Results 1  10
of
336
Optimization algorithms exploiting unitary constraints
 IEEE Trans. Signal Processing
, 2002
"... Abstract—This paper presents novel algorithms that iteratively converge to a local minimum of a realvalued function ( ) subject to the constraint that the columns of the complexvalued matrix are mutually orthogonal and have unit norm. The algorithms are derived by reformulating the constrained ..."
Abstract

Cited by 103 (13 self)
 Add to MetaCart
(Show Context)
Abstract—This paper presents novel algorithms that iteratively converge to a local minimum of a realvalued function ( ) subject to the constraint that the columns of the complexvalued matrix are mutually orthogonal and have unit norm. The algorithms are derived by reformulating the constrained optimization problem as an unconstrained one on a suitable manifold. This significantly reduces the dimensionality of the optimization problem. Pertinent features of the proposed framework are illustrated by using the framework to derive an algorithm for computing the eigenvector associated with either the largest or the smallest eigenvalue of a Hermitian matrix. Index Terms—Constrained optimization, eigenvalue problems, optimization on manifolds, orthogonal constraints. I.
Joint Approximate Diagonalization Of Positive Definite Hermitian Matrices
"... This paper provides an iterative algorithm to jointly approximately diagonalize K Hermitian positive definite matrices Γ_1, ..., Γ_K . Specifically it calculates the matrix B which minimizes the criterion P K k=1 n k [log det diag(BC k B ) log det(BC k B )], n k being positive ..."
Abstract

Cited by 80 (11 self)
 Add to MetaCart
(Show Context)
This paper provides an iterative algorithm to jointly approximately diagonalize K Hermitian positive definite matrices &Gamma;_1, ..., &Gamma;_K . Specifically it calculates the matrix B which minimizes the criterion P K k=1 n k [log det diag(BC k B ) log det(BC k B )], n k being positive numbers, which is a measure of the deviation from diagonality of the matrices BC_k B*. The convergence of the algorithm is discussed and some numerical experiments are performed showing the good performance of the algorithm.
Singletrial analysis and classification of ERP components  a tutorial
, 2010
"... Analyzing brain states that correspond to event related potentials (ERPs) on a single trial basis is a hard problem due to the high trialtotrial variability and the unfavorable ratio between signal (ERP) and noise (artifacts and neural background activity). In this tutorial, we provide a comprehen ..."
Abstract

Cited by 74 (13 self)
 Add to MetaCart
Analyzing brain states that correspond to event related potentials (ERPs) on a single trial basis is a hard problem due to the high trialtotrial variability and the unfavorable ratio between signal (ERP) and noise (artifacts and neural background activity). In this tutorial, we provide a comprehensive framework for decoding ERPs, elaborating on linear concepts, namely spatiotemporal patterns and filters as well as linear ERP classification. However, the bottleneck of these techniques is that they require an accurate covariance matrix estimation in high dimensional sensor spaces which is a highly intricate problem. As a remedy, we propose to use shrinkage estimators and show that appropriate regularization of linear discriminant analysis (LDA) by shrinkage yields excellent results for singletrial ERP classification that are far superior to classical LDA classification. Furthermore, we give practical hints on the interpretation of what classifiers learned from the data and demonstrate in particular that the tradeoff between goodnessoffit and model complexity in regularized LDA relates to a morphing between a difference pattern of ERPs and a spatial filter which cancels non taskrelated brain activity.
Separation of Nonnegative Mixture of Nonnegative Sources using a Bayesian Approach and MCMC Sampling
, 2004
"... This paper considers the problem of blind source separation in the case where both the source signals and the mixing coefficients are nonnegatives. The problem is referred to as nonnegative source separation and the analysis is achieved in a Bayesian framework by taking the nonnegativity of sourc ..."
Abstract

Cited by 65 (20 self)
 Add to MetaCart
This paper considers the problem of blind source separation in the case where both the source signals and the mixing coefficients are nonnegatives. The problem is referred to as nonnegative source separation and the analysis is achieved in a Bayesian framework by taking the nonnegativity of source signals and mixing coefficients as prior information. Since the main application concerns the analysis of spectral signals, to encode jointly nonnegativity, sparsity and possible background in the sources, Gamma densities are used as priors. The source signals and the mixing coefficients are estimated by implementing a Monte Carlo Markov Chain (MCMC) for sampling their joint posterior density. Synthetic and experimental results motivate the problem of nonnegative source separation and illustrate the effectiveness of the proposed method.
Automatic removal of eye movement and blink artifacts from EEG data using blind component separation." Psychophysiology 41(2
, 2004
"... Abstract Signals from eye movements and blinks can be orders of magnitude larger than braingenerated electrical potentials and are one of the main sources of artifacts in electroencephalographic (EEG) data. Rejecting contaminated trials causes substantial data loss, and restricting eye movements/b ..."
Abstract

Cited by 64 (2 self)
 Add to MetaCart
(Show Context)
Abstract Signals from eye movements and blinks can be orders of magnitude larger than braingenerated electrical potentials and are one of the main sources of artifacts in electroencephalographic (EEG) data. Rejecting contaminated trials causes substantial data loss, and restricting eye movements/blinks limits the experimental designs possible and may impact the cognitive processes under investigation. This article presents a method based on blind source separation (BSS) for automatic removal of electroocular artifacts from EEG data. BBS is a signalprocessing methodology that includes independent component analysis (ICA). In contrast to previously explored ICAbased methods for artifact removal, this method is automated. Moreover, the BSS algorithm described herein can isolate correlated electroocular components with a high degree of accuracy. Although the focus is on eliminating ocular artifacts in EEG data, the approach can be extended to other sources of EEG contamination such as cardiac signals, environmental noise, and electrode drift, and adapted for use with magnetoencephalographic (MEG) data, a magnetic correlate of EEG.
Kernel methods for measuring independence
 Journal of Machine Learning Research
, 2005
"... We introduce two new functionals, the constrained covariance and the kernel mutual information, to measure the degree of independence of random variables. These quantities are both based on the covariance between functions of the random variables in reproducing kernel Hilbert spaces (RKHSs). We prov ..."
Abstract

Cited by 59 (19 self)
 Add to MetaCart
(Show Context)
We introduce two new functionals, the constrained covariance and the kernel mutual information, to measure the degree of independence of random variables. These quantities are both based on the covariance between functions of the random variables in reproducing kernel Hilbert spaces (RKHSs). We prove that when the RKHSs are universal, both functionals are zero if and only if the random variables are pairwise independent. We also show that the kernel mutual information is an upper bound near independence on the Parzen window estimate of the mutual information. Analogous results apply for two correlationbased dependence functionals introduced earlier: we show the kernel canonical correlation and the kernel generalised variance to be independence measures for universal kernels, and prove the latter to be an upper bound on the mutual information near independence. The performance of the kernel dependence functionals in measuring independence is verified in the context of independent component analysis.
Computation of the canonical decomposition by means of a simultaneous generalized schur decomposition
 SIAM J. Matrix Anal. Appl
, 2004
"... Abstract. The canonical decomposition of higherorder tensors is a key tool in multilinear algebra. First we review the state of the art. Then we show that, under certain conditions, the problem can be rephrased as the simultaneous diagonalization, by equivalence or congruence, of a set of matrices. ..."
Abstract

Cited by 55 (10 self)
 Add to MetaCart
(Show Context)
Abstract. The canonical decomposition of higherorder tensors is a key tool in multilinear algebra. First we review the state of the art. Then we show that, under certain conditions, the problem can be rephrased as the simultaneous diagonalization, by equivalence or congruence, of a set of matrices. Necessary and sufficient conditions for the uniqueness of these simultaneous matrix decompositions are derived. In a next step, the problem can be translated into a simultaneous generalized Schur decomposition, with orthogonal unknowns [A.J. van der Veen and A. Paulraj, IEEE Trans. Signal Process., 44 (1996), pp. 1136–1155]. A firstorder perturbation analysis of the simultaneous generalized Schur decomposition is carried out. We discuss some computational techniques (including a new Jacobi algorithm) and illustrate their behavior by means of a number of numerical experiments.
Blind Source Separation and Deconvolution: The Dynamic Component Analysis Algorithm
 Neural Computation
, 1998
"... We derive a novel family of unsupervised learning algorithms for blind separation of mixed and convolved sources. Our approach is based on formulating the separation problem as a learning task of a spatiotemporal generative model, whose parameters are adapted iteratively to minimize suitable error ..."
Abstract

Cited by 55 (7 self)
 Add to MetaCart
We derive a novel family of unsupervised learning algorithms for blind separation of mixed and convolved sources. Our approach is based on formulating the separation problem as a learning task of a spatiotemporal generative model, whose parameters are adapted iteratively to minimize suitable error functions, thus ensuring stability of the algorithms. The resulting learning rules achieve separation by exploiting highorder spatiotemporal statistics of the mixture data. Different rules are obtained by learning generative models in the frequency and time domains, whereas a hybrid frequency/time model leads to the best performance. These algorithms generalize independent component analysis to the case of convolutive mixtures and exhibit superior performance on instantaneous mixtures. An extension of the relativegradient concept to the spatiotemporal case leads to fast and efficient learning rules with equivariant properties. Our approach can incorporate information about the mixing sit...
Mutual Information Approach to Blind Separation of Stationary Sources
 IEEE Transactions on Information Theory
, 1999
"... This paper presents an unified approach to the problem of separation of sources, based on the consideration of mutual information. The basic setup is that the sources are independent stationary random processes which are mixed either instantaneously or through a convolution, to produce the observed ..."
Abstract

Cited by 44 (8 self)
 Add to MetaCart
(Show Context)
This paper presents an unified approach to the problem of separation of sources, based on the consideration of mutual information. The basic setup is that the sources are independent stationary random processes which are mixed either instantaneously or through a convolution, to produce the observed records. We define the entropy of stationary processes and then the mutual information between them as a measure of their independence. This provides us with a contrast for the separation of source problem. For practical implementation, we introduce several degraded forms of this contrast, which can be computed from a finite dimensional distribution of the reconstructed source processes only. From them, we derive several sets of estimating equations generalising those considered earlier. 1 Introduction Blind separation of sources is a topic which have received much attention recently, as it has many important applications (speech analysis, radar, sonar, : : : ). Basically, one observes seve...
A SURVEY OF CONVOLUTIVE BLIND SOURCE SEPARATION METHODS
 SPRINGER HANDBOOK ON SPEECH PROCESSING AND SPEECH COMMUNICATION
"... In this chapter, we provide an overview of existing algorithms for blind source separation of convolutive audio mixtures. We provide a taxonomy, wherein many of the existing algorithms can be organized, and we present published results from those algorithms that have been applied to realworld audio ..."
Abstract

Cited by 39 (0 self)
 Add to MetaCart
In this chapter, we provide an overview of existing algorithms for blind source separation of convolutive audio mixtures. We provide a taxonomy, wherein many of the existing algorithms can be organized, and we present published results from those algorithms that have been applied to realworld audio separation tasks.