Analysing ICA components by injecting noise

Usually, noise is considered to be destructive. We present a new method that constructively injects noise to assess the reliability and the group structure of empirical ICA components. Simulations show that the true root-mean squared angle distances between the real sources and some source estimates can be approximated by our method. In a toy experiment, we see that we are also able to reveal the underlying group structure of extracted ICA components. Furthermore, an experiment with fetal ECG data demonstrates that our approach is useful for exploratory data analysis of real-world data. 1

BioPhysConnectoR: Connecting Sequence Information and Biophysical Models

<p>Abstract</p> <p>Background</p> <p>One of the most challenging aspects of biomolecular systems is the understanding of the coevolution in and among the molecule(s).</p> <p>A complete, theoretical picture of the selective advantage, and thus a functional annotation, of (co-)mutations is still lacking. Using sequence-based and information theoretical inspired methods we can identify coevolving residues in proteins without understanding the underlying biophysical properties giving rise to such coevolutionary dynamics. Detailed (atomistic) simulations are prohibitively expensive. At the same time reduced molecular models are an efficient way to determine the reduced dynamics around the native state. The combination of sequence based approaches with such reduced models is therefore a promising approach to annotate evolutionary sequence changes.</p> <p>Results</p> <p>With the <monospace>R</monospace> package <monospace>BioPhysConnectoR</monospace> we provide a framework to connect the information theoretical domain of biomolecular sequences to biophysical properties of the encoded molecules - derived from reduced molecular models. To this end we have integrated several fragmented ideas into one single package ready to be used in connection with additional statistical routines in <monospace>R</monospace>. Additionally, the package leverages the power of modern multi-core architectures to reduce turn-around times in evolutionary and biomolecular design studies. Our package is a first step to achieve the above mentioned annotation of coevolution by reduced dynamics around the native state of proteins.</p> <p>Conclusions</p> <p><monospace>BioPhysConnectoR</monospace> is implemented as an <monospace>R</monospace> package and distributed under GPL 2 license. It allows for efficient and perfectly parallelized functional annotation of coevolution found at the sequence level.</p

Fast and accurate methods of independent component analysis: A survey

summary:This paper presents a survey of recent successful algorithms for blind separation of determined instantaneous linear mixtures of independent sources such as natural speech or biomedical signals. These algorithms rely either on non-Gaussianity, nonstationarity, spectral diversity, or on a combination of them. Performance of the algorithms will be demonstrated on separation of a linear instantaneous mixture of audio signals (music, speech) and on artifact removal in electroencephalogram (EEG)

Sur la diagonalisation conjointe approchée par un critère des moindres carrés

Nous présentons un nouvel algorithme de diagonalisation conjointe approchée d'un ensemble de matrices. Utilisant le critère des moindres carrés, sans contrainte d'orthogonalité, il est comparé à un algorithme analogue pour la séparation de sources. Le critère de notre algorithme porte sur la matrice de séparation alors que l'autre porte sur la matrice de mélange. Ceci améliore de façon significative la vitesse de convergence avec de meilleures performances

A BRUTE-FORCE ANALYTICAL FORMULATION OF THE INDEPENDENT COMPONENTS ANALYSIS SOLUTION

ABSTRACT Many algorithms based on information theoretic measures and/or temporal statistics of the signals have been proposed for ICA in the literature. There have also been analytical solutions suggested based on predictive modeling of the signals. In this paper, we show that finding an analytical solution for the ICA problem through solving a system of nonlinear equations is possible. We demonstrate that this solution is robust to decreasing sample size and measurement SNR. Nevertheless, finding the root of the nonlinear function proves to be a challenge. Besides the analytical solution approach, we try finding the solution using a least squares approach with the derived analytical equations. Monte Carlo simulations using the least squares approach are performed to investigate the effect of sample size and measurement noise on the performance