Abstract
The growth of various Web-enabled networks has enabled numerous models of recommendation. For example, the Web itself is a large and distributed repository of data, and a search engine such as Google can be considered a keyword-centric variation of the notion of recommendation. In fact, a major discourse in the recommendation literature is to distinguish between the notions of search and recommendations. While search technologies also recommend content to users, the results are often not personalized to the user at hand. This lack of personalization has traditionally been the case because of the historical difficulty in tracking large numbers of Web users. However, in recent years, many personalized notions of search have arisen, where the Web pages recommended to users are based on personal interests. Many search engine providers, such as Google, now provide the ability to determine personalized results. This problem is exactly equivalent to that of ranking nodes in networks with the use of personalized preferences.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
A formal mathematical treatment characterizes this in terms of the ergodicity of the underlying Markov chains. In ergodic Markov chains, a necessary requirement is that it is possible to reach any state from any other state using a sequence of one or more transitions. This condition is referred to as strong connectivity. An informal description is provided here to facilitate understanding.
- 2.
In some applications such as bibliographic networks, the edge (i, j) may have a weight denoted by w ij . The transition probability p ij is defined in such cases by \(\frac{w_{ij}} {\sum _{j\in Out(i)}w_{ij}}\).
- 3.
An alternative way to achieve this goal is to modify G by multiplying existing edge-transition probabilities by the factor (1 −α) and then adding α∕n to the transition probability between each pair of nodes in G. As a result, G will become a directed clique with bidirectional edges between each pair of nodes. Such strongly connected Markov chains have unique steady-state probabilities. The resulting graph can then be treated as a Markov chain without having to separately account for the teleportation component. This model is equivalent to that discussed in the chapter.
- 4.
The left eigenvector \(\overline{X}\) of P is a row vector satisfying \(\overline{X}P =\lambda \overline{X}\). The right eigenvector \(\overline{Y }\) is a column vector satisfying \(P\overline{Y } =\lambda \overline{Y }\). For asymmetric matrices, the left and right eigenvectors are not the same. However, the eigenvalues are always the same. The unqualified term “eigenvector” refers to the right eigenvector by default.
- 5.
- 6.
It is possible to ameliorate this problem to some extent by making minor modifications such as adding self-loops to the graph. However, such methods are not a formal part of the original SimRank algorithm.
- 7.
- 8.
An implicit assumption here is that the matrix A is positive semi-definite. However, by setting the (unobserved) diagonal entries of A to the node degrees, it can be shown that A is positive semi-definite. These unobserved diagonal entries do not affect the final solution because they are not a part of the optimization problem.
- 9.
Sammy Sosa is a retired Major League baseball player.
Bibliography
E. Agichtein, C. Castillo, D. Donato, A. Gionis, and G. Mishne. Finding high-quality content in social media. Web Search and Data Mining Conference, pp. 183–194, 2008.
C. Aggarwal. Data mining: the textbook. Springer, New York, 2015.
C. Aggarwal and J. Han. Frequent pattern mining. Springer, New York, 2014.
C. Aggarwal, Y. Xie, and P. Yu. On dynamic link inference in heterogeneous networks. SIAM Conference on Data Mining, pp. 415–426, 2012.
M. Al Hasan, and M. J. Zaki. A survey of link prediction in social networks. Social network data analytics, Springer, pp. 243–275, 2011.
A. Azran. The rendezvous algorithm: Multiclass semi-supervised learning with markov random walks. International Conference on Machine Learning, pp. 49–56, 2007.
S. Bhagat, G. Cormode, and S. Muthukrishnan. Node classification in social networks. Social Network Data Analytics, Springer, pp. 115–148. 2011.
B. Bi, Y. Tian, Y. Sismanis, A. Balmin, and J. Cho. Scalable topic-specific influence analysis on microblogs. Web Search and Data Mining Conference, pp. 513–522, 2014.
J. Bian, Y. Liu, D. Zhou, E. Agichtein, and H. Zha. Learning to recognize reliable users and content in social media with coupled mutual reinforcement. World Wide Web Conference, pp. 51–60, 2009.
S. Brin, and L. Page. The anatomy of a large-scale hypertextual web search engine. Computer Networks, 30(1–7), pp. 107–117, 1998.
S. Chakrabarti, B. Dom, and P. Indyk. Enhanced hypertext categorization using hyperlinks. ACM SIGMOD Conference, pp. 307–318, 1998.
W. Chen, Y. Wang, and S. Yang. Efficient influence maximization in social networks. ACM KDD Conference, pp. 199–208, 2009.
W. Chen, C. Wang, and Y. Wang. Scalable influence maximization for prevalent viral marketing in large-scale social networks. ACM KDD Conference, pp. 1029–1038, 2010.
W. Chen, Y. Yuan, and L. Zhang. Scalable influence maximization in social networks under the linear threshold model. IEEE International Conference on Data Mining, pp. 88–97, 2010.
K. Y. Chiang, C. J. Hsieh, N. Natarajan, I. S., Dhillon, and A. Tewari. Prediction and clustering in signed networks: a local to global perspective. The Journal of Machine Learning Research, 15(1), pp. 1177–1213, 2014.
P. Domingos and M. Richardson. Mining the network value of customers. ACM KDD Conference, pp. 57–66, 2001.
M. Gori and A. Pucci. Itemrank: a random-walk based scoring algorithm for recommender engines. IJCAI Conference, pp. 2766–2771, 2007.
A. Goyal, F. Bonchi, and L. V. S. Lakshmanan. A data-based approach to social influence maximization. VLDB Conference, pp. 73–84, 2011.
A. Goyal, F. Bonchi, and L. V. S. Lakshmanan. Learning influence probabilities in social networks. ACM WSDM Conference, pp. 241–250, 2011.
Q. Gu, J. Zhou, and C. Ding. Collaborative filtering: Weighted nonnegative matrix factorization incorporating user and item graphs. SIAM Conference on Data Mining, pp. 199–210, 2010.
T. H. Haveliwala. Topic-sensitive pagerank. World Wide Web Conference, pp. 517–526, 2002.
Y. Hu, Y. Koren, and C. Volinsky. Collaborative filtering for implicit feedback datasets. IEEE International Conference on Data Mining, pp. 263–272, 2008.
G. Jeh, and J. Widom. SimRank: a measure of structural-context similarity. ACM KDD Conference, pp. 538–543, 2003.
D. Kempe, J. Kleinberg, and E. Tardos. Maximizing the spread of influence through a social network. ACM KDD Conference, pp. 137–146, 2003.
J. Kleinberg. Authoritative sources in a hyperlinked environment. Journal of the ACM (JACM), 46(5), pp. 604–632, 1999.
X. Kong, X. Shi, and P. S. Yu. Multi-Label collective classification. SIAM Conference on Data Mining, pp. 618–629, 2011.
J. Kunegis, S. Schmidt, A. Lommatzsch, J. Lerner, E. De Luca, and S. Albayrak. Spectral analysis of signed graphs for clustering, prediction and visualization. SIAM Conference on Data Mining, pp. 559–559, 2010.
J. Kunegis, E. De Luca, and S. Albayrak. The link prediction problem in bipartite networks. Computational Intelligence for Knowledge-based Systems Design, Springer, pp. 380–389, 2010.
J. Kunegis and A. Lommatzsch. Learning spectral graph transformations for link prediction. International Conference on Machine Learning, pp. 562–568, 2009.
J. Leskovec, D. Huttenlocher, and J. Kleinberg. Predicting positive and negative links in online social networks. World Wide Web Conference, pp. 641–650, 2010.
M. Li, B. M. Dias, I. Jarman, W. El-Deredy, and P. J. Lisboa. Grocery shopping recommendations based on basket-sensitive random walk. KDD Conference, pp. 1215–1224, 2009.
D. Liben-Nowell and J. Kleinberg. The link-prediction problem for social networks. Journal of the American society for information science and technology, 58(7), pp. 1019–1031, 2007.
R. Lichtenwalter, J. Lussier, and N. Chawla. New perspectives and methods in link prediction. ACM KDD Conference, pp. 243–252, 2010.
L. Liu, J. Tang, J. Han, M. Jiang, and S. Yang. Mining topic-level influence in heterogeneous networks. ACM CIKM Conference, pp. 199–208, 2010.
B. London, and L. Getoor. Collective classification of network data. Data Classification: Algorithms and Applications, CRC Press, pp. 399–416, 2014.
Q. Lu, and L. Getoor. Link-based classification. ICML Conference, pp. 496–503, 2003.
S. Macskassy, and F. Provost. A simple relational classifier. Second Workshop on Multi-Relational Data Mining (MRDM) at ACM KDD Conference, 2003.
S. A. Macskassy, and F. Provost. Classification in networked data: A toolkit and a univariate case study. Joirnal of Machine Learning Research, 8, pp. 935–983, 2007.
A. K. Menon, and C. Elkan. Link prediction via matrix factorization. Machine Learning and Knowledge Discovery in Databases, pp. 437–452, 2011.
G. Nemhauser, and L. Wolsey. Integer and combinatorial optimization. Wiley, New York, 1988.
J. Neville, and D. Jensen. Iterative classification in relational data. AAAI Workshop on Learning Statistical Models from Relational Data, pp. 13–20, 2000.
L. Page, S. Brin, R. Motwani, and T. Winograd. The PageRank citation engine: Bringing order to the web. Technical Report, 1999–0120, Computer Science Department, Stanford University, 1998.
G. Qi, C. Aggarwal, and T. Huang. Link prediction across networks by biased cross-network sampling. IEEE ICDE Conference, pp. 793–804, 2013.
M. Richardson and P. Domingos. Mining knowledge-sharing sites for viral marketing. ACM KDD Conference, pp. 61–70, 2002.
K. Subbian, C. Aggarwal, and J. Srivasatava. Content-centric flow mining for influence analysis in social streams. CIKM Conference, pp. 841–846, 2013.
J. Sun and J. Tang. A survey of models and algorithms for social influence analysis. Social Network Data Analytics, Springer, pp. 177–214, 2011.
Y. Sun, J. Han, C. Aggarwal, and N. Chawla. When will it happen?: relationship prediction in heterogeneous information networks. ACM International Conference on Web Search and Data Mining, pp. 663–672, 2012.
Y. Sun, R. Barber, M. Gupta, C. Aggarwal, and J. Han. Co-author relationship prediction in heterogeneous bibliographic networks. Advances in Social Networks Analysis and Mining (ASONAM), pp. 121–128, 2011.
J. Tang, J. Sun, C. Wang, and Z. Yang. Social influence analysis in large-scale networks. ACM KDD Conference, pp. 807–816, 2009.
J. Tang, S. Chang, C. Aggarwal, and H. Liu. Negative link prediction in social media. Web Search and Data Mining Conference, 2015.
M.-H. Tsai, C. Aggarwal, and T. Huang. Ranking in heterogeneous social media. Web Search and Data Mining Conference, 2014.
L. Xiang, Q. Yuan, S. Zhao, L. Chen, X. Zhang, Q. Yang, and J. Sun. Temporal recommendation on graphs via long-and short-term preference fusion. ACM KDD Conference, pp. 723–732, 2010.
Z. Xiang and U. Gretzel. Role of social media in online travel information search. Tourism Management, 31(2), pp. 179–188, 2010.
J. Zhang, M. Ackerman, and L. Adamic. Expertise networks in online communities: structure and algorithms. World Wide Web Conference, pp. 221–230, 2007.
D. Zhou, O. Bousquet, T. Lal, J. Weston, and B. Scholkopf. Learning with local and global consistency. Advances in Neural Information Processing Systems, 16(16), pp. 321–328, 2004.
D. Zhou, J. Huang, and B. Scholkopf. Learning from labeled and unlabeled data on a directed graph. ICML Conference, pp. 1036–1043, 2005.
X. Zhu, Z. Ghahramani, and J. Lafferty. Semi-supervised learning using gaussian fields and harmonic functions. ICML Conference, pp. 912–919, 2003.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Aggarwal, C.C. (2016). Structural Recommendations in Networks. In: Recommender Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-29659-3_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-29659-3_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-29657-9
Online ISBN: 978-3-319-29659-3
eBook Packages: Computer ScienceComputer Science (R0)