Fast Alternating LS Algorithms for High Order CANDECOMP/PARAFAC Tensor Factorizations

Phan, Anh-Huy; Tichavský, Petr; Cichocki, Andrzej

doi:10.1109/tsp.2013.2269903

Cited by 138 publications

(143 citation statements)

References 47 publications

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“…It is desirable to avoid explicitly forming these matrices where possible. Efficient algorithms computing the matricized-tensor times string of Khatri-Rao products are available [85], [86], and can be generalized to strings of Kronecker products with little effort. Although these algorithms obviate the need to permute the tensor's elements in memory or explicitly form the Khatri-Rao or Kronecker products, they are ill-suited for big data because of their sizable intermediate results.…”

Section: Modularizing Decompositions and Structurementioning

confidence: 99%

Structured Data Fusion

Sorber

Barel

Lathauwer

2015

IEEE J. Sel. Top. Signal Process.

178

192

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We present structured data fusion (SDF) as a framework for the rapid prototyping of knowledge discovery in one or more possibly incomplete data sets. In SDF, each data set-stored as a dense, sparse, or incomplete tensor-is factorized with a matrix or tensor decomposition. Factorizations can be coupled, or fused, with each other by indicating which factors should be shared between data sets. At the same time, factors may be imposed to have any type of structure that can be constructed as an explicit function of some underlying variables. With the right choice of decomposition type and factor structure, even well-known matrix factorizations such as the eigenvalue decomposition, singular value decomposition and QR factorization can be computed with SDF. A domain specific language (DSL) for SDF is implemented as part of the software package Tensorlab, with which we offer a library of tensor decompositions and factor structures to choose from. The versatility of the SDF framework is demonstrated by means of four diverse applications, which are all solved entirely within Tensorlab's DSL.Index Terms-Big data, tensor, data fusion, structured matrices, canonical polyadic decomposition, block term decomposition, structured factors, domain specific language.

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Section: Modularizing Decompositions and Structurementioning

confidence: 99%

Structured Data Fusion

Sorber

Barel

Lathauwer

2015

IEEE J. Sel. Top. Signal Process.

178

192

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“…2 ) performances to two state-of-the-art methods: 1) fast HALS algorithm [18] and 2) Bro's N -way algorithm [1] for which, to be fair, we used the non-negativity constrained versions). Algorithm initialization is random.…”

Section: Numerical Simulations: Application To 4-th Order Cpdmentioning

confidence: 99%

A Proximal Approach for Nonnegative Tensor Decomposition

Chaux

Thirion-Moreau

et al. 2017

Latent Variable Analysis and Signal Separation

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Abstract. This communication deals with N -th order tensor decompositions. More precisely, we are interested in the (Canonical) Polyadic Decomposition. In our case, this problem is formulated under a variational approach where the considered criterion to be minimized is composed of several terms: one accounting for the fidelity to data and others that can represent not only regularization (such as sparsity prior) but also hard constraints (such as nonnegativity). The resulting optimization problem is solved by using the Block-Coordinate Variable Metric ForwardBackward (BC-VMFB) algorithm. The robustness and efficiency of the suggested approach is illustrated on realistic synthetic data such as those encountered in the context of environmental data analysis and fluorescence spectroscopy. Our simulations are performed on 4-th order tensors.

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“…However, we can simply compute each row of E j,k multiplied by Since dictionary learning is an off-line task, the time complexity for learning dictionary is secondary and is not a main issue in our proposed algorithm. Since CP decomposition is well-known in tensor decomposition, however, some researches focus on analyzing the complexity of CP decomposition and speeding it up [11] [12].…”

Section: B Separable 2d Dictionary Learningmentioning

confidence: 99%

2D sparse dictionary learning via tensor decomposition

Hsieh

Pei

2014

2014 IEEE Global Conference on Signal and Information Processing (GlobalSIP)

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Abstract-The existing dictionary learning methods mostly focus on 1D signals, leading to the disadvantage of incurring overload of memory and computation if the size of training samples is large enough. Recently, 2D dictionary learning paradigm has been validated to save massive memory usage, especially for large-scale problems.To address this issue, we propose novel 2D dictionary learning algorithms based on tensors in this paper. Our learning problem is efficiently solved by CANDECOMP/PARAFAC (CP) decomposition. In addition, our algorithms guarantee sparsity constraint, which makes that sparse representation of the learned dictionary is equivalent to the ground truth. Experimental results confirm the effectness of our methods.

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Fast Alternating LS Algorithms for High Order CANDECOMP/PARAFAC Tensor Factorizations

Cited by 138 publications

References 47 publications

Structured Data Fusion

Structured Data Fusion

A Proximal Approach for Nonnegative Tensor Decomposition

2D sparse dictionary learning via tensor decomposition

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