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
A third class of distance measures includes @cite_14 @cite_29 @cite_17 , which express similarity of the nodes of two networks recursively, use a fix-point iteration to compute node similarities, and, then, aggregate node similarities to obtain the similarity of two networks. Iterative distance measures share the problem of GED -- they do not capture the way opinions spread in the network.
@cite_29 @cite_14 @cite_17
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A local distance measure is shown to optimize the performance of the nearest neighbor two-class classifier for a finite number of samples. The difference between the finite sample error and the asymptotic error is used as the criterion of improvement. This new distance measure is compared to the well-known Euclidean distance. An algorithm for practical implementation is introduced. This algorithm is shown to be computationally competitive with the present nearest neighbor procedures and is illustrated experimentally. A closed form for the corresponding second-order moment of this criterion is found. Finally, the above results are extended to Most methods for document image retrieval rely solely on text information to find similar documents. This paper describes a way to use layout information for document image retrieval instead. A new class of distance measures is introduced for documents with Manhattan layouts, based on a two-step procedure: First, the distances between the blocks of two layouts are calculated. Then, the blocks of one layout are assigned to the blocks of the other layout in a matching step. Different block distances and matching methods are compared and evaluated using the publicly available MARG database. On this dataset, the layout type can be determined successfully in 92.6 of the cases using the best distance measure in a nearest neighbor classifier. The experiments show that the best distance measure for this task is the overlapping area combined with the Manhattan distance of the corner points as block distance together with the minimum weight edge cover matching. We address the problem of distance metric learning (DML), defined as learning a distance consistent with a notion of semantic similarity. Traditionally, for this problem supervision is expressed in the form of sets of points that follow an ordinal relationship – an anchor point x is similar to a set of positive points Y , and dissimilar to a set of negative points Z, and a loss defined over these distances is minimized. While the specifics of the optimization differ, in this work we collectively call this type of supervision Triplets and all methods that follow this pattern Triplet-Based methods. These methods are challenging to optimize. A main issue is the need for finding informative triplets, which is usually achieved by a variety of tricks such as increasing the batch size, hard or semi-hard triplet mining, etc. Even with these tricks, the convergence rate of such methods is slow. In this paper we propose to optimize the triplet loss on a different space of triplets, consisting of an anchor data point and similar and dissimilar proxy points which are learned as well. These proxies approximate the original data points, so that a triplet loss over the proxies is a tight upper bound of the original loss. This proxy-based loss is empirically better behaved. As a result, the proxy-loss improves on state-of-art results for three standard zero-shot learning datasets, by up to 15 points, while converging three times as fast as other triplet-based losses. Distance or similarity measures are essential to solve many pattern recognition problems such as classification, clustering, and retrieval problems. Various distance similarity measures that are applicable to compare two probability density functions, pdf in short, are reviewed and categorized in both syntactic and semantic relationships. A correlation coefficient and a hierarchical clustering technique are adopted to reveal similarities among numerous distance similarity measures.