966 research outputs found
Distributed canonical correlation analysis in wireless sensor networks with application to distributed blind source separation
status: publishe
Sparse component separation for accurate CMB map estimation
The Cosmological Microwave Background (CMB) is of premier importance for the
cosmologists to study the birth of our universe. Unfortunately, most CMB
experiments such as COBE, WMAP or Planck do not provide a direct measure of the
cosmological signal; CMB is mixed up with galactic foregrounds and point
sources. For the sake of scientific exploitation, measuring the CMB requires
extracting several different astrophysical components (CMB, Sunyaev-Zel'dovich
clusters, galactic dust) form multi-wavelength observations. Mathematically
speaking, the problem of disentangling the CMB map from the galactic
foregrounds amounts to a component or source separation problem. In the field
of CMB studies, a very large range of source separation methods have been
applied which all differ from each other in the way they model the data and the
criteria they rely on to separate components. Two main difficulties are i) the
instrument's beam varies across frequencies and ii) the emission laws of most
astrophysical components vary across pixels. This paper aims at introducing a
very accurate modeling of CMB data, based on sparsity, accounting for beams
variability across frequencies as well as spatial variations of the components'
spectral characteristics. Based on this new sparse modeling of the data, a
sparsity-based component separation method coined Local-Generalized
Morphological Component Analysis (L-GMCA) is described. Extensive numerical
experiments have been carried out with simulated Planck data. These experiments
show the high efficiency of the proposed component separation methods to
estimate a clean CMB map with a very low foreground contamination, which makes
L-GMCA of prime interest for CMB studies.Comment: submitted to A&
Canonical correlation analysis based on sparse penalty and through rank-1 matrix approximation
Canonical correlation analysis (CCA) is a well-known technique used to characterize the relationship between two sets of multidimensional variables by finding linear combinations of variables with maximal correlation. Sparse CCA and smooth or regularized CCA are two widely used variants of CCA because of the improved interpretability of the former and the better performance of the later. So far the cross-matrix product of the two sets of multidimensional variables has been widely used for the derivation of these variants. In this paper two new algorithms for sparse CCA and smooth CCA are proposed. These algorithms differ from the existing ones in their derivation which is based on penalized rank one matrix approximation and the orthogonal projectors onto the space spanned by the columns of the two sets of multidimensional variables instead of the simple cross-matrix product. The performance and effectiveness of the proposed algorithms are tested on simulated experiments. On these results it can be observed that they outperforms the state of the art sparse CCA algorithms
Sparse Canonical Correlation Analysis Based on Rank-1 Matrix Approximation and its Application for fMRI Signals
International audienceCanonical correlation analysis (CCA) is a well-known technique used to characterize the relationship between two sets of multidimensional variables by finding linear combinations of variables with maximal correlation. Sparse CCA or regularized CCA are two widely used variants of CCA because of the improved interpretability of the former and the better performance of the later. So far the cross-matrix product of the two sets of multidimensional variables has been widely used for the derivation of these variants. In this paper a new algorithm for sparse CCA is proposed. This algorithm differs from the existing ones in their derivation which is based on penalized rank one matrix approximation and the orthogonal projectors onto the space spanned by the two sets of multidimensional variables instead of the simple cross-matrix product. The performance and effectiveness of the proposed algorithm are tested on simulated experiments. On these results it can be observed that they outperform the state of the art sparse CCA algorithms
The Incomplete Rosetta Stone Problem: Identifiability Results for Multi-View Nonlinear ICA
We consider the problem of recovering a common latent source with independent
components from multiple views. This applies to settings in which a variable is
measured with multiple experimental modalities, and where the goal is to
synthesize the disparate measurements into a single unified representation. We
consider the case that the observed views are a nonlinear mixing of
component-wise corruptions of the sources. When the views are considered
separately, this reduces to nonlinear Independent Component Analysis (ICA) for
which it is provably impossible to undo the mixing. We present novel
identifiability proofs that this is possible when the multiple views are
considered jointly, showing that the mixing can theoretically be undone using
function approximators such as deep neural networks. In contrast to known
identifiability results for nonlinear ICA, we prove that independent latent
sources with arbitrary mixing can be recovered as long as multiple,
sufficiently different noisy views are available
Generalized Canonical Correlation Analysis and Its Application to Blind Source Separation Based on a Dual-Linear Predictor Structure
Blind source separation (BSS) is one of the most important and established
research topics in signal processing and many algorithms have been proposed
based on different statistical properties of the source signals. For
second-order statistics (SOS) based methods, canonical correlation analysis
(CCA) has been proved to be an effective solution to the problem. In this work,
the CCA approach is generalized to accommodate the case with added white noise
and it is then applied to the BSS problem for noisy mixtures. In this approach,
the noise component is assumed to be spatially and temporally white, but the
variance information of noise is not required. An adaptive blind source
extraction algorithm is derived based on this idea and a further extension is
proposed by employing a dual-linear predictor structure for blind source
extraction (BSE).Comment: 7 pages and 5 figures. The main aim is to show the inherent
relationship between generalised canonical correlation analysis and the
dual-linear predictor approach presented in two separate conference papers
(references [15] and [16]
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