Nonlinear least squares updating of the canonical polyadic decomposition

Vandecappelle, Michiel; Vervliet, Nico; Lathauwer, Lieven De

doi:10.23919/eusipco.2017.8081290

Cited by 23 publications

(27 citation statements)

References 17 publications

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“…However, the same approach can also be applied on datasets with fewer or more electrodes without adjustments. Finally, the tensor decomposition can be updated in an efficient way whenever a new batch of EEG data is available [35]. This allows real time tracking of neonatal sleep states.…”

Section: Discussionmentioning

confidence: 99%

Decomposition of a Multiscale Entropy Tensor for Sleep Stage Identification in Preterm Infants

Wel

Lavanga

Caicedo

et al. 2019

Entropy

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Established sleep cycling is one of the main hallmarks of early brain development in preterm infants, therefore, automated classification of the sleep stages in preterm infants can be used to assess the neonate’s cerebral maturation. Tensor algebra is a powerful tool to analyze multidimensional data and has proven successful in many applications. In this paper, a novel unsupervised algorithm to identify neonatal sleep stages based on the decomposition of a multiscale entropy tensor is presented. The method relies on the difference in electroencephalography(EEG) complexity between the neonatal sleep stages and is evaluated on a dataset of 97 EEG recordings. An average sensitivity, specificity, accuracy and area under the receiver operating characteristic curve of 0.80, 0.79, 0.79 and 0.87 was obtained if the rank of the tensor decomposition is selected based on the age of the infant.

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Section: Discussionmentioning

confidence: 99%

Decomposition of a Multiscale Entropy Tensor for Sleep Stage Identification in Preterm Infants

Wel

Lavanga

Caicedo

et al. 2019

Entropy

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show abstract

“…The ML approach, as mentioned, is widely used for existing tensor methods and can be solved using alternating optimization [2,62], all-at-once optimization [63], or non-linear least squares [64,65]. Constraints such as non-negativity can be imposed using either active set procedures [66], or alternating direction method of multipliers [67,68].…”

Section: Maximum Likelihoodmentioning

confidence: 99%

The probabilistic tensor decomposition toolbox

Hinrich¹,

Madsen²,

Mørup³

2020

Mach. Learn.: Sci. Technol.

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This article introduces the probabilistic tensor decomposition toolbox -a MATLAB toolbox for tensor decomposition using Variational Bayesian inference and Gibbs sampling. An introduction and overview of probabilistic tensor decomposition and its connection with classical tensor decomposition methods based on maximum likelihood is provided. We subsequently describe the probabilistic tensor decomposition toolbox which encompasses the Canonical Polyadic, Tucker, and Tensor Train decomposition models. Currently, unconstrained, non-negative, orthogonal, and sparse factors are supported. Bayesian inference forms a principled way of incorporating prior knowledge, prediction of held-out data, and estimating posterior probabilities. Furthermore, it facilitates automatic model order determination, automatic regularization on factors (e.g. sparsity), and inherently penalizes model complexity which is beneficial when inferring hierarchical models, such as heteroscedastic noise modelling. The toolbox allows researchers to easily apply Bayesian tensor decomposition methods without the need to derive or implement these methods themselves. Furthermore, it serves as a reference implementation for comparing existing and new tensor decomposition methods. The software is available from https://github.com/JesperLH/prob-tensor-toolbox/. © 2020 The Author(s). Published by IOP Publishing Ltd Mach. Learn.: Sci. Technol. 1 (2020) 025011 J L Hinrich et al Bayesian tensor decompositionFor comprehensive reviews of maximum likelihood based tensor decomposition methods the reader is referred to existing tensor decomposition reviews [6-9, 22, 23]. We presently provide a short overview of Bayesian tensor decomposition. For brevity, this section will drop the prefix Bayesian and unless otherwise stated all models are based on fully Bayesian inference.Currently, probabilistic models are primarily based on the Tucker and CP decomposition. The earliest works using Tucker decomposition are found in [24,25] where both the core array and factors follow a normal distribution. The latter also considered enforcing sparsity on the core array to automatically learn the most prominent multi-linear interactions. However, neither of these methods were fully Bayesian as they relied on maximum-a-posteriori estimation which provides a point estimate of the posterior distribution. The first fully Bayesian Tucker model with normal factors using Gibbs sampling was proposed in [26] and the indeterminacy and structure of the core array was explored in [27]. The Tucker decomposition was extended to handle missing values and sparse noise based on variational Bayesian (VB) inference [28] whereas the Tucker model with an infinite core size was explored in [29][30][31] with factors specified as Gaussian processes and inference based on VB. Extensions of the Tucker model to count data was explored in [32,33] using the Poisson likelihood and either Gamma or Dirichlet factors. For categorical data, a Tucker model with multinomial likelihood and factors was considered in [34]....

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“…RBS can achieve a high accuracy through step restriction strategies. Updating algorithms can be used to track tensor decompositions that change over time [98,99,100], but can also be used to decompose large-scale tensors as follows. Rather than loading the whole tensor into memory at once, a smaller subtensor is decomposed first.…”

Section: Sampling: Incompleteness Randomization and Updatingmentioning

confidence: 99%

“…This process is then repeated until all slices have been added. Hence, at any given iteration, only the factorization constructed using the previous slices and one new slice are in memory; see [100].…”

Section: Sampling: Incompleteness Randomization and Updatingmentioning

confidence: 99%

Numerical Optimization-Based Algorithms for Data Fusion

Vervliet

Lathauwer

2019

Data Handling in Science and Technology

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Combining various sources of information to discover hidden patterns is key in data analysis. These sources can often be represented as matrices and/or multiway arrays, or tensors, which can be factorized jointly, e.g. as sums of simple terms, to gain insight into the data. In this chapter, an overview of (the rationale behind) numerically wellfounded optimization techniques based on a Gauss-Newton framework is given, which has superior convergence properties and allows all multilinear structure to be exploited. Prior knowledge in the form of parametric, box or soft constraints as well as regularization can be incorporated easily. We show how matrices and/or tensors can be coupled through (partially) shared factors or through common underlying variables. The framework is further extended to more general divergences allowing more suitable statistical assumptions. Finally, as tensor problems become large-scale quickly, due to the curse of dimensionality, techniques used to alleviate or overcome this curse are discussed.

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Nonlinear least squares updating of the canonical polyadic decomposition

Cited by 23 publications

References 17 publications

Decomposition of a Multiscale Entropy Tensor for Sleep Stage Identification in Preterm Infants

Decomposition of a Multiscale Entropy Tensor for Sleep Stage Identification in Preterm Infants

The probabilistic tensor decomposition toolbox

Numerical Optimization-Based Algorithms for Data Fusion

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