13,055 research outputs found
Tensor Decompositions for Signal Processing Applications From Two-way to Multiway Component Analysis
The widespread use of multi-sensor technology and the emergence of big
datasets has highlighted the limitations of standard flat-view matrix models
and the necessity to move towards more versatile data analysis tools. We show
that higher-order tensors (i.e., multiway arrays) enable such a fundamental
paradigm shift towards models that are essentially polynomial and whose
uniqueness, unlike the matrix methods, is guaranteed under verymild and natural
conditions. Benefiting fromthe power ofmultilinear algebra as theirmathematical
backbone, data analysis techniques using tensor decompositions are shown to
have great flexibility in the choice of constraints that match data properties,
and to find more general latent components in the data than matrix-based
methods. A comprehensive introduction to tensor decompositions is provided from
a signal processing perspective, starting from the algebraic foundations, via
basic Canonical Polyadic and Tucker models, through to advanced cause-effect
and multi-view data analysis schemes. We show that tensor decompositions enable
natural generalizations of some commonly used signal processing paradigms, such
as canonical correlation and subspace techniques, signal separation, linear
regression, feature extraction and classification. We also cover computational
aspects, and point out how ideas from compressed sensing and scientific
computing may be used for addressing the otherwise unmanageable storage and
manipulation problems associated with big datasets. The concepts are supported
by illustrative real world case studies illuminating the benefits of the tensor
framework, as efficient and promising tools for modern signal processing, data
analysis and machine learning applications; these benefits also extend to
vector/matrix data through tensorization. Keywords: ICA, NMF, CPD, Tucker
decomposition, HOSVD, tensor networks, Tensor Train
Space-by-time non-negative matrix factorization for single-trial decoding of M/EEG activity
We develop a novel methodology for the single-trial analysis of multichannel time-varying neuroimaging signals. We introduce the space-by-time M/EEG decomposition, based on Non-negative Matrix Factorization (NMF), which describes single-trial M/EEG signals using a set of non-negative spatial and temporal components that are linearly combined with signed scalar activation coefficients. We illustrate the effectiveness of the proposed approach on an EEG dataset recorded during the performance of a visual categorization task. Our method extracts three temporal and two spatial functional components achieving a compact yet full representation of the underlying structure, which validates and summarizes succinctly results from previous studies. Furthermore, we introduce a decoding analysis that allows determining the distinct functional role of each component and relating them to experimental conditions and task parameters. In particular, we demonstrate that the presented stimulus and the task difficulty of each trial can be reliably decoded using specific combinations of components from the identified space-by-time representation. When comparing with a sliding-window linear discriminant algorithm, we show that our approach yields more robust decoding performance across participants. Overall, our findings suggest that the proposed space-by-time decomposition is a meaningful low-dimensional representation that carries the relevant information of single-trial M/EEG signals
Total Variation Regularized Tensor RPCA for Background Subtraction from Compressive Measurements
Background subtraction has been a fundamental and widely studied task in
video analysis, with a wide range of applications in video surveillance,
teleconferencing and 3D modeling. Recently, motivated by compressive imaging,
background subtraction from compressive measurements (BSCM) is becoming an
active research task in video surveillance. In this paper, we propose a novel
tensor-based robust PCA (TenRPCA) approach for BSCM by decomposing video frames
into backgrounds with spatial-temporal correlations and foregrounds with
spatio-temporal continuity in a tensor framework. In this approach, we use 3D
total variation (TV) to enhance the spatio-temporal continuity of foregrounds,
and Tucker decomposition to model the spatio-temporal correlations of video
background. Based on this idea, we design a basic tensor RPCA model over the
video frames, dubbed as the holistic TenRPCA model (H-TenRPCA). To characterize
the correlations among the groups of similar 3D patches of video background, we
further design a patch-group-based tensor RPCA model (PG-TenRPCA) by joint
tensor Tucker decompositions of 3D patch groups for modeling the video
background. Efficient algorithms using alternating direction method of
multipliers (ADMM) are developed to solve the proposed models. Extensive
experiments on simulated and real-world videos demonstrate the superiority of
the proposed approaches over the existing state-of-the-art approaches.Comment: To appear in IEEE TI
60 GHz Blockage Study Using Phased Arrays
The millimeter wave (mmWave) frequencies offer the potential for enormous
capacity wireless links. However, designing robust communication systems at
these frequencies requires that we understand the channel dynamics over both
time and space: mmWave signals are extremely vulnerable to blocking and the
channel can thus rapidly appear and disappear with small movement of obstacles
and reflectors. In rich scattering environments, different paths may experience
different blocking trajectories and understanding these multi-path blocking
dynamics is essential for developing and assessing beamforming and
beam-tracking algorithms. This paper presents the design and experimental
results of a novel measurement system which uses phased arrays to perform
mmWave dynamic channel measurements. Specifically, human blockage and its
effects across multiple paths are investigated with only several microseconds
between successive measurements. From these measurements we develop a modeling
technique which uses low-rank tensor factorization to separate the available
paths so that their joint statistics can be understood.Comment: To appear in the Proceedings of the 51st Asilomar Conference on
Signals, Systems, and Computers, 201
Non-negative mixtures
This is the author's accepted pre-print of the article, first published as M. D. Plumbley, A. Cichocki and R. Bro. Non-negative mixtures. In P. Comon and C. Jutten (Ed), Handbook of Blind Source Separation: Independent Component Analysis and Applications. Chapter 13, pp. 515-547. Academic Press, Feb 2010. ISBN 978-0-12-374726-6 DOI: 10.1016/B978-0-12-374726-6.00018-7file: Proof:p\PlumbleyCichockiBro10-non-negative.pdf:PDF owner: markp timestamp: 2011.04.26file: Proof:p\PlumbleyCichockiBro10-non-negative.pdf:PDF owner: markp timestamp: 2011.04.2
Ensemble Joint Sparse Low Rank Matrix Decomposition for Thermography Diagnosis System
Composite is widely used in the aircraft industry and it is essential for manufacturers to monitor its health and quality. The most commonly found defects of composite are debonds and delamination. Different inner defects with complex irregular shape is difficult to be diagnosed by using conventional thermal imaging methods. In this paper, an ensemble joint sparse low rank matrix decomposition (EJSLRMD) algorithm is proposed by applying the optical pulse thermography (OPT) diagnosis system. The proposed algorithm jointly models the low rank and sparse pattern by using concatenated feature space. In particular, the weak defects information can be separated from strong noise and the resolution contrast of the defects has significantly been improved. Ensemble iterative sparse modelling are conducted to further enhance the weak information as well as reducing the computational cost. In order to show the robustness and efficacy of the model, experiments are conducted to detect the inner debond on multiple carbon fiber reinforced polymer (CFRP) composites. A comparative analysis is presented with general OPT algorithms. Not withstand above, the proposed model has been evaluated on synthetic data and compared with other low rank and sparse matrix decomposition algorithms
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