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101
Tensor Decompositions and Applications
 SIAM REVIEW
, 2009
"... This survey provides an overview of higherorder tensor decompositions, their applications, and available software. A tensor is a multidimensional or N way array. Decompositions of higherorder tensors (i.e., N way arrays with N â¥ 3) have applications in psychometrics, chemometrics, signal proce ..."
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Cited by 512 (15 self)
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This survey provides an overview of higherorder tensor decompositions, their applications, and available software. A tensor is a multidimensional or N way array. Decompositions of higherorder tensors (i.e., N way arrays with N â¥ 3) have applications in psychometrics, chemometrics, signal processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, etc. Two particular tensor decompositions can be considered to be higherorder extensions of the matrix singular value decompo
sition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum of rankone tensors, and the Tucker decomposition is a higherorder form of principal components analysis. There are many other tensor decompositions, including INDSCAL, PARAFAC2, CANDELINC, DEDICOM, and PARATUCK2 as well as nonnegative variants of all of the above. The Nway Toolbox and Tensor Toolbox, both for MATLAB, and the Multilinear Engine are examples of software packages for working with tensors.
A largescale evaluation and analysis of personalized search strategies
 In WWW
, 2007
"... Although personalized search has been proposed for many years and many personalization strategies have been investigated, it is still unclear whether personalization is consistently effective on different queries for different users, and under different search contexts. In this paper, we study thi ..."
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Cited by 117 (2 self)
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Although personalized search has been proposed for many years and many personalization strategies have been investigated, it is still unclear whether personalization is consistently effective on different queries for different users, and under different search contexts. In this paper, we study this problem and provide some preliminary conclusions. We present a largescale evaluation framework for personalized search based on query logs, and then evaluate five personalized search strategies (including two clickbased and three profilebased ones) using 12day MSN query logs. By analyzing the results, we reveal that personalized search has significant improvement over common web search on some queries but it has little effect on other queries (e.g., queries with small click entropy). It even harms search accuracy under some situations. Furthermore, we show that straightforward clickbased personalization strategies perform consistently and considerably well, while profilebased ones are unstable in our experiments. We also reveal that both longterm and shortterm contexts are very important in improving search performance for profilebased personalized search strategies.
Automatic Identification of User Interest For Personalized Search
, 2006
"... One hundred users, one hundred needs. As more and more topics are being discussed on the web and our vocabulary remains relatively stable, it is increasingly difficult to let the search engine know what we want. Coping with ambiguous queries has long been an important part in the research of Informa ..."
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Cited by 91 (2 self)
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One hundred users, one hundred needs. As more and more topics are being discussed on the web and our vocabulary remains relatively stable, it is increasingly difficult to let the search engine know what we want. Coping with ambiguous queries has long been an important part in the research of Information Retrieval, but still remains to be a challenging task. Personalized search has recently got significant attention to address this challenge in the web search community, based on the premise that a user’s general preference may help the search engine disambiguate the true intention of a query. However, studies have shown that users are reluctant to provide any explicit input on their personal preference. In this paper, we study how a search engine can learn a user’s preference automatically based on her past click history and how it can use the user preference to personalize search results. Our experiments show that users’ preferences can be learned accurately even from small clickhistory data and personalized search based on user preference yields significant improvements over the best existing ranking mechanism in the literature.
Efficient MATLAB computations with sparse and factored tensors
 SIAM JOURNAL ON SCIENTIFIC COMPUTING
, 2007
"... In this paper, the term tensor refers simply to a multidimensional or $N$way array, and we consider how specially structured tensors allow for efficient storage and computation. First, we study sparse tensors, which have the property that the vast majority of the elements are zero. We propose stori ..."
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Cited by 69 (14 self)
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In this paper, the term tensor refers simply to a multidimensional or $N$way array, and we consider how specially structured tensors allow for efficient storage and computation. First, we study sparse tensors, which have the property that the vast majority of the elements are zero. We propose storing sparse tensors using coordinate format and describe the computational efficiency of this scheme for various mathematical operations, including those typical to tensor decomposition algorithms. Second, we study factored tensors, which have the property that they can be assembled from more basic components. We consider two specific types: A Tucker tensor can be expressed as the product of a core tensor (which itself may be dense, sparse, or factored) and a matrix along each mode, and a Kruskal tensor can be expressed as the sum of rank1 tensors. We are interested in the case where the storage of the components is less than the storage of the full tensor, and we demonstrate that many elementary operations can be computed using only the components. All of the efficiencies described in this paper are implemented in the Tensor Toolbox for MATLAB.
HigherOrder Web Link Analysis Using Multilinear Algebra
 IEEE INTERNATIONAL CONFERENCE ON DATA MINING
, 2005
"... Linear algebra is a powerful and proven tool in web search. Techniques, such as the PageRank algorithm of Brin and Page and the HITS algorithm of Kleinberg, score web pages based on the principal eigenvector (or singular vector) of a particular nonnegative matrix that captures the hyperlink structu ..."
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Cited by 58 (18 self)
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Linear algebra is a powerful and proven tool in web search. Techniques, such as the PageRank algorithm of Brin and Page and the HITS algorithm of Kleinberg, score web pages based on the principal eigenvector (or singular vector) of a particular nonnegative matrix that captures the hyperlink structure of the web graph. We propose and test a new methodology that uses multilinear algebra to elicit more information from a higherorder representation of the hyperlink graph. We start by labeling the edges in our graph with the anchor text of the hyperlinks so that the associated linear algebra representation is a sparse, threeway tensor. The first two dimensions of the tensor represent the web pages while the third dimension adds the anchor text. We then use the rank1 factors of a multilinear PARAFAC tensor decomposition, which are akin to singular vectors of the SVD, to automatically identify topics in the collection along with the associated authoritative web pages.
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 50 (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
Tag recommendations based on tensor dimensionality reduction
 In RecSys ’08: Proc. of the ACM Conference on Recommender systems, 43–50
, 2008
"... Social tagging is the process by which many users add metadata in the form of keywords, to annotate and categorize information items (songs, pictures, web links, products etc.). Collaborative tagging systems recommend tags to users based on what tags other users have used for the same items, aiming ..."
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Cited by 47 (1 self)
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Social tagging is the process by which many users add metadata in the form of keywords, to annotate and categorize information items (songs, pictures, web links, products etc.). Collaborative tagging systems recommend tags to users based on what tags other users have used for the same items, aiming to develop a common consensus about which tags best describe an item. However, they fail to provide appropriate tag recommendations, because: (i) users may have different interests for an information item and (ii) information items may have multiple facets. In contrast to the current tag recommendation algorithms, our approach develops a unified framework to model the three types of entities that exist in a social tagging system: users, items and tags. These data is represented by a 3order tensor, on which latent semantic analysis and dimensionality reduction is performed using the Higher Order Singular Value Decomposition (HOSVD) technique. We perform experimental comparison of the proposed method against two stateoftheart tag recommendations algorithms with two real data sets (Last.fm and BibSonomy). Our results show significant improvements in terms of effectiveness measured through recall/precision.
Models of searching and browsing: languages, studies and applications
 In Proc. IJCAI
, 2007
"... We describe the formulation, construction, and evaluation of predictive models of human information seeking from a large dataset of Web search activities. We first introduce an expressive language for describing searching and browsing behavior, and use this language to characterize several prior stu ..."
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Cited by 41 (11 self)
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We describe the formulation, construction, and evaluation of predictive models of human information seeking from a large dataset of Web search activities. We first introduce an expressive language for describing searching and browsing behavior, and use this language to characterize several prior studies of search behavior. Then, we focus on the construction of predictive models from the data. We review several analyses, including an exploration of the properties of users, queries, and search sessions that are most predictive of future behavior. We also investigate the influence of temporal delay on user actions, and representational tradeoffs with varying the number of steps of user activity considered. Finally, we discuss applications of the predictive models, and focus on the example of performing principled prefetching of content. 1
Webpage summarization using clickthrough data
 In: Proceedings of the 28th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, ( SIGIR’05
, 2005
"... Most previous Webpage summarization methods treat a Web page as plain text. However, such methods fail to uncover the full knowledge associated with a Web page to build a highquality summary, because the Web contains many hidden relationships that are not used in these methods. Uncovering the inhe ..."
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Cited by 36 (1 self)
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Most previous Webpage summarization methods treat a Web page as plain text. However, such methods fail to uncover the full knowledge associated with a Web page to build a highquality summary, because the Web contains many hidden relationships that are not used in these methods. Uncovering the inherent knowledge is important to building good Webpage summarizers. In this paper, we extract the extra knowledge from the clickthrough data of a Web search engine to improve Webpage summarization. We first analyze the feasibility to utilize clickthrough data in text summarization, and then propose two adapted summarization methods that take advantage of the relationships discovered from the clickthrough data. For those pages not covered by the clickthrough data, we put forward a thematic lexicon approach to generate implicit knowledge for them. Our methods are evaluated on a relatively small dataset consisting of manually annotated pages as well as a large dataset that is crawled from the Open Directory Project website. The experimental results indicate that significant improvements can be achieved through our proposed summarizer as compared with summarizers without using the clickthrough data. Categories and Subject Descriptors H.4 [Information Systems Applications]: Miscellaneous; I.5.4 [Pattern Recognition]: Applications—Text processing
Multilinear operators for higherorder decompositions
, 2006
"... We propose two new multilinear operators for expressing the matrix compositions that are needed in the Tucker and PARAFAC (CANDECOMP) decompositions. The ﬁrst operator,
which we call the Tucker operator, is shorthand for performing an nmode matrix multiplication for every mode of a given tensor and ..."
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Cited by 36 (10 self)
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We propose two new multilinear operators for expressing the matrix compositions that are needed in the Tucker and PARAFAC (CANDECOMP) decompositions. The ﬁrst operator,
which we call the Tucker operator, is shorthand for performing an nmode matrix multiplication for every mode of a given tensor and can be employed to consisely express the Tucker decomposition. The second operator, which we call the Kruskal operator, is shorthand for the sum of the outerproducts of the columns of N matrices and allows a divorce from a matricized representation and a very consise expression of the PARAFAC decomposition. We explore the
properties of the Tucker and Kruskal operators independently of the related decompositions.
Additionally, we provide a review of the matrix and tensor operations that are frequently used in the context of tensor decompositions.