steps from the seed. In the stranger approximation, TPA estimates RWR scores for nodes far from the seed using their PageRank. The stranger and neighbor approximations are conducted in the preprocessing phase and the online phase, respectively. Through extensive experiments, we show that TPA requires up to 3.5× less time with up to 40× less memory space than other state-of-the-art methods for the preprocessing phase. In the online phase, TPA computes approximate RWR up to 30× faster than existing methods while maintaining high accuracy.

PPRviz: Effective and Efficient Graph Visualization based on Personalized PageRank

“…Lemma 5.4 indicates that the error bound 𝜖 depends on DPPR itself, where more important node pairs (i.e., with larger DPPR) require a tighter error bound. Further, the premier objective turns to approximate level-ℓ DPPR, which can be solved by extending the PPR approximation methods [5,16,28,40,43,49,50,58,59,74,76,[88][89][90][91][92]94].…”

“…PPR computation. The efficient computation of PPR has been extensively studied [5,16,28,40,43,49,50,58,59,74,76,[88][89][90][91][92][93][94]. Among these works, BEAR [76] and BePI [50] improve the power iteration method [40] and achieve high efficiency by indexing several large matrices.…”

Private Recommender Systems: How Can Users Build Their Own Fair Recommender Systems without Log Data?

“…where ˜ denotes the row-wise normalized adjacency vector, i.e., ˜ = / , and ( ) is the -th standard basis, i.e., ( ) = 0 if ≠ and ( ) = 1. We compute the personalized PageRank using the cumulative power iteration [40]:…”

“…We use = 10 in the experiments. We point out that other approximation algorithms for the personalized PageRank, such as TopPPR [36], TPA [40], forward push [1], and Monte-Carlo methods [2,9] can be employed. Such methods may be beneficial when the recommendation graph is large.…”

Efficient and scalable techniques for pagerank-based graph analytics

“…However, exploiting these PageRank-based techniques and making connections from them to addressing specific graph processing tasks remains challenging especially when graphs are sizable because the computation is immensely expensive. We observe that, in recent years, there have been rapid advancements [45,47,48,64,82,124,125,147,149,173,174] in scalable algorithms for computing approximate PPR, which enable us to design scalable PPR-based techniques for different graph processing tasks over massive graphs as well.…”