Temporal Analysis of Semantic Graphs Using ASALSAN

Bader, Brett W.; Harshman, Richard A.; Kolda, Tamara G.

doi:10.1109/icdm.2007.54

Cited by 97 publications

(81 citation statements)

References 18 publications

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“…This result is also consistent with that illustrated in [8]. More detailed analysis of matrices R and D can be found in [11,20].…”

Section: Analysis Of Enron Email Databasesupporting

confidence: 90%

“…We decomposed the Enron tensor with a factor A having 4 components. The results showed that the four groups in our experiment corresponded to the four categories that Bader et al labeled in [11]: legal, executive/government affairs, executive and pipeline. We illustrate the interactions among the components using Hinton diagram of the communication pattern matrix R in Fig.…”

Section: Analysis Of Enron Email Databasesupporting

confidence: 51%

“…The original experiment first introduced in [8,11] used the Enron email database [57]. We here replicate this experiment to illustrate the benefits of our HALS algorithm for DEDICOM.…”

Section: Analysis Of Enron Email Databasementioning

confidence: 99%

“…That means the complexity of estimation of a component a j by (78) is still of the order Θ(I 2 K). In order to estimate matrices D and R, we can use the same learning rules as in the ASALSAN algorithm [11]. We note that the ASALSAN algorithm uses the multiplicative learning rule to estimate the factor A.…”

Section: Application Of Tucker-2 For Social Network Analysis Using Dmentioning

confidence: 99%

“…Tensor decompositions capture multilinear structures in higher-order data-sets, where the data have more than two modes [5][6][7][8][9]. Tensor decompositions and multi-way analysis allow naturally to extract hidden (latent) components and investigate complex relationships among them, for example, in exploration of social networks [4,10,11].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Extended HALS algorithm for nonnegative Tucker decomposition and its applications for multiway analysis and classification

Phan

Cichocki

2011

Neurocomputing

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“…This result is also consistent with that illustrated in [8]. More detailed analysis of matrices R and D can be found in [11,20].…”

Section: Analysis Of Enron Email Databasesupporting

confidence: 90%

Section: Analysis Of Enron Email Databasesupporting

confidence: 51%

“…The original experiment first introduced in [8,11] used the Enron email database [57]. We here replicate this experiment to illustrate the benefits of our HALS algorithm for DEDICOM.…”

Section: Analysis Of Enron Email Databasementioning

confidence: 99%

Section: Application Of Tucker-2 For Social Network Analysis Using Dmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Extended HALS algorithm for nonnegative Tucker decomposition and its applications for multiway analysis and classification

Phan

Cichocki

2011

Neurocomputing

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Nonnegative Matrix and Tensor Factorizations

Cichocki¹,

Zdunek²,

Phan³

et al. 2009

1,193

463

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Introduction – Problem Statements and Models

Cichocki

Zdunek

Phan

et al. 2009

Nonnegative Matrix and Tensor Factorizations

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Introduction -Problem Statements and ModelsMatrix factorization is an important and unifying topic in signal processing and linear algebra, which has found numerous applications in many other areas. This chapter introduces basic linear and multi-linear 1 models for matrix and tensor factorizations and decompositions, and formulates the analysis framework for the solution of problems posed in this book. The workhorse in this book is Nonnegative Matrix Factorization (NMF) for sparse representation of data and its extensions including the multi-layer NMF, semi-NMF, sparse NMF, tri-NMF, symmetric NMF, orthogonal NMF, non-smooth NMF (nsNMF), overlapping NMF, convolutive NMF (CNMF), and large-scale NMF. Our particular emphasis is on NMF and semi-NMF models and their extensions to multi-way models (i.e., multi-linear models which perform multi-way array (tensor) decompositions) with nonnegativity and sparsity constraints, including, Nonnegative Tucker Decompositions (NTD), Constrained Tucker Decompositions, Nonnegative and semi-nonnegative Tensor Factorizations (NTF) that are mostly based on a family of the TUCKER, PARAFAC and PARATUCK models.As the theory and applications of NMF, NTF and NTD are still being developed, our aim is to produce a unified, state-of-the-art framework for the analysis and development of efficient and robust algorithms. In doing so, our main goals are to:1. Develop various working tools and algorithms for data decomposition and feature extraction based on nonnegative matrix factorization (NMF) and sparse component analysis (SCA) approaches. We thus integrate several emerging techniques in order to estimate physically, physiologically, and neuroanatomically meaningful sources or latent (hidden) components with morphological constraints. These constraints include nonnegativity, sparsity, orthogonality, smoothness, and semi-orthogonality. 2. Extend NMF models to multi-way array (tensor) decompositions, factorizations, and filtering, and to derive efficient learning algorithms for these models. 3. Develop a class of advanced blind source separation (BSS), unsupervised feature extraction and clustering algorithms, and to evaluate their performance using a priori knowledge and morphological constraints. 4. Develop computational methods to efficiently solve the bi-linear system Y = AX + E for noisy data, where Y is an input data matrix, A and X represent unknown matrix factors to be estimated, and the matrix E represents error or noise (which should be minimized using suitably designed cost function).1 A function in two or more variables is said to be multi-linear if it is linear in each variable separately.

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Temporal Analysis of Semantic Graphs Using ASALSAN

Cited by 97 publications

References 18 publications

Extended HALS algorithm for nonnegative Tucker decomposition and its applications for multiway analysis and classification

Extended HALS algorithm for nonnegative Tucker decomposition and its applications for multiway analysis and classification

Nonnegative Matrix and Tensor Factorizations

Introduction – Problem Statements and Models

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