3,013 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
Supervised Dictionary Learning and Sparse Representation-A Review
Dictionary learning and sparse representation (DLSR) is a recent and
successful mathematical model for data representation that achieves
state-of-the-art performance in various fields such as pattern recognition,
machine learning, computer vision, and medical imaging. The original
formulation for DLSR is based on the minimization of the reconstruction error
between the original signal and its sparse representation in the space of the
learned dictionary. Although this formulation is optimal for solving problems
such as denoising, inpainting, and coding, it may not lead to optimal solution
in classification tasks, where the ultimate goal is to make the learned
dictionary and corresponding sparse representation as discriminative as
possible. This motivated the emergence of a new category of techniques, which
is appropriately called supervised dictionary learning and sparse
representation (S-DLSR), leading to more optimal dictionary and sparse
representation in classification tasks. Despite many research efforts for
S-DLSR, the literature lacks a comprehensive view of these techniques, their
connections, advantages and shortcomings. In this paper, we address this gap
and provide a review of the recently proposed algorithms for S-DLSR. We first
present a taxonomy of these algorithms into six categories based on the
approach taken to include label information into the learning of the dictionary
and/or sparse representation. For each category, we draw connections between
the algorithms in this category and present a unified framework for them. We
then provide guidelines for applied researchers on how to represent and learn
the building blocks of an S-DLSR solution based on the problem at hand. This
review provides a broad, yet deep, view of the state-of-the-art methods for
S-DLSR and allows for the advancement of research and development in this
emerging area of research
Faster Matrix Completion Using Randomized SVD
Matrix completion is a widely used technique for image inpainting and
personalized recommender system, etc. In this work, we focus on accelerating
the matrix completion using faster randomized singular value decomposition
(rSVD). Firstly, two fast randomized algorithms (rSVD-PI and rSVD- BKI) are
proposed for handling sparse matrix. They make use of an eigSVD procedure and
several accelerating skills. Then, with the rSVD-BKI algorithm and a new
subspace recycling technique, we accelerate the singular value thresholding
(SVT) method in [1] to realize faster matrix completion. Experiments show that
the proposed rSVD algorithms can be 6X faster than the basic rSVD algorithm [2]
while keeping same accuracy. For image inpainting and movie-rating estimation
problems, the proposed accelerated SVT algorithm consumes 15X and 8X less CPU
time than the methods using svds and lansvd respectively, without loss of
accuracy.Comment: 8 pages, 5 figures, ICTAI 2018 Accepte
Low-Rank Modeling and Its Applications in Image Analysis
Low-rank modeling generally refers to a class of methods that solve problems
by representing variables of interest as low-rank matrices. It has achieved
great success in various fields including computer vision, data mining, signal
processing and bioinformatics. Recently, much progress has been made in
theories, algorithms and applications of low-rank modeling, such as exact
low-rank matrix recovery via convex programming and matrix completion applied
to collaborative filtering. These advances have brought more and more
attentions to this topic. In this paper, we review the recent advance of
low-rank modeling, the state-of-the-art algorithms, and related applications in
image analysis. We first give an overview to the concept of low-rank modeling
and challenging problems in this area. Then, we summarize the models and
algorithms for low-rank matrix recovery and illustrate their advantages and
limitations with numerical experiments. Next, we introduce a few applications
of low-rank modeling in the context of image analysis. Finally, we conclude
this paper with some discussions.Comment: To appear in ACM Computing Survey
Two Algorithms for Orthogonal Nonnegative Matrix Factorization with Application to Clustering
Approximate matrix factorization techniques with both nonnegativity and
orthogonality constraints, referred to as orthogonal nonnegative matrix
factorization (ONMF), have been recently introduced and shown to work
remarkably well for clustering tasks such as document classification. In this
paper, we introduce two new methods to solve ONMF. First, we show athematical
equivalence between ONMF and a weighted variant of spherical k-means, from
which we derive our first method, a simple EM-like algorithm. This also allows
us to determine when ONMF should be preferred to k-means and spherical k-means.
Our second method is based on an augmented Lagrangian approach. Standard ONMF
algorithms typically enforce nonnegativity for their iterates while trying to
achieve orthogonality at the limit (e.g., using a proper penalization term or a
suitably chosen search direction). Our method works the opposite way:
orthogonality is strictly imposed at each step while nonnegativity is
asymptotically obtained, using a quadratic penalty. Finally, we show that the
two proposed approaches compare favorably with standard ONMF algorithms on
synthetic, text and image data sets.Comment: 17 pages, 8 figures. New numerical experiments (document and
synthetic data sets
Robust Matrix Completion via Maximum Correntropy Criterion and Half Quadratic Optimization
Robust matrix completion aims to recover a low-rank matrix from a subset of
noisy entries perturbed by complex noises, where traditional methods for matrix
completion may perform poorly due to utilizing error norm in
optimization. In this paper, we propose a novel and fast robust matrix
completion method based on maximum correntropy criterion (MCC). The correntropy
based error measure is utilized instead of using -based error norm to
improve the robustness to noises. Using the half-quadratic optimization
technique, the correntropy based optimization can be transformed to a weighted
matrix factorization problem. Then, two efficient algorithms are derived,
including alternating minimization based algorithm and alternating gradient
descend based algorithm. The proposed algorithms do not need to calculate
singular value decomposition (SVD) at each iteration. Further, the adaptive
kernel selection strategy is proposed to accelerate the convergence speed as
well as improve the performance. Comparison with existing robust matrix
completion algorithms is provided by simulations, showing that the new methods
can achieve better performance than existing state-of-the-art algorithms
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
Longitudinal data analysis using matrix completion
In clinical practice and biomedical research, measurements are often
collected sparsely and irregularly in time while the data acquisition is
expensive and inconvenient. Examples include measurements of spine bone mineral
density, cancer growth through mammography or biopsy, a progression of defect
of vision, or assessment of gait in patients with neurological disorders. Since
the data collection is often costly and inconvenient, estimation of progression
from sparse observations is of great interest for practitioners.
From the statistical standpoint, such data is often analyzed in the context
of a mixed-effect model where time is treated as both random and fixed effect.
Alternatively, researchers analyze Gaussian processes or functional data where
observations are assumed to be drawn from a certain distribution of processes.
These models are flexible but rely on probabilistic assumptions and require
very careful implementation.
In this study, we propose an alternative elementary framework for analyzing
longitudinal data, relying on matrix completion. Our method yields point
estimates of progression curves by iterative application of the SVD. Our
framework covers multivariate longitudinal data, regression and can be easily
extended to other settings.
We apply our methods to understand trends of progression of motor impairment
in children with Cerebral Palsy. Our model approximates individual progression
curves and explains 30% of the variability. Low-rank representation of
progression trends enables discovering that subtypes of Cerebral Palsy exhibit
different progression trends
A survey of dimensionality reduction techniques
Experimental life sciences like biology or chemistry have seen in the recent
decades an explosion of the data available from experiments. Laboratory
instruments become more and more complex and report hundreds or thousands
measurements for a single experiment and therefore the statistical methods face
challenging tasks when dealing with such high dimensional data. However, much
of the data is highly redundant and can be efficiently brought down to a much
smaller number of variables without a significant loss of information. The
mathematical procedures making possible this reduction are called
dimensionality reduction techniques; they have widely been developed by fields
like Statistics or Machine Learning, and are currently a hot research topic. In
this review we categorize the plethora of dimension reduction techniques
available and give the mathematical insight behind them
Cascaded Channel Estimation for Large Intelligent Metasurface Assisted Massive MIMO
In this letter, we consider the problem of channel estimation for large
intelligent metasurface (LIM) assisted massive multiple-input multiple-output
(MIMO) systems. The main challenge of this problem is that the LIM integrated
with a large number of low-cost metamaterial antennas can only passively
reflect the incident signal by a certain phase shift, and does not have any
signal processing capability. To deal with this, we introduce a general
framework for the estimation of the transmitter-LIM and LIM-receiver cascaded
channel, and propose a two-stage algorithm that includes a sparse matrix
factorization stage and a matrix completion stage. Simulation results
illustrate that the proposed method can achieve accurate channel estimation for
LIM-assisted massive MIMO systems.Comment: 3 figures, 5 page
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