text: The automated analysis of social networks has become an important problem due to the proliferation of social networks, such as LiveJournal, Flickr and Facebook. The scale of these social networks is massive and continues to grow rapidly. An important problem in social network analysis is proximity estimation that infers the closeness of different users. Link prediction, in turn, is an important application of proximity estimation. However, many methods for computing proximity measures have high computational complexity and are thus prohibitive for large-scale link prediction problems. One way to address this problem is to estimate proximity measures via low-rank approximation. However, a single low-rank approximation may not be sufficient to represent the behavior of the entire network. In this paper, we propose Multi-Scale Link Prediction (MSLP), a framework for link prediction, which can handle massive networks. The basis idea of MSLP is to construct low rank approximations of the network at multiple scales in an efficient manner. Based on this approach, MSLP combines predictions at multiple scales to make robust and accurate predictions. Experimental results on real-life datasets with more than a million nodes show the superior performance and scalability of our method.
  @cite_7: Networks have recently emerged as a powerful tool to describe and quantify many complex systems, with applications in engineering, communications, ecology, biochemistry and genetics. A general technique to divide network vertices in groups and sub-groups is reported. Revealing such underlying hierarchies in turn allows the predicting of missing links from partial data with higher accuracy than previous methods.
summary: Very little work has been done using hierarchical structures for link prediction. One exception is the method proposed by @cite_7 , which works by sampling a number of competitive hierarchical random graphs from a large pool of such graphs. Each sampled graph is associated with a probability indicating the strength of community structure over the original network. The probability of a link appearing between any two nodes is averaged over the corresponding connecting probability on the sampled graphs. However, to predict potential links, this algorithm needs to enumerate and average over almost all possible hierarchical partitions of a given network and thus is very costly to compute even with small networks. Compared with @cite_7 , our algorithm is much more efficient in terms of speed and thus can be scaled up to large-scale link prediction problems with millions of users.