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# Personalized PageRank to a Target Node, Revisited

KDD '20: The 26th ACM SIGKDD Conference on Knowledge Discovery and Data Mining Virtual Event..., pp.657-667, (2020)

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摘要

Personalized PageRank (PPR) is a widely used node proximity measure in graph mining and network analysis. Given a source node s and a target node t, the PPR value π(s,t) represents the probability that a random walk from s terminates at t, and thus indicates the bidirectional importance between s and t. The majority of the existing work f...更多

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简介

- Personalized PageRank (PPR), as a variant of PageRank [45], focuses on the relative significance of a target node with respect to a source node in a graph.
- Given a directed graph G = (V , E) with n nodes and m edges, the PPR value π (s, t) of a target node t with respect to a source node s is defined as the probability that an α-discounted random walk from node s terminates at t.

重点内容

- Personalized PageRank (PPR), as a variant of PageRank [45], focuses on the relative significance of a target node with respect to a source node in a graph
- We demonstrate that the Randomized Backward Search algorithm improves the complexity of single-source SimRank computation, heavy hitters Personalized PageRank query, and Personalized PageRank-related graph neural networks in Section 5
- We study the single-target Personalized PageRank query, which measures the importance of a given target node t to every node s in the graph
- We present an algorithm Randomized Backward Search to compute approximate single-target Personalized PageRank query with optimal computational complexity
- We show that Randomized Backward Search improves three concrete applications in graph mining: heavy hitters Personalized PageRank query, single-source SimRank computation, and scalable graph neural networks
- An interesting open problem is whether we can replace the Backward Search algorithm with Randomized Backward Search to further improve the complexity of these algorithms

方法

- This section experimentally evaluates the performance of RBS against state-of-the-art methods.
- Section 6.1 presents the empirical study for single-target PPR queries.
- Section 6.2 applies RBS to three concrete applications to show its effectiveness.
- The information of the datasets the authors used is listed in table 3.
- All datasets are obtained from [1, 2].
- All experiments are conducted on a machine with an Intel(R) Xeon(R) E7-4809 @2.10GHz CPU and 196GB memory

结果

- The authors evaluate the performance of RBS against Backward Search [37] for the single-target PPR query.
- For Backward Search (BS), the authors set ε = δ for relative error.
- Figure 2 shows the tradeoffs between the MaxAdditiveErr and the query time for the additive error experiments.
- Figure 3 presents the tradeoffs between Precision@k and the query time for the relative error experiments.
- To obtain an additive error of 10−6 on IT, the authors observe a 100x query time speedup for RBS.
- From Figure 3, the authors observe that the precision of RBS with relative error approaches 1 more rapidly, which concurs with the theoretical analysis

结论

- The authors study the single-target PPR query, which measures the importance of a given target node t to every node s in the graph.
- The authors present an algorithm RBS to compute approximate single-target PPR query with optimal computational complexity.
- The authors note that a few works combine the Backward Search algorithm with the Monte-Carlo algorithm to obtain nearoptimal query cost for single-pair queries [36, 39].
- An interesting open problem is whether the authors can replace the Backward Search algorithm with RBS to further improve the complexity of these algorithms

- Table1: Complexity of single-source and single-target PPR queries
- Table2: Table of notations
- Table3: Data Sets

基金

- This research is supported by National Natural Science Foundation of China (No 61832017, No 61972401, No 61932001, No.U1936205), by Beijing Outstanding Young Scientist Program NO
- BJJWZYJH012019100020098, and by the Fundamental Research Funds for the Central Universities and the Research Funds of Renmin University of China under Grant 18XNLG21
- Junhao Gan is supported by Australian Research Council (ARC) DECRA DE190101118
- Sibo Wang is also supported by Hong Kong RGC ECS Grant No 24203419
- Zengfeng Huang is supported by Shanghai Science and Technology Commission Grant No 17JC1420200, and by Shanghai Sailing Program Grant No 18YF1401200

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- 0. Assume Var[πi (x, t)]

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