8,238 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
Frequency Recognition in SSVEP-based BCI using Multiset Canonical Correlation Analysis
Canonical correlation analysis (CCA) has been one of the most popular methods
for frequency recognition in steady-state visual evoked potential (SSVEP)-based
brain-computer interfaces (BCIs). Despite its efficiency, a potential problem
is that using pre-constructed sine-cosine waves as the required reference
signals in the CCA method often does not result in the optimal recognition
accuracy due to their lack of features from the real EEG data. To address this
problem, this study proposes a novel method based on multiset canonical
correlation analysis (MsetCCA) to optimize the reference signals used in the
CCA method for SSVEP frequency recognition. The MsetCCA method learns multiple
linear transforms that implement joint spatial filtering to maximize the
overall correlation among canonical variates, and hence extracts SSVEP common
features from multiple sets of EEG data recorded at the same stimulus
frequency. The optimized reference signals are formed by combination of the
common features and completely based on training data. Experimental study with
EEG data from ten healthy subjects demonstrates that the MsetCCA method
improves the recognition accuracy of SSVEP frequency in comparison with the CCA
method and other two competing methods (multiway CCA (MwayCCA) and phase
constrained CCA (PCCA)), especially for a small number of channels and a short
time window length. The superiority indicates that the proposed MsetCCA method
is a new promising candidate for frequency recognition in SSVEP-based BCIs
A Comparison of Relaxations of Multiset Cannonical Correlation Analysis and Applications
Canonical correlation analysis is a statistical technique that is used to
find relations between two sets of variables. An important extension in pattern
analysis is to consider more than two sets of variables. This problem can be
expressed as a quadratically constrained quadratic program (QCQP), commonly
referred to Multi-set Canonical Correlation Analysis (MCCA). This is a
non-convex problem and so greedy algorithms converge to local optima without
any guarantees on global optimality. In this paper, we show that despite being
highly structured, finding the optimal solution is NP-Hard. This motivates our
relaxation of the QCQP to a semidefinite program (SDP). The SDP is convex, can
be solved reasonably efficiently and comes with both absolute and
output-sensitive approximation quality. In addition to theoretical guarantees,
we do an extensive comparison of the QCQP method and the SDP relaxation on a
variety of synthetic and real world data. Finally, we present two useful
extensions: we incorporate kernel methods and computing multiple sets of
canonical vectors
Canonical correlation analysis based on sparse penalty and through rank-1 matrix approximation
Canonical correlation analysis (CCA) is a well-known technique used to characterize the relationship between two sets of multidimensional variables by finding linear combinations of variables with maximal correlation. Sparse CCA and smooth or regularized CCA are two widely used variants of CCA because of the improved interpretability of the former and the better performance of the later. So far the cross-matrix product of the two sets of multidimensional variables has been widely used for the derivation of these variants. In this paper two new algorithms for sparse CCA and smooth CCA are proposed. These algorithms differ from the existing ones in their derivation which is based on penalized rank one matrix approximation and the orthogonal projectors onto the space spanned by the columns of the two sets of multidimensional variables instead of the simple cross-matrix product. The performance and effectiveness of the proposed algorithms are tested on simulated experiments. On these results it can be observed that they outperforms the state of the art sparse CCA algorithms
Improved physiological noise regression in fNIRS: a multimodal extension of the General Linear Model using temporally embedded Canonical Correlation Analysis
For the robust estimation of evoked brain activity from functional Near-Infrared Spectroscopy (fNIRS) signals, it is crucial to reduce nuisance signals from systemic physiology and motion. The current best practice incorporates short-separation (SS) fNIRS measurements as regressors in a General Linear Model (GLM). However, several challenging signal characteristics such as non-instantaneous and non-constant coupling are not yet addressed by this approach and additional auxiliary signals are not optimally exploited. We have recently introduced a new methodological framework for the unsupervised multivariate analysis of fNIRS signals using Blind Source Separation (BSS) methods. Building onto the framework, in this manuscript we show how to incorporate the advantages of regularized temporally embedded Canonical Correlation Analysis (tCCA) into the supervised GLM. This approach allows flexible integration of any number of auxiliary modalities and signals. We provide guidance for the selection of optimal parameters and auxiliary signals for the proposed GLM extension. Its performance in the recovery of evoked HRFs is then evaluated using both simulated ground truth data and real experimental data and compared with the GLM with short-separation regression. Our results show that the GLM with tCCA significantly improves upon the current best practice, yielding significantly better results across all applied metrics: Correlation (HbO max. +45%), Root Mean Squared Error (HbO max. -55%), F-Score (HbO up to 3.25-fold) and p-value as well as power spectral density of the noise floor. The proposed method can be incorporated into the GLM in an easily applicable way that flexibly combines any available auxiliary signals into optimal nuisance regressors. This work has potential significance both for conventional neuroscientific fNIRS experiments as well as for emerging applications of fNIRS in everyday environments, medicine and BCI, where high Contrast to Noise Ratio is of importance for single trial analysis.Published versio
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