Dynamic Tensor Clustering

Sun, Will Wei; Li, Lexin

doi:10.1080/01621459.2018.1527701

Cited by 56 publications

(35 citation statements)

References 52 publications

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“…Nonetheless, we leave for future work a more principled approach to rank selection. One promising angle of pursuit would be to leverage the equivalence between CCA and a least squares problem (Sun, Ji, & Ye, ) and then derive an information criterion, a strategy commonly used to select the rank parameter in several recently proposed tensor estimation procedures (Zhou et al, ; Sun et al, ; Sun & Li, ).…”

Section: Discussionmentioning

confidence: 99%

Tensor canonical correlation analysis

Min

Chabrière

Zhou

2019

Stat

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Canonical correlation analysis (CCA) is a multivariate analysis technique for estimating a linear relationship between two sets of measurements. Modern acquisition technologies, for example, those arising in neuroimaging and remote sensing, produce data in the form of multidimensional arrays or tensors. Classic CCA is not appropriate for dealing with tensor data due to the multidimensional structure and ultrahigh dimensionality of such modern data. In this paper, we present tensor CCA (TCCA) to discover relationships between two tensors while simultaneously preserving multidimensional structure of the tensors and utilizing substantially fewer parameters. Furthermore, we show how to employ a parsimonious covariance structure to gain additional stability and efficiency. We delineate population and sample problems for each model and propose efficient estimation algorithms with global convergence guarantees. Also we describe a probabilistic model for TCCA that enables the generation of synthetic data with desired canonical variates and correlations. Simulation studies illustrate the performance of our methods.

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Section: Discussionmentioning

confidence: 99%

Tensor canonical correlation analysis

Min

Chabrière

Zhou

2019

Stat

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“…Remark 1 It is worth mentioning that our framework is related but distinct from the CP low-rank-based decomposition framework in literature (see De Silva and Lim (2008); Kolda and Bader (2009);Anandkumar et al (2014a,b); Sun et al (2015); Sun and Li (2017); Wang et al…”

Section: Sparse Tensor Svd Modelmentioning

confidence: 96%

Optimal Sparse Singular Value Decomposition for High-Dimensional High-Order Data

Zhang

Han

2019

Journal of the American Statistical Association

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In this article, we consider the sparse tensor singular value decomposition, which aims for dimension reduction on high-dimensional high-order data with certain sparsity structure.A method named sparse tensor alternating thresholding for singular value decomposition (STAT-SVD) is proposed. The proposed procedure features a novel double projection & thresholding scheme, which provides a sharp criterion for thresholding in each iteration.Compared with regular tensor SVD model, STAT-SVD permits more robust estimation under weaker assumptions. Both the upper and lower bounds for estimation accuracy are developed.The proposed procedure is shown to be minimax rate-optimal in a general class of situations.Simulation studies show that STAT-SVD performs well under a variety of configurations.We also illustrate the merits of the proposed procedure on a longitudinal tensor dataset on European country mortality rates.

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“…[246] further extended this approach to handle large networks. [204] proposed a structured tensor factorization approach that encourages sparsity and smoothness in parameters along the specified tensor modes. They then built a dynamic tensor clustering method, and applied to brain dynamic functional connectivity analysis.…”

Section: Network Estimationmentioning

confidence: 99%

Network Modeling in Biology: Statistical Methods for Gene and Brain Networks

Wang

et al. 2021

Statist. Sci.

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The rise of network data in many different domains has offered researchers new insights into the problem of modeling complex systems and propelled the development of numerous innovative statistical methodologies and computational tools. In this paper, we primarily focus on two types of biological networks, gene networks and brain networks, where statistical network modeling has found both fruitful and challenging applications. Unlike other network examples such as social networks where network edges can be directly observed, both gene and brain networks require careful estimation of edges using measured data as a first step. We provide a discussion on existing statistical and computational methods for edge estimation and subsequent statistical inference problems in these two types of biological networks.

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Dynamic Tensor Clustering

Cited by 56 publications

References 52 publications

Tensor canonical correlation analysis

Tensor canonical correlation analysis

Optimal Sparse Singular Value Decomposition for High-Dimensional High-Order Data

Network Modeling in Biology: Statistical Methods for Gene and Brain Networks

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