Search results for "nonnegative"
showing 10 items of 11 documents
Extracting multi-mode ERP features using fifth-order nonnegative tensor decomposition
2018
Background Preprocessed Event-related potential (ERP) data are usually organized in multi-way tensor, in which tensor decomposition serves as a powerful tool for data processing. Due to the limitation of computation burden for multi-way data and the low algorithm performance of stability and efficiency, multi-way ERP data are conventionally reorganized into low-order tensor or matrix before further analysis. However, the reorganization may hamper mode specification and spoil the interaction information among different modes. New method In this study, we applied a fifth-order tensor decomposition to a set of fifth-order ERP data collected by exerting proprioceptive stimulus on left and right…
Classifying Healthy Children and Children with Attention Deficit through Features Derived from Sparse and Nonnegative Tensor Factorization Using Even…
2010
In this study, we use features extracted by Nonnegative Tensor Factorization (NTF) from event-related potentials (ERPs) to discriminate healthy children and children with attention deficit (AD). The peak amplitude of an ERP has been extensively used to discriminate different groups of subjects for the clinical research. However, such discriminations sometimes fail because the peak amplitude may vary severely with the increased number of subjects and wider range of ages and it can be easily affected by many factors. This study formulates a framework, using NTF to extract features of the evoked brain activities from time-frequency represented ERPs. Through using the estimated features of a ne…
Identical fits of nonnegative matrix/tensor factorization may correspond to different extracted event-related potentials
2010
Nonnegative Matrix / Tensor factorization (NMF/NTF) have been used in the study of EEG, and the fit (explained variation) is often used to evaluate the performance of a nonnegative decomposition algorithm. However, this parameter only reveals the information derived from the mathematical model and just exhibits the reliability of the algorithms, and the property of EEG can not be reflected. If fits of two algorithms are identical, it is necessary to examine whether the desired components extracted by them are identical too. In order to verify this doubt, we performed NMF and NTF on the same dataset of an auditory event-related potentials (ERPs), and found that the identical fits of NMF and …
Increasing Stability of EEG Components Extraction Using Sparsity Regularized Tensor Decomposition
2018
Tensor decomposition has been widely employed for EEG signal processing in recent years. Constrained and regularized tensor decomposition often attains more meaningful and interpretable results. In this study, we applied sparse nonnegative CANDECOMP/PARAFAC tensor decomposition to ongoing EEG data under naturalistic music stimulus. Interesting temporal, spectral and spatial components highly related with music features were extracted. We explored the ongoing EEG decomposition results and properties in a wide range of sparsity levels, and proposed a paradigm to select reasonable sparsity regularization parameters. The stability of interesting components extraction from fourteen subjects’ dat…
Group analysis of ongoing EEG data based on fast double-coupled nonnegative tensor decomposition
2019
Abstract Background Ongoing EEG data are recorded as mixtures of stimulus-elicited EEG, spontaneous EEG and noises, which require advanced signal processing techniques for separation and analysis. Existing methods cannot simultaneously consider common and individual characteristics among/within subjects when extracting stimulus-elicited brain activities from ongoing EEG elicited by 512-s long modern tango music. New method Aiming to discover the commonly music-elicited brain activities among subjects, we provide a comprehensive framework based on fast double-coupled nonnegative tensor decomposition (FDC-NTD) algorithm. The proposed algorithm with a generalized model is capable of simultaneo…
Assessment of nonnegative matrix factorization algorithms for electroencephalography spectral analysis.
2020
AbstractBackgroundNonnegative matrix factorization (NMF) has been successfully used for electroencephalography (EEG) spectral analysis. Since NMF was proposed in the 1990s, many adaptive algorithms have been developed. However, the performance of their use in EEG data analysis has not been fully compared. Here, we provide a comparison of four NMF algorithms in terms of accuracy of estimation, stability (repeatability of the results) and time complexity of algorithms with simulated data. In the practical application of NMF algorithms, stability plays an important role, which was an emphasis in the comparison. A Hierarchical clustering algorithm was implemented to evaluate the stability of NM…
Quasilinear Dirichlet Problems with Degenerated p-Laplacian and Convection Term
2021
The paper develops a sub-supersolution approach for quasilinear elliptic equations driven by degenerated p-Laplacian and containing a convection term. The presence of the degenerated operator forces a substantial change to the functional setting of previous works. The existence and location of solutions through a sub-supersolution is established. The abstract result is applied to find nontrivial, nonnegative and bounded solutions.
Sparse nonnegative tensor decomposition using proximal algorithm and inexact block coordinate descent scheme
2021
Nonnegative tensor decomposition is a versatile tool for multiway data analysis, by which the extracted components are nonnegative and usually sparse. Nevertheless, the sparsity is only a side effect and cannot be explicitly controlled without additional regularization. In this paper, we investigated the nonnegative CANDECOMP/PARAFAC (NCP) decomposition with the sparse regularization item using l1-norm (sparse NCP). When high sparsity is imposed, the factor matrices will contain more zero components and will not be of full column rank. Thus, the sparse NCP is prone to rank deficiency, and the algorithms of sparse NCP may not converge. In this paper, we proposed a novel model of sparse NCP w…
Higher-order Nonnegative CANDECOMP/PARAFAC Tensor Decomposition Using Proximal Algorithm
2019
Tensor decomposition is a powerful tool for analyzing multiway data. Nowadays, with the fast development of multisensor technology, more and more data appear in higherorder (order > 4) and nonnegative form. However, the decomposition of higher-order nonnegative tensor suffers from poor convergence and low speed. In this study, we propose a new nonnegative CANDECOM/PARAFAC (NCP) model using proximal algorithm. The block principal pivoting method in alternating nonnegative least squares (ANLS) framework is employed to minimize the objective function. Our method can guarantee the convergence and accelerate the computation. The results of experiments on both synthetic and real data demonstrate …
Spectral density of the correlation matrix of factor models: a random matrix theory approach.
2005
We studied the eigenvalue spectral density of the correlation matrix of factor models of multivariate time series. By making use of the random matrix theory, we analytically quantified the effect of statistical uncertainty on the spectral density due to the finiteness of the sample. We considered a broad range of models, ranging from one-factor models to hierarchical multifactor models.