Higher-Order Web Link Analysis Using Multilinear Algebra

Kolda, Tamara G.; Bader, Brett W.; Kenny, Joseph P.

doi:10.1109/icdm.2005.77

Cited by 188 publications

(158 citation statements)

References 31 publications

(17 reference statements)

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“…In [1], various tensor decompositions of (user × key word × time) data are used to separate different streams of conversation in chatroom data. In [26,25] a PARAFAC decomposition [11] (also known as the Canonical Decomposition or CANDECOMP decomposition [4]) on a (web page × web page × anchor text) was used on a sparse, three-way tensor representing the web graph with anchor-textlabeled edges. This was the first use of PARAFAC for analyzing semantic graphs as well as the first instance of applying PARAFAC to sparse data.…”

Section: Dedicom and Multi-way Modelsmentioning

confidence: 99%

Temporal analysis of social networks using three-way DEDICOM.

Bader¹,

Harshman²,

Kolda

2006

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DEDICOM is an algebraic model for analyzing intrinsically asymmetric relationships, such as the balance of trade among nations or the flow of information among organizations or individuals. It provides information on latent components in the data that can be regarded as "properties" or "aspects" of the objects, and it finds a few patterns that can be combined to describe many relationships among these components. When we apply this technique to adjacency matrices arising from directed graphs, we obtain a smaller graph that gives an idealized description of its patterns. Three-way DEDICOM is a higher-order extension of the model that has certain uniqueness properties. It allows for a third mode of the data, such as time, and permits the analysis of semantic graphs. We present an improved algorithm for computing three-way DEDICOM on sparse data and demonstrate it by applying it to the adjacency tensor of a semantic graph with time-labeled edges. Our application uses the Enron email corpus, from which we construct a semantic graph corresponding to email exchanges among Enron personnel over a series of 44 months. Meaningful patterns are recovered in which the representation of asymmetries adds insight into the social networks at Enron.

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Section: Dedicom and Multi-way Modelsmentioning

confidence: 99%

Temporal analysis of social networks using three-way DEDICOM.

Bader¹,

Harshman²,

Kolda

2006

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“…For further details on tensor nomenclature see also [5,2]. One of the most common approaches to find the loading matrices is by alternatingly solving the above matrix factorization problems for each mode.…”

Section: Methodsmentioning

confidence: 99%

“…Furthermore, if we restrict the loadings (and corearray) to be non-negative the problem becomes a Non-Negative Tensor Factorization (NTF), see also [4]. Tensor factorization has seen use in fields including computational chemistry, neuroimaging, signal processing, and web mining [2,5,6]. When solving for the NTF problem the alternating least squares procedure is commonly used where the tensor decomposition problem is recast into multiple standard non-negative matrix factorizations (NMF) problems.…”

Section: Introductionmentioning

confidence: 99%

Non-negative Tensor Factorization with missing data for the modeling of gene expressions in the Human Brain

Nielsen

Mørup

2014

2014 IEEE International Workshop on Machine Learning for Signal Processing (MLSP)

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Non-negative Tensor Factorization (NTF) has become a prominent tool for analyzing high dimensional multi-way structured data. In this paper we set out to analyze gene expression across brain regions in multiple subjects based on data from the Allen Human Brain Atlas [1] with more than 40 % data missing in our problem. Our analysis is based on the non-negativity constrained Canonical Polyadic (CP) decomposition where we handle the missing data using marginalization considering three prominent alternating least squares procedures; multiplicative updates, column-wise, and row-wise updating of the component matrices. We examine three gene expression prediction scenarios based on data missing at random, whole genes missing and whole areas missing within a subject. We find that the column-wise updating approach also known as HALS performs the most efficient when fitting the model. We further observe that the non-negativity constrained CP model is able to predict gene expressions better than predicting by the subject average when data is missing at random. When whole genes and whole areas are missing it is in general better to predict by subject averages. However, we find that when whole genes are missing from all subjects the model based predictions are useful. When analyzing the structure of the components derived for one of the best predicting model orders the components identified in general constitute localized regions of the brain. Non-negative tensor factorization based on marginalization thus forms a promising framework for imputing missing values and characterizing gene expression in the human brain. However, care also has to be taken in particular when predicting the genetic expression levels at a whole region of the brain missing as our analysis indicates that this requires a substantial amount of subjects with data for this region in order for the model predictions to be reliable.

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“…Tensor factorizations have been widely applied to chemometrices and recently researches have applied tensor factorizations in web link analysis [11], network traffic analyzation [12] and also in social networks for analysis of chat room [13] and email communications [14] Moreover those works based on tensor factorization have achieved good results. More details of tensor factorizations and their applications can refer this excellent review paper [15].…”

Section: Related Workmentioning

confidence: 99%

Link Prediction in Heterogeneous Networks Based on Tensor Factorization

Yong¹,

Li²,

Jiang³

2014

TOCSJ

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Link Prediction, that is, predicting the formation of links or interactions in a network in the future, is an important task in network analysis. Link prediction provides useful insights for other applications, such as recommendation system, disease-gene candidate detection and so on. Most link prediction methods assume that there is only one single type in the network. However, many real-world networks have heterogeneous interactions. Link prediction in such networks is challenging since (a) the network has a complicated dependency structure; and (b) the links of different types may carry different kinds of semantic meanings, which is important to distinguish the formation mechanisms of each link type. In this paper, we address these challenges by proposing a general method based on tensor factorization for link prediction in heterogeneous networks. Using a CANDECOMP/PARAFAC tensor factorization of the data, we illustrate the usefulness of exploring the natural three-dimensional structure of heterogeneous network. The experiment on real-world heterogeneous network demonstrates the effectiveness and efficiency of our methodology.

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Higher-Order Web Link Analysis Using Multilinear Algebra

Cited by 188 publications

References 31 publications

Temporal analysis of social networks using three-way DEDICOM.

Temporal analysis of social networks using three-way DEDICOM.

Non-negative Tensor Factorization with missing data for the modeling of gene expressions in the Human Brain

Link Prediction in Heterogeneous Networks Based on Tensor Factorization

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