Approximate rank-detecting factorization of low-rank tensors

Király, Franz J.; Ziehe, Andreas

doi:10.1109/icassp.2013.6638397

Cited by 4 publications

(8 citation statements)

References 20 publications

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“…While in the former category, the parameters of the model and the model order itself are estimated simultaneously, (e.g. [78,113]), or the model order is estimated first and then parameters of the model for that order are estimated separately, (e.g. [103,111]).…”

Section: Rank Selection Techniquesmentioning

confidence: 99%

“…However, in some scenarios a complete diagonalization may not be necessary, and the problem is finding a single common rank one constituents of the matrices. A new framework called AROFAC2 [113] can be used for CANDECOMP/PARAFAC decomposition and rank selection. AROFAC2 algorithm uses the intrinsic algebraic structure of a low-rank degree tensor in the calculations, and reduces determination of rank to a clustering problem.…”

Section: Approximate Rank-detecting Factorizationmentioning

confidence: 99%

“…and also rank selection based on the AROFAC2 [113], the SORTE [88], the Convexhull method [68], the RADOI method [118], and R-D AIC, R-D MDL and R-D EFT methods [111]. In the proposed scheme, we set α = 100 and β = 200 (refer to [117] for the discussion on selection of these parameters).…”

Section: Additive White Noisementioning

confidence: 99%

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Tensor analysis of electroencephalogram signal for localization of event-related potentials

Pouryazdian¹

2021

Preprint

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Electroencephalogram (EEG) is widely used for monitoring, diagnosis purposes and also for study of brains physiological, mental and functional abnormalities. EEG is known to be a high-dimensional signal in which processing of information by the brain is reected in dynamical changes of the electrical activity in time, frequency, and space. EEG signal processing tends to describe and quantify these variations into functions with known spatio-temporal-spectral properties or at least easier to characterize. Multi-channel EEG recordings naturally include multiple modes. Matrix analysis, via stacking or concatenating other modes with the retained two modes, has been extensively used to represent and analyze the EEG data. On the other hand, Multi-way (tensor) analysis techniques keep the structure of the data, and by analyzing more dimensions simultaneously, summarize the data into more interpretable components. This work presents a generalized multi-way array analysis methodology in pattern classification systems as related to source separation and discriminant feature selection in EEG signal processing problems. Analysis of ERPs, as one of the main categories of EEG signals, requires systems that can exploit the variation of the signals in different contextual domains in order to reveal the hidden structures in the data. Temporal, spectral, spatial, and subjects/experimental conditions of multi-channel ERP signals are exploited here to generate three-way and four-way ERP tensors. Two key elements of this framework are the Time-Frequency representation (TFR) and CANDECOMP/PARAFAC model order selection techniques we incorporate for analysis. Here, we propose a fully data-driven TFR scheme, via combining the Empirical Mode Decomposition and Reassignment method, which yields a high resolution and cross-term free TFR. Furthermore, we develop a robust and effective model order selection scheme that outperforms conventional techniques in mid and low SNRs (i.e. 0􀀀10 dB) with a better Probability of Detection (PoD) and almost no extra computational overhead after the CANDECOMP/PARAFAC decomposition. ERP tensor can be regarded as a mixture that includes different kinds of brain activity, artifacts, interference, and noise. Using this framework, the desired brain activity could be extracted out from the mixture. The extracted signatures are then translated for different applications in brain-computer interface and cognitive neuroscience.

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Section: Rank Selection Techniquesmentioning

confidence: 99%

Section: Approximate Rank-detecting Factorizationmentioning

confidence: 99%

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Tensor analysis of electroencephalogram signal for localization of event-related potentials

Pouryazdian¹

2021

Preprint

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“…The main advantage of such an approach is obviously that there is no need to know in advance what are the components expected to be present in the solution to be able to separate their contribution and then to classify or identify them. Yet, the unknown number of fluorophores, namely F here, remains a difficulty even if different approaches have been suggested to estimate this number (split‐half Analysis , core consistency diagnostic or CORCONDIA , LTMC , Threshold‐CORCONDIA , DIFFIT , a convex hull‐based method , SORTE , AROFAC2 ). In addition, as the quantities that have to be estimated (spectra or concentrations) are inherently nonnegative, it has become important to develop CP decomposition algorithms that ensure this nonnegativity constraint.…”

Section: Problem Statement: Canonical Polyadic Decomposition Of Fluormentioning

confidence: 99%

A regularized nonnegative canonical polyadic decomposition algorithm with preprocessing for 3D fluorescence spectroscopy

Royer

Thirion-Moreau

Comon

et al. 2015

Journal of Chemometrics

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International audienceWe consider blind source separation in chemical analysis focussing on the 3D fluorescence spectroscopy framework. We present an alternative method to process the Fluorescence Excitation-Emission Matrices (FEEM): first, a preprocessing is applied to eliminate the Raman and Rayleigh scattering peaks that clutter the FEEM. To improve its robustness versus possible improper settings, we suggest to associate the classical Zepp's method with a morphological image filtering technique. Then, in a second stage, the Canonical Polyadic (CP or Cande-comp/Parafac) decomposition of a nonnegative 3-way array has to be computed. In the fluorescence spectroscopy context, the constituent vectors of the loading matrices should be nonnegative (since standing for spectra and concentrations). Thus, we suggest a new NonNegative third order CP decomposition algorithm (NNCP) based on a non linear conjugate gradient optimisation algorithm with regularization terms and periodic restarts. Computer simulations performed on real experimental data are provided to enlighten the effectiveness and robustness of the whole processing chain and to validate the approach

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“…the rank F of the tensor is unknown. It can be either overestimated or estimated by different methods among which are Split Half Analysis [16], COre CONsistency DIAgnostic (CORDONDIA) [17], LTMC [18], Threshold-CORCONDIA [19], DIFFIT [20], SORTE [21], AROFAC2 [22] to mention only the most known. Yet, those estimation methods can be subject to forecast errors.…”

Section: Nonnegative 3-way Array Factorization: Nncp Decompositionmentioning

confidence: 99%

Study of different strategies for the Canonical Polyadic decomposition of nonnegative third order tensors with application to the separation of spectra in 3D fluorescence spectroscopy

Chaux

Maire

et al. 2014

2014 IEEE International Workshop on Machine Learning for Signal Processing (MLSP)

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In this communication, the problem of blind source separation in chemical analysis and more precisely in the fluorescence spectroscopy framework is addressed. Classically multi-linear Canonical Polyadic (CP or Candecomp/Parafac) decompositions algorithms are used to perform that task. Yet, as the constituent vectors of the loading matrices should be nonnegative since they stand for nonnegative quantities (spectra and concentrations), we focus on NonNegative CP decomposition algorithms (NNCP). In the unconstrained case, two types of trilinear (or triadic) decomposition model have been studied. Here, our aim is to investigate different strategies concerning the choice of models and optimization schemes in the case of a nonnegativity constraint. Computer simulations are performed on synthetic data to illustrate the robustness of the proposed approaches versus overfactoring problems but also the critical importance of the use of regularization terms.

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Approximate rank-detecting factorization of low-rank tensors

Cited by 4 publications

References 20 publications

Tensor analysis of electroencephalogram signal for localization of event-related potentials

Tensor analysis of electroencephalogram signal for localization of event-related potentials

A regularized nonnegative canonical polyadic decomposition algorithm with preprocessing for 3D fluorescence spectroscopy

Study of different strategies for the Canonical Polyadic decomposition of nonnegative third order tensors with application to the separation of spectra in 3D fluorescence spectroscopy

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