Liben-Nowell Kleinberg J. Am.Soc.Inf.Sci.2007

The Link-Prediction Problem for Social Networks

This is not a final version, under construction!

Citation

Liben-Nowell, D. and Kleinberg, J. (2007), The link-prediction problem for social networks. J. Am. Soc. Inf. Sci., 58: 1019–1031. doi: 10.1002/asi.20591

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Summary

This paper extensively evaluates many unsupervised methods using topological features of the network for link prediction and compares their performances over different data sets. The result shows that Adamic-Adar, which measures the node similarity, has the best performance.

Problem Setup

Given a social network $G=<V,E>$ in which each edge represents an interaction at a particular time $t(e)$. For two times $t<t^{'}$, $G[t,t^{'}]$ denote the sub-graph of $G$ consisting of all edges representing the interactions happening between $t$ and $t^{'}$. A link-prediction problem can be formalized as given four time $t_{0}<t_{0}^{'}<t_{1}<t_{1}^{'}$ and the network $G[t_{0},t_{0}^{'}]$, to output or predict a list of edges not present in $G[t_{0},t_{0}^{'}]$ but appear in the network $G[t_{1},t_{1}^{'}]$.

A List of Methods for Link Prediction

All the following methods assign a connection weight ${\textrm {score}}(x,y)$ to node pair $<x,y>$. We can group them in a less strict way and you can check the definition of each method in its own page.

Methods Based on Node Neighborhoods	common neighbors, Jaccard's coefficient, Adamic/Adar, Preferential Attachment
Methods Based on the Ensemble of All Paths	Katz, Hitting Time, rooted PageRank
Others	graph distance, SimRank

Data sets and Experiments

The paper works with five co-authorship networks, obtained from the author lists of articles contained in five sections of the physics e-Print arXiv. The training interval is defined to be the 3 years from 1994 through 1996 and test interval to be the 3 years from 1997 through 1999.

Each link predictor outputs a ranked list of pairs and the paper takes the first $n$, which is the number of new links from the test set, and count how many of edges from these $n$ are in the test set.

Result

The performance is compared with a random predictor.

We can see that Adamic/Adar outperforms other methods and for more detailed results please refer to the paper.

Related papers

The widely cited Pang et al EMNLP 2002 paper was influenced by this paper - but considers supervised learning techniques. The choice of movie reviews as the domain was suggested by the (relatively) poor performance of Turney's method on movies.

An interesting follow-up paper is Turney and Littman, TOIS 2003 which focuses on evaluation of the technique of using PMI for predicting the semantic orientation of words.