1,753 research outputs found
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 Method for Finding Structured Sparse Solutions to Non-negative Least Squares Problems with Applications
Demixing problems in many areas such as hyperspectral imaging and
differential optical absorption spectroscopy (DOAS) often require finding
sparse nonnegative linear combinations of dictionary elements that match
observed data. We show how aspects of these problems, such as misalignment of
DOAS references and uncertainty in hyperspectral endmembers, can be modeled by
expanding the dictionary with grouped elements and imposing a structured
sparsity assumption that the combinations within each group should be sparse or
even 1-sparse. If the dictionary is highly coherent, it is difficult to obtain
good solutions using convex or greedy methods, such as non-negative least
squares (NNLS) or orthogonal matching pursuit. We use penalties related to the
Hoyer measure, which is the ratio of the and norms, as sparsity
penalties to be added to the objective in NNLS-type models. For solving the
resulting nonconvex models, we propose a scaled gradient projection algorithm
that requires solving a sequence of strongly convex quadratic programs. We
discuss its close connections to convex splitting methods and difference of
convex programming. We also present promising numerical results for example
DOAS analysis and hyperspectral demixing problems.Comment: 38 pages, 14 figure
Gradient Hard Thresholding Pursuit for Sparsity-Constrained Optimization
Hard Thresholding Pursuit (HTP) is an iterative greedy selection procedure
for finding sparse solutions of underdetermined linear systems. This method has
been shown to have strong theoretical guarantee and impressive numerical
performance. In this paper, we generalize HTP from compressive sensing to a
generic problem setup of sparsity-constrained convex optimization. The proposed
algorithm iterates between a standard gradient descent step and a hard
thresholding step with or without debiasing. We prove that our method enjoys
the strong guarantees analogous to HTP in terms of rate of convergence and
parameter estimation accuracy. Numerical evidences show that our method is
superior to the state-of-the-art greedy selection methods in sparse logistic
regression and sparse precision matrix estimation tasks
In-network Sparsity-regularized Rank Minimization: Algorithms and Applications
Given a limited number of entries from the superposition of a low-rank matrix
plus the product of a known fat compression matrix times a sparse matrix,
recovery of the low-rank and sparse components is a fundamental task subsuming
compressed sensing, matrix completion, and principal components pursuit. This
paper develops algorithms for distributed sparsity-regularized rank
minimization over networks, when the nuclear- and -norm are used as
surrogates to the rank and nonzero entry counts of the sought matrices,
respectively. While nuclear-norm minimization has well-documented merits when
centralized processing is viable, non-separability of the singular-value sum
challenges its distributed minimization. To overcome this limitation, an
alternative characterization of the nuclear norm is adopted which leads to a
separable, yet non-convex cost minimized via the alternating-direction method
of multipliers. The novel distributed iterations entail reduced-complexity
per-node tasks, and affordable message passing among single-hop neighbors.
Interestingly, upon convergence the distributed (non-convex) estimator provably
attains the global optimum of its centralized counterpart, regardless of
initialization. Several application domains are outlined to highlight the
generality and impact of the proposed framework. These include unveiling
traffic anomalies in backbone networks, predicting networkwide path latencies,
and mapping the RF ambiance using wireless cognitive radios. Simulations with
synthetic and real network data corroborate the convergence of the novel
distributed algorithm, and its centralized performance guarantees.Comment: 30 pages, submitted for publication on the IEEE Trans. Signal Proces
Robust PCA as Bilinear Decomposition with Outlier-Sparsity Regularization
Principal component analysis (PCA) is widely used for dimensionality
reduction, with well-documented merits in various applications involving
high-dimensional data, including computer vision, preference measurement, and
bioinformatics. In this context, the fresh look advocated here permeates
benefits from variable selection and compressive sampling, to robustify PCA
against outliers. A least-trimmed squares estimator of a low-rank bilinear
factor analysis model is shown closely related to that obtained from an
-(pseudo)norm-regularized criterion encouraging sparsity in a matrix
explicitly modeling the outliers. This connection suggests robust PCA schemes
based on convex relaxation, which lead naturally to a family of robust
estimators encompassing Huber's optimal M-class as a special case. Outliers are
identified by tuning a regularization parameter, which amounts to controlling
sparsity of the outlier matrix along the whole robustification path of (group)
least-absolute shrinkage and selection operator (Lasso) solutions. Beyond its
neat ties to robust statistics, the developed outlier-aware PCA framework is
versatile to accommodate novel and scalable algorithms to: i) track the
low-rank signal subspace robustly, as new data are acquired in real time; and
ii) determine principal components robustly in (possibly) infinite-dimensional
feature spaces. Synthetic and real data tests corroborate the effectiveness of
the proposed robust PCA schemes, when used to identify aberrant responses in
personality assessment surveys, as well as unveil communities in social
networks, and intruders from video surveillance data.Comment: 30 pages, submitted to IEEE Transactions on Signal Processin
Sparse Modeling for Image and Vision Processing
In recent years, a large amount of multi-disciplinary research has been
conducted on sparse models and their applications. In statistics and machine
learning, the sparsity principle is used to perform model selection---that is,
automatically selecting a simple model among a large collection of them. In
signal processing, sparse coding consists of representing data with linear
combinations of a few dictionary elements. Subsequently, the corresponding
tools have been widely adopted by several scientific communities such as
neuroscience, bioinformatics, or computer vision. The goal of this monograph is
to offer a self-contained view of sparse modeling for visual recognition and
image processing. More specifically, we focus on applications where the
dictionary is learned and adapted to data, yielding a compact representation
that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics
and Visio
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