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.
Many popular proximity measures that are used for link prediction have high computational complexity and do not scale well to large-scale networks. A great deal of recent work has been devoted to speedup the computation. For example, @cite_8 truncates the series expansion of Katz and only considers paths of length up to some threshold. In @cite_23 @cite_0 , dimensionality reduction methods, such as the eigen-decomposition, are used to construct low rank approximations of a graph, which are then used to compute approximated proximity measures. The more recent work in @cite_16 applies the Lanczos Stieltjes procedure to iteratively compute upper and lower bounds of a single Katz value and shows that these eventually converge to the real Katz value.
@cite_0 @cite_16 @cite_23 @cite_8
2130789338 2102523324 2420733993 2125082260
Abstract We explore methods for approximating the commute time and Katz score between a pair of nodes. These methods are based on the approach of matrices, moments, and quadrature developed in the numerical linear algebra community. They rely on the Lanczos process and provide upper and lower bounds on an estimate of the pairwise scores. We also explore methods to approximate the commute times and Katz scores from a node to all other nodes in the graph. Here, our approach for the commute times is based on a variation of the conjugate gradient algorithm, and it provides an estimate of all the diagonals of the inverse of a matrix. Our technique for the Katz scores is based on exploiting an empirical localization property of the Katz matrix. We adapt algorithms used for personalized PageRank computing to these Katz scores and theoretically show that this approach is convergent. We evaluate these methods on 17 real-world graphs ranging in size from 1000 to 1,000,000 nodes. Our results show that our pairwise c... The data in many disciplines such as social networks, Web analysis, etc. is link-based, and the link structure can be exploited for many different data mining tasks. In this article, we consider the problem of temporal link prediction: Given link data for times 1 through T, can we predict the links at time T + 1? If our data has underlying periodic structure, can we predict out even further in time, i.e., links at time T + 2, T + 3, etc.? In this article, we consider bipartite graphs that evolve over time and consider matrix- and tensor-based methods for predicting future links. We present a weight-based method for collapsing multiyear data into a single matrix. We show how the well-known Katz method for link prediction can be extended to bipartite graphs and, moreover, approximated in a scalable way using a truncated singular value decomposition. Using a CANDECOMP PARAFAC tensor decomposition of the data, we illustrate the usefulness of exploiting the natural three-dimensional structure of temporal link data. Through several numerical experiments, we demonstrate that both matrix- and tensor-based techniques are effective for temporal link prediction despite the inherent difficulty of the problem. Additionally, we show that tensor-based techniques are particularly effective for temporal data with varying periodic patterns. Purpose – The purpose of this paper is to suggest an alternative to the widely used Times Cited criterion for analysing citation networks. The approach involves taking account of the natures of the papers that cite a given paper, so as to differentiate between papers that attract the same number of citations.Design methodology approach – ArticleRank is an algorithm that has been derived from Google's PageRank algorithm to measure the influence of journal articles. ArticleRank is applied to two datasets – a citation network based on an early paper on webometrics, and a self‐citation network based on the 19 most cited papers in the Journal of Documentation – using citation data taken from the Web of Knowledge database.Findings – ArticleRank values provide a different ranking of a set of papers from that provided by the corresponding Times Cited values, and overcomes the inability of the latter to differentiate between papers with the same numbers of citations. The difference in rankings between Times Cited ... Recently there has been much interest in graph-based learning, with applications in collaborative filtering for recommender networks, link prediction for social networks and fraud detection. These networks can consist of millions of entities, and so it is very important to develop highly efficient techniques. We are especially interested in accelerating random walk approaches to compute some very interesting proximity measures of these kinds of graphs. These measures have been shown to do well empirically (Liben-Nowell & Kleinberg, 2003; Brand, 2005). We introduce a truncated variation on a well-known measure, namely commute times arising from random walks on graphs. We present a very novel algorithm to compute all interesting pairs of approximate nearest neighbors in truncated commute times, without computing it between all pairs. We show results on both simulated and real graphs of size up to 100; 000 entities, which indicate near-linear scaling in computation time. We consider the problem of computing the permanent of a 0,1n by n matrix. For a class of matrices corresponding to constant degree expanders we construct a deterministic polynomial time approximation algorithm to within a multiplicative factor ([email protected])^n, for arbitrary @e>0. This is an improvement over the best known approximation factor e^n obtained in Linial, Samorodnitsky and Wigderson (2000) [9], though the latter result was established for arbitrary non-negative matrices. Our results use a recently developed deterministic approximation algorithm for counting partial matchings of a graph (Bayati, Gamarnik, Katz, Nair and Tet ali (2007) [2]) and Jerrum-Vazirani method (Jerrum and Vazirani (1996) [8]) of approximating permanent by near perfect matchings. Abstract Documents in computer-readable form can be used to provide information about other documents, i.e. those they cite. To do this efficiently requires procedures for computer recognition of citing statements. This is not easy, especially for multi-sentence citing statements. Computer recognition procedures have been developed which are accurate to the following extent: 73 of the words in statements selected by computer procedures as being citing statements are words which are correctly attributable to the corresponding documents. The retrieval effectiveness of computer-recognized citing statements was tested in the following way. First, for eight retrieval requests in inorganiic chemistry, average recall by search of Chemical Abstracts Service indexing and Chemical Abstracts abstract text words was found to be 50 . Words from citing statements referring to the papers to be retrieved were then added to the index terms and abstract words as additional access points, and searching was repeated. Average recall increased to 70 . Only words from citing statements published within a year of the cited papers were used. The retrieval effect of citing statement words alone (published within a year) without index or abstract terms was the following: average recall was 40 . When just the words of the titles of the cited papers were added to those citing statement words, average recall increased to 50 . Proximity measures quantify the closeness or similarity between nodes in a social network and form the basis of a range of applications in social sciences, business, information technology, computer networks, and cyber security. It is challenging to estimate proximity measures in online social networks due to their massive scale (with millions of users) and dynamic nature (with hundreds of thousands of new nodes and millions of edges added daily). To address this challenge, we develop two novel methods to efficiently and accurately approximate a large family of proximity measures. We also propose a novel incremental update algorithm to enable near real-time proximity estimation in highly dynamic social networks. Evaluation based on a large amount of real data collected in five popular online social networks shows that our methods are accurate and can easily scale to networks with millions of nodes. To demonstrate the practical values of our techniques, we consider a significant application of proximity estimation: link prediction, i.e., predicting which new edges will be added in the near future based on past snapshots of a social network. Our results reveal that (i) the effectiveness of different proximity measures for link prediction varies significantly across different online social networks and depends heavily on the fraction of edges contributed by the highest degree nodes, and (ii) combining multiple proximity measures consistently yields the best link prediction accuracy. Graph embedding algorithms embed a graph into a vector space where the structure and the inherent properties of the graph are preserved. The existing graph embedding methods cannot preserve the asymmetric transitivity well, which is a critical property of directed graphs. Asymmetric transitivity depicts the correlation among directed edges, that is, if there is a directed path from u to v, then there is likely a directed edge from u to v. Asymmetric transitivity can help in capturing structures of graphs and recovering from partially observed graphs. To tackle this challenge, we propose the idea of preserving asymmetric transitivity by approximating high-order proximity which are based on asymmetric transitivity. In particular, we develop a novel graph embedding algorithm, High-Order Proximity preserved Embedding (HOPE for short), which is scalable to preserve high-order proximities of large scale graphs and capable of capturing the asymmetric transitivity. More specifically, we first derive a general formulation that cover multiple popular high-order proximity measurements, then propose a scalable embedding algorithm to approximate the high-order proximity measurements based on their general formulation. Moreover, we provide a theoretical upper bound on the RMSE (Root Mean Squared Error) of the approximation. Our empirical experiments on a synthetic dataset and three real-world datasets demonstrate that HOPE can approximate the high-order proximities significantly better than the state-of-art algorithms and outperform the state-of-art algorithms in tasks of reconstruction, link prediction and vertex recommendation. In a document network such as a citation network of scientific documents, web-logs, etc., the content produced by authors exhibits their interest in certain topics. In addition some authors influence other authors' interests. In this work, we propose to model the influence of cited authors along with the interests of citing authors. Moreover, we hypothesize that apart from the citations present in documents, the context surrounding the citation mention provides extra topical information about the cited authors. However, associating terms in the context to the cited authors remains an open problem. We propose novel document generation schemes that incorporate the context while simultaneously modeling the interests of citing authors and influence of the cited authors. Our experiments show significant improvements over baseline models for various evaluation criteria such as link prediction between document and cited author, and quantitatively explaining unseen text. The explosive growth of social networks has created numerous exciting research opportunities. A central concept in the analysis of social networks is a proximity measure, which captures the closeness or similarity between nodes in the network. Despite much research on proximity measures, there is a lack of techniques to efficiently and accurately compute proximity measures for large-scale social networks. In this paper, we embed the original massive social graph into a much smaller graph, using a novel dimensionality reduction technique termed Clustered Spectral Graph Embedding. We show that the embedded graph captures the essential clustering and spectral structure of the original graph and allow a wide range of analysis to be performed on massive social graphs. Applying the clustered embedding to proximity measurement of social networks, we develop accurate, scalable, and flexible solutions to three important social network analysis tasks: proximity estimation, missing link inference, and link prediction. We demonstrate the effectiveness of our solutions to the tasks in the context of large real-world social network datasets: Flickr, LiveJournal, and MySpace with up to 2 million nodes and 90 million links. A citing sentence is one that appears in a scientific article and cites previous work. Citing sentences have been studied and used in many applications. For example, they have been used in scientific paper summarization, automatic survey generation, paraphrase identification, and citation function classification. Citing sentences that cite multiple papers are common in scientific writing. This observation should be taken into consideration when using citing sentences in applications. For instance, when a citing sentence is used in a summary of a scientific paper, only the fragments of the sentence that are relevant to the summarized paper should be included in the summary. In this paper, we present and compare three different approaches for identifying the fragments of a citing sentence that are related to a given target reference. Our methods are: word classification, sequence labeling, and segment classification. Our experiments show that segment classification achieves the best results. Rank minimization problem can be boiled down to either Nuclear Norm Minimization (NNM) or Weighted NNM (WNNM) problem. The problems related to NNM (or WNNM) can be solved iteratively by applying a closed-form proximal operator, called Singular Value Thresholding (SVT) (or Weighted SVT), but they suffer from high computational cost to compute a Singular Value Decomposition (SVD) at each iteration. In this paper, we propose an accurate and fast approximation method for SVT, called fast randomized SVT (FRSVT), where we avoid direct computation of SVD. The key idea is to extract an approximate basis for the range of a matrix from its compressed matrix. Given the basis, we compute the partial singular values of the original matrix from a small factored matrix. While the basis approximation is the bottleneck, our method is already severalfold faster than thin SVD. By adopting a range propagation technique, we can further avoid one of the bottleneck at each iteration. Our theoretical analysis provides a stepping stone between the approximation bound of SVD and its effect to NNM via SVT. Along with the analysis, our empirical results on both quantitative and qualitative studies show our approximation rarely harms the convergence behavior of the host algorithms. We apply it and validate the efficiency of our method on various vision problems, e.g. subspace clustering, weather artifact removal, simultaneous multi-image alignment and rectification. The popular h-index used to measure scientific output can be described in terms of a pool of evaluated objects (the papers), a quality function on the evaluated objects (the number of citations received by each paper) and a sentencing line crossing the origin, whose intersection with the graph of the quality function yields the index value (in the h-index this is a line with slope 1). Based on this abstraction, we present a new index, the c-index, in which the evaluated objects are the citations received by an author, a group of authors, a journal, etc., the quality function of a citation is the collaboration distance between the authors of the cited and the citing papers, and the sentencing line can take slopes between 0 and ∞. As a result, the new index counts only those citations which are significant enough, where significance is proportional to collaboration distance. Several advantages of the new c-index with respect to previous proposals are discussed. Similarity search in large time series databases has attracted much research interest recently. It is a difficult problem because of the typically high dimensionality of the data.. The most promising solutions involve performing dimensionality reduction on the data, then indexing the reduced data with a multidimensional index structure. Many dimensionality reduction techniques have been proposed, including Singular Value Decomposition (SVD), the Discrete Fourier transform (DFT), and the Discrete Wavelet Transform (DWT). In this work we introduce a new dimensionality reduction technique which we call Adaptive Piecewise Constant Approximation (APCA). While previous techniques (e.g., SVD, DFT and DWT) choose a common representation for all the items in the database that minimizes the global reconstruction error, APCA approximates each time series by a set of constant value segments of varying lengths such that their individual reconstruction errors are minimal. We show how APCA can be indexed using a multidimensional index structure. We propose two distance measures in the indexed space that exploit the high fidelity of APCA for fast searching: a lower bounding Euclidean distance approximation, and a non-lower bounding, but very tight Euclidean distance approximation and show how they can support fast exact searching, and even faster approximate searching on the same index structure. We theoretically and empirically compare APCA to all the other techniques and demonstrate its superiority. Scholars are increasingly citing electronic “web references” which are not preserved in libraries or full text archives. WebCite is a new standard for citing web references. To “webcite” a document involves archiving the cited Web page through www.webcitation.org and citing the WebCite permalink instead of (or in addition to) the unstable live Web page. This journal has amended its “instructions for authors” accordingly, asking authors to archive cited Web pages before submitting a manuscript. Almost 200 other journals are already using the system. We discuss the rationale for WebCite, its technology, and how scholars, editors, and publishers can benefit from the service. Citing scholars initiate an archiving process of all cited Web references, ideally before they submit a manuscript. Authors of online documents and websites which are expected to be cited by others can ensure that their work is permanently available by creating an archived copy using WebCite and providing the citation information including the WebCite link on their Web document(s). Editors should ask their authors to cache all cited Web addresses (Uniform Resource Locators, or URLs) “prospectively” before submitting their manuscripts to their journal. Editors and publishers should also instruct their copyeditors to cache cited Web material if the author has not done so already. Finally, WebCite can process publisher submitted “citing articles” (submitted for example as eXtensible Markup Language [XML] documents) to automatically archive all cited Web pages shortly before or on publication. Finally, WebCite can act as a focussed crawler, caching retrospectively references of already published articles. Copyright issues are addressed by honouring respective Internet standards (robot exclusion files, no-cache and no-archive tags). Long-term preservation is ensured by agreements with libraries and digital preservation organizations. The resulting WebCite Index may also have applications for research assessment exercises, being able to measure the impact of Web services and published Web documents through access and Web citation metrics. @PARASPLIT [J Med Internet Res 2005;7(5):e60] Lanczos bidiagonalization is a competitive method for computing a partial singular value decomposition of a large sparse matrix, that is, when only a subset of the singular values and corresponding singular vectors are required. However, a straightforward implementation of the algorithm has the problem of loss of orthogonality between computed Lanczos vectors, and some reorthogonalization technique must be applied. Also, an effective restarting strategy must be used to prevent excessive growth of the cost of reorthogonalization per iteration. On the other hand, if the method is to be implemented on a distributed-memory parallel computer, then additional precautions are required so that parallel efficiency is maintained as the number of processors increases. In this paper, we present a Lanczos bidiagonalization procedure implemented in SLEPc, a software library for the solution of large, sparse eigenvalue problems on parallel computers. The solver is numerically robust and scales well up to hundreds of processors. Recovering a large matrix from a small subset of its entries is a challenging problem arising in many real applications, such as image inpainting and recommender systems. Many existing approaches formulate this problem as a general low-rank matrix approximation problem. Since the rank operator is nonconvex and discontinuous, most of the recent theoretical studies use the nuclear norm as a convex relaxation. One major limitation of the existing approaches based on nuclear norm minimization is that all the singular values are simultaneously minimized, and thus the rank may not be well approximated in practice. In this paper, we propose to achieve a better approximation to the rank of matrix by truncated nuclear norm, which is given by the nuclear norm subtracted by the sum of the largest few singular values. In addition, we develop a novel matrix completion algorithm by minimizing the Truncated Nuclear Norm. We further develop three efficient iterative procedures, TNNR-ADMM, TNNR-APGL, and TNNR-ADMMAP, to solve the optimization problem. TNNR-ADMM utilizes the alternating direction method of multipliers (ADMM), while TNNR-AGPL applies the accelerated proximal gradient line search method (APGL) for the final optimization. For TNNR-ADMMAP, we make use of an adaptive penalty according to a novel update rule for ADMM to achieve a faster convergence rate. Our empirical study shows encouraging results of the proposed algorithms in comparison to the state-of-the-art matrix completion algorithms on both synthetic and real visual datasets. Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which demonstrates that randomization offers a powerful tool for performing low-rank matrix approximation. These techniques exploit modern computational architectures more fully than classical methods and open the possibility of dealing with truly massive data sets. This paper presents a modular framework for constructing randomized algorithms that compute partial matrix decompositions. These methods use random sampling to identify a subspace that captures most of the action of a matrix. The input matrix is then compressed—either explicitly or implicitly—to this subspace, and the reduced matrix is manipulated deterministically to obtain the desired low-rank factorization. In many cases, this approach beats its classical competitors in terms of accuracy, robustness, and or speed. These claims are supported by extensive numerical experiments and a detailed error analysis. The specific benefits of randomized techniques depend on the computational environment. Consider the model problem of finding the @math dominant components of the singular value decomposition of an @math matrix. (i) For a dense input matrix, randomized algorithms require @math floating-point operations (flops) in contrast to @math for classical algorithms. (ii) For a sparse input matrix, the flop count matches classical Krylov subspace methods, but the randomized approach is more robust and can easily be reorganized to exploit multiprocessor architectures. (iii) For a matrix that is too large to fit in fast memory, the randomized techniques require only a constant number of passes over the data, as opposed to @math passes for classical algorithms. In fact, it is sometimes possible to perform matrix approximation with a single pass over the data. In recent years scholars have built maps of science by connecting the academic fields that cite each other, are cited together, or that cite a similar literature. But since scholars cannot always publish in the fields they cite, or that cite them, these science maps are only rough proxies for the potential of a scholar, organization, or country, to enter a new academic field. Here we use a large dataset of scholarly publications disambiguated at the individual level to create a map of science-or research space-where links connect pairs of fields based on the probability that an individual has published in both of them. We find that the research space is a significantly more accurate predictor of the fields that individuals and organizations will enter in the future than citation based science maps. At the country level, however, the research space and citations based science maps are equally accurate. These findings show that data on career trajectories-the set of fields that individuals have previously published in-provide more accurate predictors of future research output for more focalized units-such as individuals or organizations-than citation based science maps. This paper presents essentially optimal lower bounds on the size of linear codes C : 0, 1 n ? 0, 1 m which have the property that, for constants ?, ? > 0, any bit of the message can be recovered with probability 1 2 + ? by an algorithm reading only 2 bits of a codeword corrupted in up to ?m positions. Such codes are known to be applicable to, among other things, the construction and analysis of information-theoretically secure private information retrieval schemes. In this work, we show that m must be at least 2?(? 1-2? n). Our results extend work by Goldreich, Karloff, Schulman, and Trevisan [GKST02], which is based heavily on methods developed by Katz and Trevisan [KT00]. The key to our improved bounds is an analysis which bypasses an intermediate reduction used in both prior works. The resulting improvement in the efficiency of the overall analysis is sufficient to achieve a lower bound optimal within a constant factor in the exponent. A construction of a locally decodable linear code matching this bound is presented.