Network representation learning (NRL) aims to learn low-dimensional vectors for vertices in a network. Most existing NRL methods focus on learning representations from local context of vertices (such as their neighbors). Nevertheless, vertices in many complex networks also exhibit significant global patterns widely known as communities. It's intuitive that vertices in the same community tend to connect densely and share common attributes. These patterns are expected to improve NRL and benefit relevant evaluation tasks, such as link prediction and vertex classification. Inspired by the analogy between network representation learning and text modeling, we propose a unified NRL framework by introducing community information of vertices, named as Community-enhanced Network Representation Learning (CNRL). CNRL simultaneously detects community distribution of each vertex and learns embeddings of both vertices and communities. Moreover, the proposed community enhancement mechanism can be applied to various existing NRL models. In experiments, we evaluate our model on vertex classification, link prediction, and community detection using several real-world datasets. The results demonstrate that CNRL significantly and consistently outperforms other state-of-the-art methods while verifying our assumptions on the correlations between vertices and communities.
Traditional methods use hand-crafted similarity measurements such as common neighbors @cite_6 , Salton index @cite_10 , Jaccard index and resource allocation index @cite_5 for link prediction. Besides these topology-based methods, link propagation methods @cite_65 @cite_60 are based on graph regularization, which is a common approach in semi-supervised learning. Matrix factorization methods @cite_61 predict links by adapting matrix completion technic to the adjacency matrix. Further, people employ tensor to develop temporal model @cite_47 for link prediction on dynamic networks. Other methods improve the effect of link prediction by taking information like community affinity @cite_73 and vertex attribute @cite_20 into account.
@cite_61 @cite_60 @cite_65 @cite_6 @cite_5 @cite_47 @cite_73 @cite_10 @cite_20
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In this paper we discuss a very simple approach of combining content and link information in graph structures for the purpose of community discovery, a fundamental task in network analysis. Our approach hinges on the basic intuition that many networks contain noise in the link structure and that content information can help strengthen the community signal. This enables ones to eliminate the impact of noise (false positives and false negatives), which is particularly prevalent in online social networks and Web-scale information networks. Specifically we introduce a measure of signal strength between two nodes in the network by fusing their link strength with content similarity. Link strength is estimated based on whether the link is likely (with high probability) to reside within a community. Content similarity is estimated through cosine similarity or Jaccard coefficient. We discuss a simple mechanism for fusing content and link similarity. We then present a biased edge sampling procedure which retains edges that are locally relevant for each graph node. The resulting backbone graph can be clustered using standard community discovery algorithms such as Metis and Markov clustering. Through extensive experiments on multiple real-world datasets (Flickr, Wikipedia and CiteSeer) with varying sizes and characteristics, we demonstrate the effectiveness and efficiency of our methods over state-of-the-art learning and mining approaches several of which also attempt to combine link and content analysis for the purposes of community discovery. Specifically we always find a qualitative benefit when combining content with link analysis. Additionally our biased graph sampling approach realizes a quantitative benefit in that it is typically several orders of magnitude faster than competing approaches. The nearestor near-neighbor query problems arise in a large variety of database applications, usually in the context of similarity searching. Of late, there has been increasing interest in building search index structures for performing similarity search over high-dimensional data, e.g., image databases, document collections, time-series databases, and genome databases. Unfortunately, all known techniques for solving this problem fall prey to the of dimensionality." That is, the data structures scale poorly with data dimensionality; in fact, if the number of dimensions exceeds 10 to 20, searching in k-d trees and related structures involves the inspection of a large fraction of the database, thereby doing no better than brute-force linear search. It has been suggested that since the selection of features and the choice of a distance metric in typical applications is rather heuristic, determining an approximate nearest neighbor should su ce for most practical purposes. In this paper, we examine a novel scheme for approximate similarity search based on hashing. The basic idea is to hash the points Supported by NAVY N00014-96-1-1221 grant and NSF Grant IIS-9811904. Supported by Stanford Graduate Fellowship and NSF NYI Award CCR-9357849. Supported by ARO MURI Grant DAAH04-96-1-0007, NSF Grant IIS-9811904, and NSF Young Investigator Award CCR9357849, with matching funds from IBM, Mitsubishi, Schlumberger Foundation, Shell Foundation, and Xerox Corporation. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the VLDB copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Very Large Data Base Endowment. To copy otherwise, or to republish, requires a fee and or special permission from the Endowment. Proceedings of the 25th VLDB Conference, Edinburgh, Scotland, 1999. from the database so as to ensure that the probability of collision is much higher for objects that are close to each other than for those that are far apart. We provide experimental evidence that our method gives signi cant improvement in running time over other methods for searching in highdimensional spaces based on hierarchical tree decomposition. Experimental results also indicate that our scheme scales well even for a relatively large number of dimensions (more than 50). Missing link prediction in networks is of both theoretical interest and practical significance in modern science. In this paper, we empirically investigate a simple framework of link prediction on the basis of node similarity. We compare nine well-known local similarity measures on six real networks. The results indicate that the simplest measure, namely Common Neighbours, has the best overall performance, and the Adamic-Adar index performs second best. A new similarity measure, motivated by the resource allocation process taking place on networks, is proposed and shown to have higher prediction accuracy than common neighbours. It is found that many links are assigned the same scores if only the information of the nearest neighbours is used. We therefore design another new measure exploiting information on the next nearest neighbours, which can remarkably enhance the prediction accuracy. Abstract We propose a novel approach to solving the approximate k-nearest neighbor search problem in metric spaces. The search structure is based on a navigable small world graph with vertices corresponding to the stored elements, edges to links between them, and a variation of greedy algorithm for searching. The navigable small world is created simply by keeping old Delaunay graph approximation links produced at the start of construction. The approach is very universal, defined in terms of arbitrary metric spaces and at the same time it is very simple. The algorithm handles insertions in the same way as queries: by finding approximate neighbors for the inserted element and connecting it to them. Both search and insertion can be done in parallel requiring only local information from the structure. The structure can be made distributed. The accuracy of the probabilistic k-nearest neighbor queries can be adjusted without rebuilding the structure. The performed simulation for data in the Euclidean spaces shows that the structure built using the proposed algorithm has small world navigation properties with log 2 ( n ) insertion and search complexity at fixed accuracy, and performs well at high dimensionality. Simulation on a CoPHiR dataset revealed its high efficiency in case of large datasets (more than an order of magnitude less metric computations at fixed recall) compared to permutation indexes. Only 0.03 of the 10 million 208-dimensional vector dataset is needed to be evaluated to achieve 0.999 recall (virtually exact search). For recall 0.93 processing speed 2800 queries s can be achieved on a dual Intel X5675 Xenon server node with Java implementation.