[Seminario] Multifractal analysis, Wavelet leaders, and Sparse SVM for biomedical applications - 27 Febbraio

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Lunedì 27 febbraio
Aula Riunioni Dipartimento Ingegneria dell'Informazione
(via Caruso 16, piano terra)

h. 9.00: From Fractal Features to Sparse Feature-selection based Classification: An Intrapartum Fetal Heart Rate Analysis (P. Abry, École Normale Supérieure de Lyon, France)

h. 10.00: On a Bayesian Framework for the Multifractal Analysis of Multivariate data (H. Wendt, Centre National de la Recherche Scientifique (CNRS), Toulouse, France)



École Normale Supérieure de Lyon (France)

From Fractal Features to Sparse Feature-selection based Classification: An Intrapartum Fetal Heart Rate Analysis



Fetal Heart Rate (FHR) monitoring is routinely used in clinical practice to help obstetricians assess fetal health status during delivery. However, early detection of fetal acidosis that allows relevant decisions for operative delivery remains a challenging task, receiving considerable attention. The present work renews FHR analysis and fetal acidosis detection in two ways. First, fractal based features are shown to constitute relevant tools for the assessment of cardiac variability, that significantly outperform and thus satisfactory replace other traditional assessment of cardiac variability such as LF/HF ratio, that relies either on the splitting into a-priori chosen frequency bands of the spectral constant of data, or on spectral and DFA based scaling exponents. Second, fetal acidosis detection is commonly formulated as a pH based classification problem. Our original proposition is to promote Sparse Support Vector Machine classification that permits to select a small number of relevant features as well as to achieve efficient fetal acidosis detection. Concepts and tools are illustrated at on a large (1288 subjects) and well documented database, collected at french public academic Hospital in Lyon. It is shown that the automatic selection of a sparse subset of features achieves satisfactory classification performance (sensitivity 0.73 and specificity 0.75, outperforming clinical practice). The subset of selected features receive simple interpretation in clinical practice. A second large database collected in Czech Republic is further used to show the generalization ability of both fractal features and Sparse Support Vector Machine classification.


Patrice Abry is « Research Director » for CNRS at Ecole Normale Supérieure de lyon, France, here he is in charge of the « Signal, System and Physics » statistical signal processing research group, within the Physics departement. He received the degree of Professeur-Agrégé de Sciences Physiques, in 1989, at Ecole Normale Supérieure de Cachan and the Ph. D. degree in physics and signal processing from the Claude-Bernard University, Lyon, France, in 1994.  Patrice Abry has developed a long standing research program dedicated to the statistical multiscale analysis for the modeling of scale-free phenomena, with strong interest in researches integrating theoretical and applied developments in real-world applications, ranging from hydrodynamic turbulence to Internet traffic, heart rate variability, or neurosciences. He is the author of a book on wavelet, scale invariance and hydrodynamic turbulence and is also the coeditor of a book entitled Scaling, Fractals and Wavelets.  Dr. Abry received the AFCET-MESR-CNRS prize for best Ph.D. in signal processing 1993–1994 and serves inn the IEEE SPS SPTM Committee since 2014. He is also an IEEE fellow since 2011.



Centre National de la Recherche Scientifique (CNRS), Toulouse, France

On a Bayesian Framework for the Multifractal Analysis of Multivariate data


Multifractal analysis is a widely used signal processing tool that enables the theoretical study of scale invariance models and their practical assessment via wavelet leaders. It has been successfully used in a large panel of applications of very different natures including finance, physics, Internet, geophysics, biology (heart rate variability, fMRI, ultrasound imaging,…). Despite such successes, the accurate estimation of multifractal parameters remains a challenging task since the intricate statistical nature of multifractal processes requires large sample sizes. For a range of applications, notably biomedical, the estimation performance can potentially be improved by taking advantage of the multivariate nature of data. Yet, this has barely been considered so far.
This work introduces a Bayesian framework that enables the accurate joint estimation of the multifractal parameters of multivariate data. It builds on a statistical model for the logarithm of wavelet leaders that comprises two key ingredients: i) a versatile semi-parametric Gaussian likelihood that is valid for a large class of multifractal processes; ii) a gamma Markov random field joint prior for the multifractal parameters of the components of multivariate data, that acts as a regularizer and counterbalances the statistical variability induced by small sample size. Numerical experiments conducted on synthetic multifractal processes as well as on real biomedical data illustrate the excellent performance of the approach.


Herwig Wendt received the Ms.C. degree in Signal Processing and Telecommunications from Vienna University of Technology (Vienna, Austria) in 2005. He received the Ph.D. degree in Signal Processing and Physics from Ecole Normale Superieure de Lyon (Lyon, France) in 2008. From November 2008 to December 2011, he was a Postdoctoral Research Associate with the Department of Mathematics and with the Geomathematical Imaging Group at Purdue University (West Lafayette, Indiana).
From October to December 2010, he was a research member of the MSRI research seminar "Inverse Problems and Applications" at MSRI (Berkeley, California). Since 2012, he is a CNRS researcher with the IRIT laboratory at University of Toulouse. His research is conducted within the Signal and Communications Group located at ENSEEIHT (Toulouse, France).
Since 2016, he is serving as an Associate Editor for Signal Processing (Elsevier).
His research interests have been focused on statistical signal and image processing, with a particular interest in multifractal analysis, scale invariance phenomena and multiresolution analysis and computation.



Computational Physiology & Biomedical Instruments Group, University of Pisa


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