Jordan Frecon

Intrapartum fetal heart rate classification from trajectory in Sparse SVM feature space.

Intrapartum fetal heart rate (FHR) constitutes a prominent source of information for the assessment of fetal reactions to stress events during delivery. Yet, early detection of fetal acidosis remains a challenging signal processing task. The originality of the present contribution are three-fold: multiscale representations and wavelet leader based multifractal analysis are used to quantify FHR variability ; Supervised classification is achieved by means of Sparse-SVM that aim jointly to achieve optimal detection performance and to select relevant features in a multivariate setting ; Trajectories in the feature space accounting for the evolution along time of features while labor progresses are involved in the construction of indices quantifying fetal health. The classification performance permitted by this combination of tools are quantified on a intrapartum FHR large database (≃ 1250 subjects) collected at a French academic public hospital.

Non-Linear Wavelet Regression and Branch & Bound Optimization for the Full Identification of Bivariate Operator Fractional Brownian Motion

Self-similarity is widely considered the reference framework for modeling the scaling properties of real-world data. However, most theoretical studies and their practical use have remained univariate. Operator fractional Brownian motion (OfBm) was recently proposed as a multivariate model for self-similarity. Yet, it has remained seldom used in applications because of serious issues that appear in the joint estimation of its numerous parameters. While the univariate fractional Brownian motion requires the estimation of two parameters only, its mere bivariate extension already involves seven parameters that are very different in nature. The present contribution proposes a method for the full identification of bivariate OfBm (i.e., the joint estimation of all parameters) through an original formulation as a non-linear wavelet regression coupled with a custom-made Branch & Bound numerical scheme. The estimation performance (consistency and asymptotic normality) is mathematically established and numerically assessed by means of Monte Carlo experiments. The impact of the parameters defining OfBm on the estimation performance as well as the associated computational costs are also thoroughly investigated.

On-The-Fly Approximation of Multivariate Total Variation Minimization

In the context of change-point detection, addressed by Total Variation minimization strategies, an efficient on-the-fly algorithm has been designed leading to exact solutions for univariate data. In this contribution, an extension of such an on-the-fly strategy to multivariate data is investigated. The proposed algorithm relies on the local validation of the Karush-Kuhn-Tucker conditions on the dual problem. Showing that the non-local nature of the multivariate setting precludes to obtain an exact on-the-fly solution, we devise an on-the-fly algorithm delivering an approximate solution, whose quality is controlled by a practitioner-tunable parameter, acting as a trade-off between quality and computational cost. Performance assessment shows that high quality solutions are obtained on-the-fly while benefiting of computational costs several orders of magnitude lower than standard iterative procedures. The proposed algorithm thus provides practitioners with an efficient multivariate change-point detection on-the-fly procedure.

p-leader Multifractal Analysis and Sparse SVM for Intrapartum Fetal Acidosis Detection

Interpretation and analysis of intrapartum fetal heart rate, enabling early detection of fetal acidosis, remains a challenging signal processing task. Among the many strategies that were used to tackle this problem, scale-invariance and multifractal analysis stand out. Recently, a new and promising variant of multifractal analysis, based on p-leaders, has been proposed. In this contribution, we use sparse support vector machines applied to p-leader multifractal features with a double aim: Assessment of the features actually contributing to classification; Assessment of the contribution of non linear features (as opposed to linear ones) to classification performance. We observe and interpret that the classification rate improves when small values of the tunable parameter p are used.

Bayesian-driven criterion to automatically select the regularization parameter in the ℓ 1 -Potts model

This contribution focuses, within the ℓ1-Potts model, on the automated estimation of the regularization parameter balancing the ℓ1 data fidelity term and the TVℓ0 penalization. Variational approaches based on total variation gained considerable interest to solve piecewise constant denoising problems thanks to their deterministic setting and low computational cost. However, the quality of the achieved solution strongly depends on the tuning of the regularization parameter. While recent works have tailored various hierarchical Bayesian procedures to additionally estimate the regularization parameter for Gaussian noise, less attention has been granted to Laplacian noise, of interested in numerous applications. This contribution promotes a fast and parameter-free denoising procedure for piecewise constant signals corrupted by Laplacian noise, that includes automated selection of the regularization parameter. It relies on the minimization of a Bayesian-driven criterion whose similarities with the ℓ1-Potts model permit to derive a computationally efficient algorithm.

Non-linear regression for bivariate self-similarity identification — application to anomaly detection in Internet traffic based on a joint scaling analysis of packet and byte counts

Internet traffic monitoring is a crucial task for network security. Self-similarity, a key property for a relevant description of internet traffic statistics, has already been massively and successfully involved in anomaly detection. Self-similar analysis was however so far applied either to byte or Packet count time series independently, while both signals are jointly collected and technically deeply related. The present contribution elaborates on a recently proposed multivariate self-similar model, Operator fractional Brownian Motion (OfBm), to analyze jointly self-similarity in bytes and packets. A non-linear regression procedure, based on an original Branch & Bound resolution procedure, is devised for the full identification of bivariate OfBm. The estimation performance is assessed by means of Monte Carlo simulations. Further, an Internet traffic anomaly detection procedure is proposed, that makes use of the vector of Hurst exponents underlying the OfBm based Internet data modeling. Applied to a large set of high quality and modern Internet data from the MAWI repository, proof-of-concept results in anomaly detection are detailed and discussed.

Bayesian Selection for the

Piecewise constant denoising can be solved either by deterministic optimization approaches, based on the Potts model, or by stochastic Bayesian procedures. The former lead to low computational time but require the selection of a regularization parameter, whose value significantly impacts the achieved solution, and whose automated selection remains an involved and challenging problem. Conversely, fully Bayesian formalisms encapsulate the regularization parameter selection into hierarchical models, at the price of high computational costs. This contribution proposes an operational strategy that combines hierarchical Bayesian and Potts model formulations, with the double aim of automatically tuning the regularization parameter and maintaining computational efficiency. The proposed procedure relies on formally connecting a Bayesian framework to a

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-Potts Model Regularization Parameter: 1-D Piecewise Constant Signal Denoising

-Potts functional. Behaviors and performance for the proposed piecewise constant denoising and regularization parameter tuning techniques are studied qualitatively and assessed quantitatively, and shown to compare favorably against those of a fully Bayesian hierarchical procedure, both in accuracy and computational load.

Multifractal-based texture segmentation using variational procedure

The present contribution aims at segmenting a scale-free texture into different regions, characterized by an a priori (unknown) multifractal spectrum. The multifractal properties are quantified using multiscale quantities C_{1, j} and C_{2, j} that quantify the evolution along the analysis scales 2^j of the empirical mean and variance of a nonlinear transform of wavelet coefficients. The segmentation is performed jointly across all the scales j on the concatenation of both C_{1, j} and C_{2, j} by an efficient vectorial extension of a convex relaxation of the piecewise constant Potts segmentation problem. We provide comparisons with the scalar segmentation of the Hölder exponent as well as independent vectorial segmentations over C₁ and C₂.