6,559 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
A Unified Framework for Sparse Non-Negative Least Squares using Multiplicative Updates and the Non-Negative Matrix Factorization Problem
We study the sparse non-negative least squares (S-NNLS) problem. S-NNLS
occurs naturally in a wide variety of applications where an unknown,
non-negative quantity must be recovered from linear measurements. We present a
unified framework for S-NNLS based on a rectified power exponential scale
mixture prior on the sparse codes. We show that the proposed framework
encompasses a large class of S-NNLS algorithms and provide a computationally
efficient inference procedure based on multiplicative update rules. Such update
rules are convenient for solving large sets of S-NNLS problems simultaneously,
which is required in contexts like sparse non-negative matrix factorization
(S-NMF). We provide theoretical justification for the proposed approach by
showing that the local minima of the objective function being optimized are
sparse and the S-NNLS algorithms presented are guaranteed to converge to a set
of stationary points of the objective function. We then extend our framework to
S-NMF, showing that our framework leads to many well known S-NMF algorithms
under specific choices of prior and providing a guarantee that a popular
subclass of the proposed algorithms converges to a set of stationary points of
the objective function. Finally, we study the performance of the proposed
approaches on synthetic and real-world data.Comment: To appear in Signal Processin
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