CHESS

Two talks will be presented :

Alexandre AKSENOV
Title. Introduction to strongly b-multiplicative sequences and rarefaction.

Abstract. The class of "strongly b-multiplicative sequences" is the class of numerical sequences which are closest to the classical Thue-Morse sequence. This sequence was defined at first as a source of examples of "counter-intuitive objects", i.e. in theoretical computer science. Today, these objects can be called "transcendental", "chaotic" or "fractal".

In this talk we will see how they objects can be linked to a (seemingly) different domain: Number Theory.

The talk is planned as popular, and the quantity of technical details is intended to be reasonnable.

Marco CONGEDO
Title. Power Means and Mean Fields in the Riemannian Manifold of Symmetric Positive Matrices"

Abstract. Averaging is possibly the most common and most important operation in statistics and signal processing. This talk is concerned about recent advances in averaging of symmetric positive-definite (SPD) matrices.
In brain-computer interfaces we have introduced the use of the geometric mean on the Riemannian manifold of SDP matrices and we have found that a simple minimum distance to mean classifier outperforms state-of-the-art classifiers. The power means of SPD matrices with exponent p in the interval [-1, 1] interpolate continuously in between the Harmonic (p = -1) and the Arithmetic mean (p = 1), while the geometric mean corresponds to their limit evaluated at p -> 0. In this talk we present a new fixed point algorithm for estimating means along the interval [-1, 1]\{0}. The convergence rate of the proposed algorithm for p = ±0.5 does not deteriorate with the number or dimension of matrices given as input, which is very useful in practical applications. Along the whole interval it is also robust with respect to the dispersion of the points on the manifold (i.e., noise). Thus, the proposed algorithm allows the efficient estimation of the whole family of power means, including the geometric mean. Finally, we will introduce the concept of Mean Fields, a sampling of mean in the interval [-1, 1], with application in Riemannian signal classification and detection.

Content of the meeting
- Scientific talk
- Informations
- Presentation of newcomers (Victor, Alexandre, Saeed and Elsa)
- Drink with the traditional king pie (at about 2:45 pm)

Please register on the Doodle http://doodle.com/poll/87epukqybqt3vvn5 for evaluating of the number of pies to purchase !

There will be a unique talk, presented by Victor Maurandi, a new post-doc in CHESS/ViBS.

Title: ALGORITHMS FOR NON-UNITARY JOINT DIAGONALIZATION OF TENSORS. APPLICATION TO MIMO SOURCE SEPARATION IN DIGITAL TELECOMMUNICATIONS

Abstract:
This work develops joint diagonalization of matrices and third-order tensors methods for MIMO source separation in the field of digital telecommunications. After a state of the art, the motivations and the objectives are presented. Then the joint diagonalization and the blind source separation issues are defined and a link between both fields is established. Thereafter, five Jacobi-like iterative algorithms based on an LU parameterization are developed. For each of them, we propose to derive the diagonalization matrix by optimizing an inverse criterion. Two ways are investigated: minimizing the criterion in a direct way or assuming that we are close to a diagonalizing the elements from the considered set are almost diagonal. Regarding the parameters derivation, two strategies are implemented: one consists in estimating each parameter independently, the other consists in the independent derivation of couple of well-chosen parameters. Hence, we propose three algorithms for the joint diagonalization of symmetric complex matrices or hermitian ones. The first one relies on searching for the roots of the criterion derivative, the second one relies on a minor eigenvector research and the last one relies on a gradient descent method enhanced by computation of the optimal adaptation step. In the framework of joint diagonalization of symmetric, INDSCAL or non symmetric third-order tensors, we have developed two algorithms. For each of them, the parameters derivation is done by computing the roots of the considered criterion derivative. We also show the link between the joint diagonalization of a third-order tensor set and the canonical polyadic decomposition of a fourth-order tensor. We confront both methods through numerical simulations. The good behavior of the proposed algorithms is illustrated by means of computing simulations. Finally, they are applied to the source separation of digital telecommunication signals. The sets to diagonalize are built using high-order statistics computed from observation signals.

Paolo Zanini: Source separation for urban planning application

"A problem of urban planning application through mobile-phone traffic data in the metropolitan area of Milan, Italy, is considered. The aim is to retrieve meaningful information regarding working, residential, and mobility activities around the city. The independent component analysis (ICA) framework is used to model underlying spatial activities as independent spatial sources on a lattice. To incorporate spatial dependence within the spatial sources, a spatial colored ICA (scICA) method is developed. The method models spatial dependence within each source in the frequency domain, exploiting the power of Whittle likelihood and local linear log-spectral density estimation. An iterative algorithm is derived to estimate the model parameters through maximum Whittle likelihood."

Pierre Narvor: udiovisual Speech Source Separation: Integration of video informations in an IVA algorithm+

Abstract: In this presentation, we shall propose a way to integrate video informations about lip movements in an IVA algorithm used for separate or extract speech signals from a convolutive mixture in a reverberant environment. We want to exploit lip movements to estimate the variations of power of the speech signal which we believe can be a very strong help for separation or extraction using IVA.

Dr. B. Afsari (John Hopkins Univ.), invited scientist in the CHESS project, will present two talks on Riemannian Geometry, on Tuesday 3 Nov, from 10:00 to 12:30. The talks are followed by a buffet. Don't forget to register to the talks and the buffet, since the number of places is limited

Saloua Chlaily: Interaction of modalities

By using several modalities we aim at enhancing the quality and accuracy of the observed signal. However, the expected improvement is not always obtained. In this talk, we consider a simple model of two modalities and analyze their pertinence and interrelations, in term of mutual information, to understand what can deteriorate the estimation of the target signal.

Rafael Ando: Nonlinear blind source separation for chemical sensor arrays based on a polynomial approximation

In this presentation we shall describe how the BSS problem applies to measuring the concentration of ions in a solution using chemical sensors arrays and present a polynomial-based algorithm for solving it. The algorithm is a generalized extension of a previously presented algorithm that used a second-order degree polynomial, which was able to successfully separate the sources under some specific hypotheses and showed good results.

*Abstract: *
Technological development aims at monitoring during pregnancy using the noninvasive fetal electrocardiogram (ECG). This method allows not only to detect fetal heart rate, but also to analyze the morphology of fetal ECG, which is now limited to analysis of the invasive ECG during delivery. However, the noninvasive fetal ECG recorded from the mother’s abdomen is contaminated with several noise sources among which the maternal ECG is the most prominent. That is why this problem is still a challenge in the research which is handled by uni-modal approaches, up to now. In the present study, the problem of noninvasive fetal ECG extraction is tackled using multi-modality. In the multi-modal concept, beside ECG signal, this approach benefits from the phonocardiogram (PCG) signal as another signal modality, which can provide complementary information about the fetal ECG. A general method for quasi-periodic signal analysis and modeling is described, and its application to ECG denoising and fetal ECG extraction is explained. Multi-modality is based on the Gaussian process modeling, in this study, in order to provide the possibility of flexible models and nonlinear estimations.

COMMITTY MEMBERS:
M. Christian Jutten, Professeur, Université Joseph Fourier
M. Mohammad Bagher Shamsollahi, Professeur, Université de technologie de Sharif
M. Philippe Ravier, Maître de conférences, Université d’Orléans
M. Reza Sameni, Maître de conférences, Université de Shiraz
M. Pierre-Yves Guméry, Professeur, Université Joseph Fourier
M. Bertrand Rivet, Maître de conférences, Grenoble INP
Mme. Véronique Equy, Gynécologue-Obstétricien, CHU de Grenoble