Abstract
Node proximity estimation studies structural similarity between nodes and is the key issue of network analysis. It can exist as the node recommendation task and is a fundamental basis of other graph mining techniques. Although Discrete-time quantum walk (DTQW), a promising new technique with distinctive characters, is widely used in many graph mining problems such as graph isomorphism and graph kernel, there are only a few works estimating proximity via DTQW, limiting the further application of DTQW in graph mining. In this paper, we study the capability of DTQW for proximity estimation and propose QSIM to estimate node proximity by DTQW. By analyzing the diffusion process of biased walks, we discover two influential effects that are beneficial to proximity estimation. The Diminishing Effect shows that a node close to the starting node can generally have a high average probability during the diffusion process, which serves as the basis of QSIM. The Returning Effect shows the probability has a tendency to stay around the starting node during the diffusion, which enhances the capability for mining local information especially in densely-connected structures. Benefited from the two effects, QSIM faithfully reveals node proximity and comprehensively unifies different kinds of node proximity. QSIM is the first mature quantum-walk-based method for proximity estimation. Extensive experiments validate the effectiveness of QSIM and show that QSIM outperforms state-of-the-art methods in the node recommendation task, significantly surpassing Refex, Node2vec, and Role2vec, by up to 1094.2% in the first-order node proximity and 18.8% in the second-order node proximity.
Similar content being viewed by others
Notes
Refex is available on https://github.com/randomsurfer/refex, Node2vec is available on https://github.com/aditya-grover/node2vec, Role2vec is available on https://github.com/benedekrozemberczki/role2vec.
References
Ahmed NK, Rossi RA, Lee JB, Kong X, Willke TL, Zhou R, Eldardiry H (2018) Learning role-based graph embeddings. Stat 1050:7
Bai L, Rossi L, Cui L, Zhang Z, Ren P, Bai X, Hancock E (2017) Quantum kernels for unattributed graphs using discrete-time quantum walks. Pattern Recogn Lett 87:96–103
Cai H, Zheng VW, Chang KC (2018) A comprehensive survey of graph embedding: problems, techniques, and applications. IEEE Trans Knowl Data Eng 30(9):1616–1637
Childs AM (2010) On the relationship between continuous-and discrete-time quantum walk. Commun Math Phys 294(2):581–603
Childs AM, Cleve R, Deotto E, Farhi E, Gutmann S, Spielman DA (2003) Exponential algorithmic speedup by a quantum walk. In: Proceedings of the thirty-fifth annual ACM symposium on Theory of computing. ACM, pp 59–68
Cross R, Parker A, Christensen CM, Anthony SD, Roth EA (2004) The hidden power of social networks. Journal of Applied Management & Entrepreneurship 9(Oct)
Douglas B, Wang J (2008) A classical approach to the graph isomorphism problem using quantum walks, vol 41
Emms D, Wilson RC, Hancock ER (2009) Graph matching using the interference of discrete-time quantum walks. Image Vis Comput 27(7):934–949
Ribeiro LFR, Savarese PHP, Figueiredo DR (2017) Struc2vec: Learning node representations from structural identity. In: International ACM conference on knowledge discovery and data mining (KDD). ACM, pp 385–394
Freeman LC (1978) Centrality in social networks conceptual clarification. Soc Netw 1(3):215–239
Fujiwara Y, Nakatsuji M, Shiokawa H, Mishima T, Onizuka M (2013) Efficient ad-hoc search for personalized pagerank. In: ACM SIGMOD International conference on management of data. ACM, pp 445–456
Girvan M, Newman ME (2002) Community structure in social and biological networks. Proc Natl Acad Sci USA 99(12):7821–7826
Gleiser PM, Danon L (2003) Community structure in jazz. Adv Compl Syst 6(04):565–573
Grover A (2016) Leskovec, J.: node2vec: Scalable feature learning for networks. In: International ACM conference on knowledge discovery and data mining (KDD). ACM, pp 855–864
Grover LK (1996) A fast quantum mechanical algorithm for database search. In: Acm symposium on theory of computing, pp 212–219
Guimera R, Danon L, Diaz-Guilera A, Giralt F, Arenas A (2003) Self-similar community structure in a network of human interactions. Phys Rev E 68(6):065103
Henderson K, Gallagher B, Li L, Akoglu L, Eliassi-Rad T, Tong H, Faloutsos C (2011) It’s who you know: Graph mining using recursive structural features. In: International ACM conference on knowledge discovery and data mining (KDD). ACM, pp 663–671
Leskovec J, Kleinberg J, Faloutsos C (2007) Graph evolution: Densification and shrinking diameters. ACM Trans Knowl Discov Data (TKDD) 1(1):2
Lusseau D, Schneider K, Boisseau OJ, Haase P, Slooten E, Dawson SM (2003) The bottlenose dolphin community of doubtful sound features a large proportion of long-lasting associations. Behav Ecol Sociobiol 54(4):396–405
Mahasinghe A, Izaac JA, Wang JB, Wijerathna JK (2015) Phase-modified ctqw unable to distinguish strongly regular graphs efficiently. J Phys A: Math Theor 48(26):265301
Moody J (2001) Peer influence groups: identifying dense clusters in large networks. Soc Netw 23 (4):261–283
Newman ME (2006) Modularity and community structure in networks. Proc Natl Acad Sci U S A 103(23):8577–8582
Perozzi B, Alrfou R, Skiena S (2014) Deepwalk: online learning of social representations. In: International ACM conference on knowledge discovery and data mining (KDD). ACM, pp 701–710
Porter MA, Onnela JP, Mucha PJ (2009) Communities in networks. Not Am Math Soc 56(9):4294–4303
Rohde PP, Fedrizzi A, Ralph TC (2012) Entanglement dynamics and quasi-periodicity in discrete quantum walks. J Mod Opt 59(8):710–720
Sailer LD (1984) Proximity, sociality, and observation: The definition of social groups. Am Anthropol 86(1):91–98
Santha M (2008) Quantum walk based search algorithms. In: International conference on theory and applications of models of computation. Springer, pp 31–46
Tang L, Liu H (2009) Relational learning via latent social dimensions. In: Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining, pp 817–826
Tsomokos DI (2010) Community detection in complex networks with quantum random walks. arXiv:1012.2405
Tsomokos DI (2011) Quantum walks on complex networks with connection instabilities and community structure. Phys Rev A 83(5):052315
Acknowledgements
This work is supported by National High-level Personnel for Defense Technology Program (2017-JCJQ-ZQ-013), NSF 61902405, and the China Scholarship Council (CSC Student ID 201903170136). This work is partially done during my research visit to School of Computing, National University of Singapore.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Wang, X., Lu, K., Zhang, Y. et al. QSIM: A novel approach to node proximity estimation based on Discrete-time quantum walk. Appl Intell 51, 2574–2588 (2021). https://doi.org/10.1007/s10489-020-01970-3
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10489-020-01970-3