4,393 research outputs found
Robust Independent Component Analysis via Minimum Divergence Estimation
Independent component analysis (ICA) has been shown to be useful in many
applications. However, most ICA methods are sensitive to data contamination and
outliers. In this article we introduce a general minimum U-divergence framework
for ICA, which covers some standard ICA methods as special cases. Within the
U-family we further focus on the gamma-divergence due to its desirable property
of super robustness, which gives the proposed method gamma-ICA. Statistical
properties and technical conditions for the consistency of gamma-ICA are
rigorously studied. In the limiting case, it leads to a necessary and
sufficient condition for the consistency of MLE-ICA. This necessary and
sufficient condition is weaker than the condition known in the literature.
Since the parameter of interest in ICA is an orthogonal matrix, a geometrical
algorithm based on gradient flows on special orthogonal group is introduced to
implement gamma-ICA. Furthermore, a data-driven selection for the gamma value,
which is critical to the achievement of gamma-ICA, is developed. The
performance, especially the robustness, of gamma-ICA in comparison with
standard ICA methods is demonstrated through experimental studies using
simulated data and image data.Comment: 7 figure
An Independent Component Analysis Based Tool for Exploring Functional Connections in the Brain
This thesis describes the use of independent component analysis (ICA) as
a measure of voxel similarity, which allows the user to find and view
statistically independent maps of correlated voxel activity.
The tool developed in this work uses a specialized clustering technique,
designed to find and characterize clusters of activated voxels, to
compare the independent component spatial maps across patients. This
same method is also used to compare SPM results across patients
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
Sunyaev-Zel'dovich clusters reconstruction in multiband bolometer camera surveys
We present a new method for the reconstruction of Sunyaev-Zel'dovich (SZ)
galaxy clusters in future SZ-survey experiments using multiband bolometer
cameras such as Olimpo, APEX, or Planck. Our goal is to optimise SZ-Cluster
extraction from our observed noisy maps. We wish to emphasize that none of the
algorithms used in the detection chain is tuned on prior knowledge on the SZ
-Cluster signal, or other astrophysical sources (Optical Spectrum, Noise
Covariance Matrix, or covariance of SZ Cluster wavelet coefficients). First, a
blind separation of the different astrophysical components which contribute to
the observations is conducted using an Independent Component Analysis (ICA)
method. Then, a recent non linear filtering technique in the wavelet domain,
based on multiscale entropy and the False Discovery Rate (FDR) method, is used
to detect and reconstruct the galaxy clusters. Finally, we use the Source
Extractor software to identify the detected clusters. The proposed method was
applied on realistic simulations of observations. As for global detection
efficiency, this new method is impressive as it provides comparable results to
Pierpaoli et al. method being however a blind algorithm. Preprint with full
resolution figures is available at the URL:
w10-dapnia.saclay.cea.fr/Phocea/Vie_des_labos/Ast/ast_visu.php?id_ast=728Comment: Submitted to A&A. 32 Pages, text onl
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