MultiVis: Content-based Social Network Exploration Through Multi-way Visual Analysis

Sun, Jimeng; Papadimitriou, Spiros; Lin, Ching Yung; Cao, Nan; Liu, Shixia; Qian, Weihong

doi:10.1137/1.9781611972795.91

Cited by 74 publications

(56 citation statements)

References 35 publications

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“…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%

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

Phan

Cichocki

2011

Neurocomputing

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Section: Introductionmentioning

confidence: 99%

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

Phan

Cichocki

2011

Neurocomputing

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“…The ALS method [Yates 1933] for PARAFAC models is relatively old and has been successfully applied to the problem of tensor decomposition by Carroll and Chang [1970] and Harshman [1970]. ALS is widely used as a building block in many applications for fitting PARAFAC and Tucker models [Kolda and Bader 2006;Sun et al 2009;Kolda and Sun 2008]. ALS estimates, at each iteration, one factor matrix, maintaining other matrices fixed; this process is repeated for each factor matrix associated to the dimensions of the input tensor.…”

Section: Obtaining Tensor Decompositionsmentioning

confidence: 99%

Multiresolution Tensor Decompositions with Mode Hierarchies

Schifanella

Candan

Sapino

2014

ACM Trans. Knowl. Discov. Data

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Tensors (multidimensional arrays) are widely used for representing high-order dimensional data, in applications ranging from social networks, sensor data, and Internet traffic. Multiway data analysis techniques, in particular tensor decompositions, allow extraction of hidden correlations among multiway data and thus are key components of many data analysis frameworks. Intuitively, these algorithms can be thought of as multiway clustering schemes, which consider multiple facets of the data in identifying clusters, their weights, and contributions of each data element. Unfortunately, algorithms for fitting multiway models are, in general, iterative and very time consuming. In this article, we observe that, in many applications, there is a priori background knowledge (or metadata) about one or more domain dimensions. This metadata is often in the form of a hierarchy that clusters the elements of a given data facet (or mode). We investigate whether such single-mode data hierarchies can be used to boost the efficiency of tensor decomposition process, without significant impact on the final decomposition quality. We consider each domain hierarchy as a guide to help provide higher-or lower-resolution views of the data in the tensor on demand and we rely on these metadata-induced multiresolution tensor representations to develop a multiresolution approach to tensor decomposition. In this article, we focus on an alternating least squares (ALS)-based implementation of the two most important decomposition models such as the PARAllel FACtors (PARAFAC, which decomposes a tensor into a diagonal tensor and a set of factor matrices) and the Tucker (which produces as result a core tensor and a set of dimension-subspaces matrices). Experiment results show that, when the available metadata is used as a rough guide, the proposed multiresolution method helps fit both PARAFAC and Tucker models with consistent (under different parameters settings) savings in execution time and memory consumption, while preserving the quality of the decomposition.

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“…Multi-way data analysis is an important topic in signal processing [7], numerical linear algebra [6], computer vision [19], [20], data mining [16], [29], machine learning [27], neuroscience [22], and so on. As a generalization of scalars, vectors (first-order tensors) and matrices (second-order tensors), higher-order tensors are becoming increasingly popular.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we study the tensor completion problem, which is to estimate the missing values in the tensor. The tensor completion problem has been successfully applied to a wide range of real-world problems, such as visual data [19], [20], EEG data [1], [22], and hyperspectral data analysis [10], social network analysis [29] and link prediction [33].…”

Section: Introductionmentioning

confidence: 99%

Factor Matrix Trace Norm Minimization for Low-Rank Tensor Completion

Liu

Shang

Cheng

et al. 2014

Proceedings of the 2014 SIAM International Conference on Data Mining

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Most existing low-n-rank minimization algorithms for tensor completion suffer from high computational cost due to involving multiple singular value decompositions (SVDs) at each iteration. To address this issue, we propose a novel factor matrix trace norm minimization method for tensor completion problems. Based on the CANDECOMP/PARAFAC (CP) decomposition, we first formulate a factor matrix rank minimization model by deducing the relation between the rank of each factor matrix and the mode-n rank of a tensor. Then, we introduce a tractable relaxation of our rank function, which leads to a convex combination problem of much smaller scale matrix nuclear norm minimization. Finally, we develop an efficient alternating direction method of multipliers (ADMM) scheme to solve the proposed problem. Experimental results on both synthetic and real-world data validate the effectiveness of our approach. Moreover, our method is significantly faster than the state-of-the-art approaches and scales well to handle large datasets.

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MultiVis: Content-based Social Network Exploration Through Multi-way Visual Analysis

Cited by 74 publications

References 35 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

Multiresolution Tensor Decompositions with Mode Hierarchies

Factor Matrix Trace Norm Minimization for Low-Rank Tensor Completion

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