1,761 research outputs found
Blind source separation of tensor-valued time series
The blind source separation model for multivariate time series generally
assumes that the observed series is a linear transformation of an unobserved
series with temporally uncorrelated or independent components. Given the
observations, the objective is to find a linear transformation that recovers
the latent series. Several methods for accomplishing this exist and three
particular ones are the classic SOBI and the recently proposed generalized FOBI
(gFOBI) and generalized JADE (gJADE), each based on the use of joint lagged
moments. In this paper we generalize the methodologies behind these algorithms
for tensor-valued time series. We assume that our data consists of a tensor
observed at each time point and that the observations are linear
transformations of latent tensors we wish to estimate. The tensorial
generalizations are shown to have particularly elegant forms and we show that
each of them is Fisher consistent and orthogonal equivariant. Comparing the new
methods with the original ones in various settings shows that the tensorial
extensions are superior to both their vector-valued counterparts and to two
existing tensorial dimension reduction methods for i.i.d. data. Finally,
applications to fMRI-data and video processing show that the methods are
capable of extracting relevant information from noisy high-dimensional data.Comment: 26 pages, 6 figure
Multi-Scale Factor Analysis of High-Dimensional Brain Signals
In this paper, we develop an approach to modeling high-dimensional networks
with a large number of nodes arranged in a hierarchical and modular structure.
We propose a novel multi-scale factor analysis (MSFA) model which partitions
the massive spatio-temporal data defined over the complex networks into a
finite set of regional clusters. To achieve further dimension reduction, we
represent the signals in each cluster by a small number of latent factors. The
correlation matrix for all nodes in the network are approximated by
lower-dimensional sub-structures derived from the cluster-specific factors. To
estimate regional connectivity between numerous nodes (within each cluster), we
apply principal components analysis (PCA) to produce factors which are derived
as the optimal reconstruction of the observed signals under the squared loss.
Then, we estimate global connectivity (between clusters or sub-networks) based
on the factors across regions using the RV-coefficient as the cross-dependence
measure. This gives a reliable and computationally efficient multi-scale
analysis of both regional and global dependencies of the large networks. The
proposed novel approach is applied to estimate brain connectivity networks
using functional magnetic resonance imaging (fMRI) data. Results on
resting-state fMRI reveal interesting modular and hierarchical organization of
human brain networks during rest.Comment: 43 page
Bayesian Mixed Effect Sparse Tensor Response Regression Model with Joint Estimation of Activation and Connectivity
Brain activation and connectivity analyses in task-based functional magnetic
resonance imaging (fMRI) experiments with multiple subjects are currently at
the forefront of data-driven neuroscience. In such experiments, interest often
lies in understanding activation of brain voxels due to external stimuli and
strong association or connectivity between the measurements on a set of
pre-specified group of brain voxels, also known as regions of interest (ROI).
This article proposes a joint Bayesian additive mixed modeling framework that
simultaneously assesses brain activation and connectivity patterns from
multiple subjects. In particular, fMRI measurements from each individual
obtained in the form of a multi-dimensional array/tensor at each time are
regressed on functions of the stimuli. We impose a low-rank PARAFAC
decomposition on the tensor regression coefficients corresponding to the
stimuli to achieve parsimony. Multiway stick breaking shrinkage priors are
employed to infer activation patterns and associated uncertainties in each
voxel. Further, the model introduces region specific random effects which are
jointly modeled with a Bayesian Gaussian graphical prior to account for the
connectivity among pairs of ROIs. Empirical investigations under various
simulation studies demonstrate the effectiveness of the method as a tool to
simultaneously assess brain activation and connectivity. The method is then
applied to a multi-subject fMRI dataset from a balloon-analog risk-taking
experiment in order to make inference about how the brain processes risk.Comment: 27 pages, 7 figure
Linked Component Analysis from Matrices to High Order Tensors: Applications to Biomedical Data
With the increasing availability of various sensor technologies, we now have
access to large amounts of multi-block (also called multi-set,
multi-relational, or multi-view) data that need to be jointly analyzed to
explore their latent connections. Various component analysis methods have
played an increasingly important role for the analysis of such coupled data. In
this paper, we first provide a brief review of existing matrix-based (two-way)
component analysis methods for the joint analysis of such data with a focus on
biomedical applications. Then, we discuss their important extensions and
generalization to multi-block multiway (tensor) data. We show how constrained
multi-block tensor decomposition methods are able to extract similar or
statistically dependent common features that are shared by all blocks, by
incorporating the multiway nature of data. Special emphasis is given to the
flexible common and individual feature analysis of multi-block data with the
aim to simultaneously extract common and individual latent components with
desired properties and types of diversity. Illustrative examples are given to
demonstrate their effectiveness for biomedical data analysis.Comment: 20 pages, 11 figures, Proceedings of the IEEE, 201
Large Spectral Density Matrix Estimation by Thresholding
Spectral density matrix estimation of multivariate time series is a classical
problem in time series and signal processing. In modern neuroscience, spectral
density based metrics are commonly used for analyzing functional connectivity
among brain regions. In this paper, we develop a non-asymptotic theory for
regularized estimation of high-dimensional spectral density matrices of
Gaussian and linear processes using thresholded versions of averaged
periodograms. Our theoretical analysis ensures that consistent estimation of
spectral density matrix of a -dimensional time series using samples is
possible under high-dimensional regime as long as
the true spectral density is approximately sparse. A key technical component of
our analysis is a new concentration inequality of average periodogram around
its expectation, which is of independent interest. Our estimation consistency
results complement existing results for shrinkage based estimators of
multivariate spectral density, which require no assumption on sparsity but only
ensure consistent estimation in a regime . In addition,
our proposed thresholding based estimators perform consistent and automatic
edge selection when learning coherence networks among the components of a
multivariate time series. We demonstrate the advantage of our estimators using
simulation studies and a real data application on functional connectivity
analysis with fMRI data
Variational Mixture Models with Gamma or inverse-Gamma components
Mixture models with Gamma and or inverse-Gamma distributed mixture components
are useful for medical image tissue segmentation or as post-hoc models for
regression coefficients obtained from linear regression within a Generalised
Linear Modeling framework (GLM), used in this case to separate stochastic
(Gaussian) noise from some kind of positive or negative "activation" (modeled
as Gamma or inverse-Gamma distributed). To date, the most common choice in this
context it is Gaussian/Gamma mixture models learned through a maximum
likelihood (ML) approach; we recently extended such algorithm for mixture
models with inverse-Gamma components. Here, we introduce a fully analytical
Variational Bayes (VB) learning framework for both Gamma and/or inverse-Gamma
components. We use synthetic and resting state fMRI data to compare the
performance of the ML and VB algorithms in terms of area under the curve and
computational cost. We observed that the ML Gaussian/Gamma model is very
expensive specially when considering high resolution images; furthermore, these
solutions are highly variable and they occasionally can overestimate the
activations severely. The Bayesian Gauss-Gamma is in general the fastest
algorithm but provides too dense solutions. The maximum likelihood
Gaussian/inverse-Gamma is also very fast but provides in general very sparse
solutions. The variational Gaussian/inverse-Gamma mixture model is the most
robust and its cost is acceptable even for high resolution images. Further, the
presented methodology represents an essential building block that can be
directly used in more complex inference tasks, specially designed to analyse
MRI-fMRI data; such models include for example analytical variational mixture
models with adaptive spatial regularization or better source models for new
spatial blind source separation approaches
Decoding the Encoding of Functional Brain Networks: an fMRI Classification Comparison of Non-negative Matrix Factorization (NMF), Independent Component Analysis (ICA), and Sparse Coding Algorithms
Brain networks in fMRI are typically identified using spatial independent
component analysis (ICA), yet mathematical constraints such as sparse coding
and positivity both provide alternate biologically-plausible frameworks for
generating brain networks. Non-negative Matrix Factorization (NMF) would
suppress negative BOLD signal by enforcing positivity. Spatial sparse coding
algorithms ( Regularized Learning and K-SVD) would impose local
specialization and a discouragement of multitasking, where the total observed
activity in a single voxel originates from a restricted number of possible
brain networks.
The assumptions of independence, positivity, and sparsity to encode
task-related brain networks are compared; the resulting brain networks for
different constraints are used as basis functions to encode the observed
functional activity at a given time point. These encodings are decoded using
machine learning to compare both the algorithms and their assumptions, using
the time series weights to predict whether a subject is viewing a video,
listening to an audio cue, or at rest, in 304 fMRI scans from 51 subjects.
For classifying cognitive activity, the sparse coding algorithm of
Regularized Learning consistently outperformed 4 variations of ICA across
different numbers of networks and noise levels (p0.001). The NMF algorithms,
which suppressed negative BOLD signal, had the poorest accuracy. Within each
algorithm, encodings using sparser spatial networks (containing more
zero-valued voxels) had higher classification accuracy (p0.001). The success
of sparse coding algorithms may suggest that algorithms which enforce sparse
coding, discourage multitasking, and promote local specialization may capture
better the underlying source processes than those which allow inexhaustible
local processes such as ICA
A Journey from Improper Gaussian Signaling to Asymmetric Signaling
The deviation of continuous and discrete complex random variables from the
traditional proper and symmetric assumption to a generalized improper and
asymmetric characterization (accounting correlation between a random entity and
its complex conjugate), respectively, introduces new design freedom and various
potential merits. As such, the theory of impropriety has vast applications in
medicine, geology, acoustics, optics, image and pattern recognition, computer
vision, and other numerous research fields with our main focus on the
communication systems. The journey begins from the design of improper Gaussian
signaling in the interference-limited communications and leads to a more
elaborate and practically feasible asymmetric discrete modulation design. Such
asymmetric shaping bridges the gap between theoretically and practically
achievable limits with sophisticated transceiver and detection schemes in both
coded/uncoded wireless/optical communication systems. Interestingly,
introducing asymmetry and adjusting the transmission parameters according to
some design criterion render optimal performance without affecting the
bandwidth or power requirements of the systems. This dual-flavored article
initially presents the tutorial base content covering the interplay of
reality/complexity, propriety/impropriety and circularity/noncircularity and
then surveys majority of the contributions in this enormous journey.Comment: IEEE COMST (Early Access
Thresholded Multiscale Gaussian Processes with Application to Bayesian Feature Selection for Massive Neuroimaging Data
Motivated by the needs of selecting important features for massive
neuroimaging data, we propose a spatially varying coefficient model (SVCMs)
with sparsity and piecewise smoothness imposed on the coefficient functions. A
new class of nonparametric priors is developed based on thresholded
multiresolution Gaussian processes (TMGP). We show that the TMGP has a large
support on a space of sparse and piecewise smooth functions, leading to
posterior consistency in coefficient function estimation and feature selection.
Also, we develop a method for prior specifications of thresholding parameters
in TMGPs and discuss their theoretical properties. Efficient posterior
computation algorithms are developed by adopting a kernel convolution approach,
where a modified square exponential kernel is chosen taking the advantage that
the analytical form of the eigen decomposition is available. Based on
simulation studies, we demonstrate that our methods can achieve better
performance in estimating the spatially varying coefficient. Also, the proposed
model has been applied to an analysis of resting state functional magnetic
resonance imaging (Rs-fMRI) data from the Autism Brain Imaging Data Exchange
(ABIDE) study, it provides biologically meaningful results.Comment: 37 pages, 7 figure
Determining the Dimension of the Improper Signal Subspace in Complex-Valued Data
A complex-valued signal is improper if it is correlated with its complex
conjugate. The dimension of the improper signal subspace, i.e., the number of
improper components in a complex-valued measurement, is an important parameter
and is unknown in most applications. In this letter, we introduce two
approaches to estimate this dimension, one based on an information- theoretic
criterion and one based on hypothesis testing. We also present reduced-rank
versions of these approaches that work for scenarios where the number of
observations is comparable to or even smaller than the dimension of the data.
Unlike other techniques for determining model orders, our techniques also work
in the presence of additive colored noise
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