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219
From frequency to meaning : Vector space models of semantics
 Journal of Artificial Intelligence Research
, 2010
"... Computers understand very little of the meaning of human language. This profoundly limits our ability to give instructions to computers, the ability of computers to explain their actions to us, and the ability of computers to analyse and process text. Vector space models (VSMs) of semantics are begi ..."
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Cited by 116 (2 self)
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Computers understand very little of the meaning of human language. This profoundly limits our ability to give instructions to computers, the ability of computers to explain their actions to us, and the ability of computers to analyse and process text. Vector space models (VSMs) of semantics are beginning to address these limits. This paper surveys the use of VSMs for semantic processing of text. We organize the literature on VSMs according to the structure of the matrix in a VSM. There are currently three broad classes of VSMs, based on term–document, word–context, and pair–pattern matrices, yielding three classes of applications. We survey a broad range of applications in these three categories and we take a detailed look at a specific open source project in each category. Our goal in this survey is to show the breadth of applications of VSMs for semantics, to provide a new perspective on VSMs for those who are already familiar with the area, and to provide pointers into the literature for those who are less familiar with the field. 1.
Distributional memory: A general framework for corpusbased semantics
 Computational Linguistics
, 2010
"... “One distributional memory, many semantic tasks” ..."
The Convex Geometry of Linear Inverse Problems
, 2010
"... In applications throughout science and engineering one is often faced with the challenge of solving an illposed inverse problem, where the number of available measurements is smaller than the dimension of the model to be estimated. However in many practical situations of interest, models are constr ..."
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Cited by 38 (10 self)
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In applications throughout science and engineering one is often faced with the challenge of solving an illposed inverse problem, where the number of available measurements is smaller than the dimension of the model to be estimated. However in many practical situations of interest, models are constrained structurally so that they only have a few degrees of freedom relative to their ambient dimension. This paper provides a general framework to convert notions of simplicity into convex penalty functions, resulting in convex optimization solutions to linear, underdetermined inverse problems. The class of simple models considered are those formed as the sum of a few atoms from some (possibly infinite) elementary atomic set; examples include wellstudied cases such as sparse vectors (e.g., signal processing, statistics) and lowrank matrices (e.g., control, statistics), as well as several others including sums of a few permutations matrices (e.g., ranked elections, multiobject tracking), lowrank tensors (e.g., computer vision, neuroscience), orthogonal matrices (e.g., machine learning), and atomic measures (e.g., system identification). The convex programming formulation is based on minimizing the norm induced by the convex hull of the atomic set; this norm is referred to as the atomic norm. The facial
An Emulator Network for
 SIMD Machine Interconnection Networks, in: Proc. 6 th annual symposium on Computer architecture
, 1979
"... Fig. 0.1. [Proposed cover figure.] The largest connected component of a network of network scientists. This network was constructed based on the coauthorship of papers listed in two wellknown review articles [13,83] and a small number of additional papers that were added manually [86]. Each node is ..."
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Cited by 36 (3 self)
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Fig. 0.1. [Proposed cover figure.] The largest connected component of a network of network scientists. This network was constructed based on the coauthorship of papers listed in two wellknown review articles [13,83] and a small number of additional papers that were added manually [86]. Each node is colored according to community membership, which was determined using a leadingeigenvector spectral method followed by KernighanLin nodeswapping steps [64, 86, 107]. To determine community placement, we used the FruchtermanReingold graph visualization [45], a forcedirected layout method that is related to maximizing a quality function known as modularity [92]. To apply this method, we treated the communities as if they were themselves the nodes of a (significantly smaller) network with connections rescaled by intercommunity links. We then used the KamadaKawaii springembedding graph visualization algorithm [62] to place the nodes of each individual community (ignoring intercommunity links) and then to rotate and flip the communities for optimal placement (including intercommunity links). We gratefully acknowledge Amanda Traud for preparing this figure. COMMUNITIES IN NETWORKS
Scalable tensor decompositions for multiaspect data mining
 In ICDM 2008: Proceedings of the 8th IEEE International Conference on Data Mining
, 2008
"... Modern applications such as Internet traffic, telecommunication records, and largescale social networks generate massive amounts of data with multiple aspects and high dimensionalities. Tensors (i.e., multiway arrays) provide a natural representation for such data. Consequently, tensor decompositi ..."
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Cited by 32 (1 self)
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Modern applications such as Internet traffic, telecommunication records, and largescale social networks generate massive amounts of data with multiple aspects and high dimensionalities. Tensors (i.e., multiway arrays) provide a natural representation for such data. Consequently, tensor decompositions such as Tucker become important tools for summarization and analysis. One major challenge is how to deal with highdimensional, sparse data. In other words, how do we compute decompositions of tensors where most of the entries of the tensor are zero. Specialized techniques are needed for computing the Tucker decompositions for sparse tensors because standard algorithms do not account for the sparsity of the data. As a result, a surprising phenomenon is observed by practitioners: Despite the fact that there is enough memory to store both the input tensors and the factorized output tensors, memory overflows occur during the tensor factorization process. To address this intermediate blowup problem, we propose MemoryEfficient Tucker (MET). Based on the available memory, MET adaptively selects the right execution strategy during the decomposition. We provide quantitative and qualitative evaluation of MET on real tensors. It achieves over 1000X space reduction without sacrificing speed; it also allows us to work with much larger tensors that were too big to handle before. Finally, we demonstrate a data mining casestudy using MET. 1
Triplerank: Ranking semantic web data by tensor decomposition
 In ISWC
, 2009
"... Abstract. The Semantic Web fosters novel applications targeting a more efficient and satisfying exploitation of the data available on the web, e.g. faceted browsing of linked open data. Large amounts and high diversity of knowledge in the Semantic Web pose the challenging question of appropriate rel ..."
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Cited by 27 (0 self)
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Abstract. The Semantic Web fosters novel applications targeting a more efficient and satisfying exploitation of the data available on the web, e.g. faceted browsing of linked open data. Large amounts and high diversity of knowledge in the Semantic Web pose the challenging question of appropriate relevance ranking for producing finegrained and rich descriptions of the available data, e.g. to guide the user along most promising knowledge aspects. Existing methods for graphbased authority ranking lack support for finegrained latent coherence between resources and predicates (i.e. support for link semantics in the linked data model). In this paper, we present TripleRank, a novel approach for faceted authority ranking in the context of RDF knowledge bases. TripleRank captures the additional latent semantics of Semantic Web data by means of statistical methods in order to produce richer descriptions of the available data. We model the Semantic Web by a 3dimensional tensor that enables the seamless representation of arbitrary semantic links. For the analysis of that model, we apply the PARAFAC decomposition, which can be seen as a multimodal counterpart to Web authority ranking with HITS. The result are groupings of resources and predicates that characterize their authority and navigational (hub) properties with respect to identified topics. We have applied TripleRank to multiple data sets from the linked open data community and gathered encouraging feedback in a user evaluation where TripleRank results have been exploited in a faceted browsing scenario. 1
Fast Local Algorithms for Large Scale Nonnegative Matrix and Tensor Factorizations
, 2008
"... Nonnegative matrix factorization (NMF) and its extensions such as Nonnegative Tensor Factorization (NTF) have become prominent techniques for blind sources separation (BSS), analysis of image databases, data mining and other information retrieval and clustering applications. In this paper we propose ..."
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Cited by 26 (8 self)
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Nonnegative matrix factorization (NMF) and its extensions such as Nonnegative Tensor Factorization (NTF) have become prominent techniques for blind sources separation (BSS), analysis of image databases, data mining and other information retrieval and clustering applications. In this paper we propose a family of efficient algorithms for NMF/NTF, as well as sparse nonnegative coding and representation, that has many potential applications in computational neuroscience, multisensory processing, compressed sensing and multidimensional data analysis. We have developed a class of optimized local algorithms which are referred to as Hierarchical Alternating Least Squares (HALS) algorithms. For these purposes, we have performed sequential constrained minimization on a set of squared Euclidean distances. We then extend this approach to robust cost functions using the Alpha and Beta divergences and derive flexible update rules. Our algorithms are locally stable and work well for NMFbased blind source separation (BSS) not only for the overdetermined case but also for an underdetermined (overcomplete) case (i.e., for a system which has less sensors than sources) if data are sufficiently sparse. The NMF learning rules are extended and generalized for Nth order nonnegative tensor factorization (NTF). Moreover, these algorithms can be tuned to different noise statistics by adjusting a single parameter. Extensive experimental results confirm the accuracy and computational performance of the developed algorithms, especially, with usage of multilayer hierarchical NMF approach [3].
Temporal Collaborative Filtering with Bayesian Probabilistic Tensor Factorization
"... Realworld relational data are seldom stationary, yet traditional collaborative filtering algorithms generally rely on this assumption. Motivated by our sales prediction problem, we propose a factorbased algorithm that is able to take time into account. By introducing additional factors for time, w ..."
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Cited by 20 (0 self)
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Realworld relational data are seldom stationary, yet traditional collaborative filtering algorithms generally rely on this assumption. Motivated by our sales prediction problem, we propose a factorbased algorithm that is able to take time into account. By introducing additional factors for time, we formalize this problem as a tensor factorization with a special constraint on the time dimension. Further, we provide a fully Bayesian treatment to avoid tuning parameters and achieve automatic model complexity control. To learn the model we develop an efficient sampling procedure that is capable of analyzing largescale data sets. This new algorithm, called Bayesian Probabilistic Tensor Factorization (BPTF), is evaluated on several realworld problems including sales prediction and movie recommendation. Empirical results demonstrate the superiority of our temporal model. 1
Krylov subspace methods for linear systems with tensor product structure
 SIAM J. Matrix Anal. Appl
"... Abstract. The numerical solution of linear systems with certain tensor product structures is considered. Such structures arise, for example, from the finite element discretization of a linear PDE on a ddimensional hypercube. Linear systems with tensor product structure can be regarded as linear mat ..."
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Cited by 18 (5 self)
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Abstract. The numerical solution of linear systems with certain tensor product structures is considered. Such structures arise, for example, from the finite element discretization of a linear PDE on a ddimensional hypercube. Linear systems with tensor product structure can be regarded as linear matrix equations for d = 2 and appear to be their most natural extension for d> 2. A standard Krylov subspace method applied to such a linear system suffers from the curse of dimensionality and has a computational cost that grows exponentially with d. The key to breaking the curse is to note that the solution can often be very well approximated by a vector of low tensor rank. We propose and analyse a new class of methods, so called tensor Krylov subspace methods, which exploit this fact and attain a computational cost that grows linearly with d.