Analysis of opinion dynamics in social networks plays an important role in today's life. For applications such as predicting users' political preference, it is particularly important to be able to analyze the dynamics of competing opinions. While observing the evolution of polar opinions of a social network's users over time, can we tell when the network "behaved" abnormally? Furthermore, can we predict how the opinions of the users will change in the future? Do opinions evolve according to existing network opinion dynamics models? To answer such questions, it is not sufficient to study individual user behavior, since opinions can spread far beyond users' egonets. We need a method to analyze opinion dynamics of all network users simultaneously and capture the effect of individuals' behavior on the global evolution pattern of the social network. In this work, we introduce Social Network Distance (SND) - a distance measure that quantifies the "cost" of evolution of one snapshot of a social network into another snapshot under various models of polar opinion propagation. SND has a rich semantics of a transportation problem, yet, is computable in time linear in the number of users, which makes SND applicable to the analysis of large-scale online social networks. In our experiments with synthetic and real-world Twitter data, we demonstrate the utility of our distance measure for anomalous event detection. It achieves a true positive rate of 0.83, twice as high as that of alternatives. When employed for opinion prediction in Twitter, our method's accuracy is 75.63 , which is 7.5 higher than that of the next best method. Source Code: this https URL
Abstract Error-tolerant graph matching is a powerful concept that has various applications in pattern recognition and machine vision. In the present paper, a new distance measure on graphs is proposed. It is based on the maximal common subgraph of two graphs. The new measure is superior to edit distance based measures in that no particular edit operations together with their costs need to be defined. It is formally shown that the new distance measure is a metric. Potential algorithms for the efficient computation of the new measure are discussed. Inexact graph matching has been one of the significant research foci in the area of pattern analysis. As an important way to measure the similarity between pairwise graphs error-tolerantly, graph edit distance (GED) is the base of inexact graph matching. The research advance of GED is surveyed in order to provide a review of the existing literatures and offer some insights into the studies of GED. Since graphs may be attributed or non-attributed and the definition of costs for edit operations is various, the existing GED algorithms are categorized according to these two factors and described in detail. After these algorithms are analyzed and their limitations are identified, several promising directions for further research are proposed.