94 research outputs found
Computing Large-Scale Matrix and Tensor Decomposition with Structured Factors: A Unified Nonconvex Optimization Perspective
The proposed article aims at offering a comprehensive tutorial for the
computational aspects of structured matrix and tensor factorization. Unlike
existing tutorials that mainly focus on {\it algorithmic procedures} for a
small set of problems, e.g., nonnegativity or sparsity-constrained
factorization, we take a {\it top-down} approach: we start with general
optimization theory (e.g., inexact and accelerated block coordinate descent,
stochastic optimization, and Gauss-Newton methods) that covers a wide range of
factorization problems with diverse constraints and regularization terms of
engineering interest. Then, we go `under the hood' to showcase specific
algorithm design under these introduced principles. We pay a particular
attention to recent algorithmic developments in structured tensor and matrix
factorization (e.g., random sketching and adaptive step size based stochastic
optimization and structure-exploiting second-order algorithms), which are the
state of the art---yet much less touched upon in the literature compared to
{\it block coordinate descent} (BCD)-based methods. We expect that the article
to have an educational values in the field of structured factorization and hope
to stimulate more research in this important and exciting direction.Comment: Final Version; to appear in IEEE Signal Processing Magazine; title
revised to comply with the journal's rul
Tensor Decomposition for EEG Signal Retrieval
Prior studies have proposed methods to recover multi-channel
electroencephalography (EEG) signal ensembles from their partially sampled
entries. These methods depend on spatial scenarios, yet few approaches aiming
to a temporal reconstruction with lower loss. The goal of this study is to
retrieve the temporal EEG signals independently which was overlooked in data
pre-processing. We considered EEG signals are impinging on tensor-based
approach, named nonlinear Canonical Polyadic Decomposition (CPD). In this
study, we collected EEG signals during a resting-state task. Then, we defined
that the source signals are original EEG signals and the generated tensor is
perturbed by Gaussian noise with a signal-to-noise ratio of 0 dB. The sources
are separated using a basic non-negative CPD and the relative errors on the
estimates of the factor matrices. Comparing the similarities between the source
signals and their recovered versions, the results showed significantly high
correlation over 95%. Our findings reveal the possibility of recoverable
temporal signals in EEG applications
Exploring Numerical Priors for Low-Rank Tensor Completion with Generalized CP Decomposition
Tensor completion is important to many areas such as computer vision, data
analysis, and signal processing. Enforcing low-rank structures on completed
tensors, a category of methods known as low-rank tensor completion has recently
been studied extensively. While such methods attained great success, none
considered exploiting numerical priors of tensor elements. Ignoring numerical
priors causes loss of important information regarding the data, and therefore
prevents the algorithms from reaching optimal accuracy. This work attempts to
construct a new methodological framework called GCDTC (Generalized CP
Decomposition Tensor Completion) for leveraging numerical priors and achieving
higher accuracy in tensor completion. In this newly introduced framework, a
generalized form of CP Decomposition is applied to low-rank tensor completion.
This paper also proposes an algorithm known as SPTC (Smooth Poisson Tensor
Completion) for nonnegative integer tensor completion as an instantiation of
the GCDTC framework. A series of experiments on real-world data indicated that
SPTC could produce results superior in completion accuracy to current
state-of-the-arts.Comment: 11 pages, 4 figures, 3 pseudocode algorithms, and 1 tabl
Tensor decomposition for EEG signals retrieval
© 2019 IEEE. Prior studies have proposed methods to recover multi-channel electroencephalography (EEG) signal ensembles from their partially sampled entries. These methods depend on spatial scenarios, yet few approaches aiming to a temporal reconstruction with lower loss. The goal of this study is to retrieve the temporal EEG signals independently which was overlooked in data pre-processing. We considered EEG signals are impinging on tensor-based approach, named nonlinear Canonical Polyadic Decomposition (CPD). In this study, we collected EEG signals during a resting-state task. Then, we defined that the source signals are original EEG signals and the generated tensor is perturbed by Gaussian noise with a signal-to-noise ratio of 0 dB. The sources are separated using a basic nonnegative CPD and the relative errors on the estimates of the factor matrices. Comparing the similarities between the source signals and their recovered versions, the results showed significantly high correlation over 95%. Our findings reveal the possibility of recoverable temporal signals in EEG applications
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