Publications HAL de Pierrick, Legrand

2023

Journal articles

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Eric Grivel, Jeremie Soetens, Gaetan Colin, Pierrick Legrand. Combining the global trends of DFA or CDFA of different orders. Digital Signal Processing, 2023. ⟨hal-03920420⟩
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2022

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Tara Vanhatalo, Pierrick Legrand, Myriam Desainte-Catherine, Pierre Hanna, Antoine Brusco, et al.. A Review of Neural Network-Based Emulation of Guitar Amplifiers. Applied Sciences, 2022, 12 (12), pp.5894. ⟨10.3390/app12125894⟩. ⟨hal-03881859⟩
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Vacuum tube amplifiers present sonic characteristics frequently coveted by musicians, that are often due to the distinct nonlinearities of their circuits, and accurately modelling such effects can be a challenging task. A recent rise in machine learning methods has lead to the ubiquity of neural networks in all fields of study including virtual analog modelling. This has lead to the appearance of a variety of architectures tailored to this task. This article aims to provide an overview of the current state of the research in neural emulation of analog distortion circuits by first presenting preceding methods in the field and then focusing on a complete review of the deep learning landscape that has appeared in recent years, detailing each subclass of available architectures. This is done in order to bring to light future possible avenues of work in this field.
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Alexis Saadoun, Antoine Schein, Vincent Péan, Pierrick Legrand, Ludwig Serge Aho Glélé, et al.. Frequency Fitting Optimization Using Evolutionary Algorithm in Cochlear Implant Users with Bimodal Binaural Hearing. Brain Sciences, 2022, 12 (2), pp.253. ⟨10.3390/brainsci12020253⟩. ⟨hal-03610651⟩
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Optimizing hearing in patients with a unilateral cochlear implant (CI) and contralateral acoustic hearing is a challenge. Evolutionary algorithms (EA) can explore a large set of potential solutions in a stochastic manner to approach the optimum of a minimization problem. The objective of this study was to develop and evaluate an EA-based protocol to modify the default frequency settings of a MAP (fMAP) of the CI in patients with bimodal hearing. Methods: This monocentric prospective study included 27 adult CI users (with post-lingual deafness and contralateral functional hearing). A fitting program based on EA was developed to approach the best fMAP. Generated fMAPs were tested by speech recognition (word recognition score, WRS) in noise and free-field-like conditions. By combining these first fMAPs and adding some random changes, a total of 13 fMAPs over 3 generations were produced. Participants were evaluated before and 45 to 60 days after the fitting by WRS in noise and questionnaires on global sound quality and music perception in bimodal binaural conditions. Results: WRS in noise improved with the EA-based fitting in comparison to the default fMAP (41.67 ± 9.70% versus 64.63 ± 16.34%, respectively, p = 0.0001, signed-rank test). The global sound quality and music perception were also improved, as judged by ratings on questionnaires and scales. Finally, most patients chose to keep the new fitting definitively. Conclusions: By modifying the default fMAPs, the EA improved the speech discrimination in noise and the sound quality in bimodal binaural conditions.
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Conference papers

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Tara Vanhatalo, Pierrick Legrand, Myriam Desainte-Catherine, Pierre Hanna, Antoine Brusco, et al.. Neural Network-based Virtual Analog Modelling. Artificial Evolution 2022, Oct 2022, Exeter, United Kingdom. ⟨hal-03852692⟩
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2021

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Eric Grivel, Bastien Berthelot, Pierrick Legrand, Audrey Giremus. DFA-based abacuses providing the Hurst exponent estimate for short-memory processes. Digital Signal Processing, 2021, 116, ⟨10.1016/j.dsp.2021.103102⟩. ⟨hal-03225784⟩
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The detrended fluctuation analysis (DFA) and its higher-order variant make it possible to estimate the Hurst exponent and therefore to quantify the long-range dependence of a random process. These methods are popular and used in a wide range of applications where they have been proven to be discriminative to characterize or classify processes. Nevertheless, in practice, the signal may be short-memory. In addition, depending on the number of samples available, there is no guarantee that these methods provide the true value of the Hurst exponent, leading the user to draw erroneous conclusions on the long-range dependence of the signal under study. In this paper, using a matrix formulation and making no approximation, we first propose to analyze how the DFA and its higher-order variant behave with respect to the number of samples available. Illustrations dealing with short-memory data that can be modeled by a white noise, a moving-average process and a random process whose autocorrelation function exponentially decays are given. Finally, to avoid any wrong conclusions, we propose to derive abacuses linking the value provided by the DFA or its variant with the properties of the signal and the number of samples available.
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Bastien Berthelot, Eric Grivel, Pierrick Legrand, Audrey Giremus. Definition of the fluctuation function in the detrendred fluctuation analysis and its variant. The European Physical Journal B: Condensed Matter and Complex Systems, 2021, 94, ⟨10.1140/epjb/s10051-021-00231-7⟩. ⟨hal-03409799⟩
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The detrended fluctuation analysis (DFA) and its variants are popular methods to analyze the self-similarity of a signal. Two steps characterize them: firstly, the trend of the centered integrated signal is estimated and removed. Secondly, the properties of the so-called fluctuation function which is an approximation of the standard deviation of the resulting process is analyzed. However, it appears that the statistical mean was assumed to be equal to zero to obtain it. As there is no guarantee that this assumption is true a priori, this hypothesis is debatable. The purpose of this paper is to propose two alternative definitions of the fluctuation function. Then, we compare all of them based on a matrix formulation and the filter-based interpretation we recently proposed. This analysis will be useful to show that the approach proposed in the original paper remains a good compromise in terms of accuracy and computational cost.
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Eric Grivel, Bastien Berthelot, Pierrick Legrand. A matrix approach to get the variance of the square of the fluctuation function of the DFA. Digital Signal Processing, 2021, ⟨10.1016/j.dsp.2021.103346⟩. ⟨hal-03456525⟩
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The fluctuation analysis (FA) and the detrended fluctuation analysis (DFA) make it possible to estimate the Hurst exponent H, which characterizes the self-similarity of a signal. Both are based on the fact that the so-called fluctuation function, which can be seen as an approximation of the standard deviation of the process scaled in time by multiplying the time variable by a positive constant, depends on H. The main novelty of the paper is to provide the expression of the variance of the square of the fluctuation function, by using a matrix formulation. We show that it depends on the correlation function of the signal under study when it is zero-mean and Gaussian. Illustrations are given when dealing with a zero-mean white Gaussian noise. Moving average processes and first-order autoregressive processes are also addressed.
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Conference papers

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Bastien Berthelot, Eric Grivel, Pierrick Legrand. New variants of DFA based on loess and lowess methods: generalization of the detrending moving average. ICASSP 2021 - IEEE International Conference on Acoustics, Speech and Signal Processing, Jun 2021, Totonto, Canada. ⟨hal-03125981⟩
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2020

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Emigdio Z-Flores, Leonardo Trujillo, Pierrick Legrand, Frédérique Faïta-Aïnseba. EEG Feature Extraction Using Genetic Programming for the Classification of Mental States. Algorithms, 2020, 13 (9), pp.221. ⟨10.3390/a13090221⟩. ⟨hal-02943474⟩
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The design of efficient electroencephalogram (EEG) classification systems for the detectionof mental states is still an open problem. Such systems can be used to provide assistance to humansin tasks where a certain level of alertness is required, like in surgery or in the operation of heavymachines, among others. In this work, we extend a previous study where a classification system isproposed using a Common Spatial Pattern (CSP) and Linear Discriminant Analysis (LDA) for theclassification of two mental states, namely a relaxed and a normal state. Here, we propose an enhancedfeature extraction algorithm (Augmented Feature Extraction with Genetic Programming, or+FEGP)that improves upon previous results by employing a Genetic-Programming-based methodologyon top of the CSP. The proposed algorithm searches for non-linear transformations that build newfeatures and simplify the classification task. Although the proposed algorithm can be coupled withany classifier, LDA achieves 78.8% accuracy, the best predictive accuracy among tested classifiers,significantly improving upon previously published results on the same real-world dataset.
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Leonardo Trujillo, Uriel Lopez, Pierrick Legrand. SOAP: Semantic Outliers Automatic Preprocessing. Information Sciences, 2020, 526 (81-101), pp.20. ⟨10.1016/j.ins.2020.03.071⟩. ⟨hal-02551161⟩
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Genetic Programming (GP) is an evolutionary algorithm for the automatic generation of symbolic models expressed as syntax trees. GP has been successfully applied in many domain, but most research in this area has not considered the presence of outliers in the training set. Outliers make supervised learning problems difficult, and sometimes impossible, to solve. For instance, robust regression methods cannot handle more than 50% of outlier contamination, referred to as their breakdown point. This paper studies problems where outlier contamination is high, reaching up to 90% contamination levels, extreme cases that can appear in some domains. This work shows, for the first time, that a random population of GP individuals can detect outliers in the output variable. From this property, a new filtering algorithm is proposed called Semantic Outlier Automatic Preprocessing (SOAP), which can be used with any learning algorithm to differentiate between inliers and outliers. Since the method uses a GP population, the algorithm can be carried out for free in a GP symbolic regression system. The approach is the only method that can perform such an automatic cleaning of a dataset without incurring an exponential cost as the percentage of outliers in the dataset increases.
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Mahdi Saleh, Samir-Mohamad Omar, Eric Grivel, Pierrick Legrand. A Variable Chirp Rate Stepped Frequency Linear Frequency Modulation Waveform Designed to Approximate Wideband Non-Linear Radar Waveforms. Digital Signal Processing, 2020, ⟨10.1016/j.dsp.2020.102884⟩. ⟨hal-02963775⟩
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The non-linear frequency modulation (NLFM) waveform is one of the existing waveforms that can be used in high range resolution radar applications. However, a high sampling frequency and consequently an expensive ADC are required. To overcome this drawback while taking advantage of the features of the NLFM waveform, we suggest approximating the wideband NLFM waveform by a piecewise linear waveform and using it in a stepped frequency (SF) framework. Thus, a variable chirp rate SF-LFM waveform is proposed where SF is combined with a train of LFM pulses having different chirp rates, durations, and bandwidths. In this paper, these parameters are derived from a tangent-based NLFM waveform. At the receiver, a generalized version of the time domain (TD) algorithm is proposed to process the received echoes. Our purpose is to obtain the high range resolution profile (HRRP) whose properties are of the same magnitude orders as those obtained using a tangent-based NLFM waveform. These properties are the peak sidelobe ratio, the integrated sidelobe, and the range resolution. Toward this goal, a multi-objective optimization issue is addressed to deduce the parameters of the proposed waveform by using two types of approaches based on evolutionary algorithms. Their relevance is compared. Our analysis and simulations show that the proposed approaches attain the targeted performance goals with a smaller sampling frequency at the receiver.
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Bastien Berthelot, Eric Grivel, Pierrick Legrand, Jean-Marc André, Patrick Mazoyer. Alternative Ways to Compare the Detendred Fluctuation Analysis and its Variants. Application to Visual Tunneling Detection. Digital Signal Processing, 2020, ⟨10.1016/j.dsp.2020.102865⟩. ⟨hal-02940122⟩
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The detrended fluctuation analysis (DFA) and its variants such as the detrended moving average (DMA) are widely used to estimate the Hurst exponent. These methods are very popular as they do not require advanced skills in the field of signal processing and statistics while providing accurate results. As a consequence, a great deal of interest has been paid to compare them and to better understand their behaviors from a mathematical point of view. In this paper, our contribution is threefold. Firstly, we propose another variant avoiding the discontinuities between consecutive local trends of the DFA by a priori constraining them to be continuous. Secondly, we show that, in all these approaches, the square of the fluctuation function can be presented in a similar matrix form. When the process is wide-sense stationary (w.s.s.), the latter can be seen as the power of the output of a linear filtering whose frequency response depends on the given method. In the general case, an interpretation of the square of the fluctuation function is also given by expressing it as the convolution between the 2D-Fourier transform of two matrices, one whose elements correspond to the instantaneous correlation function of the signal and the other which depends on the detrending method. To end up, an illustration is provided in the field of avionics for the detection of the visual tunneling, a deleterious cognitive state.
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Conference papers

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Bastien Berthelot, Eric Grivel, Pierrick Legrand, Jean-Marc André, Patrick Mazoyer. Regularized Dfa To Study The Gaze Position Of An Airline Pilot. EUSIPCO 2020 - 28th European Signal Processing Conference, Aug 2020, Amsterdam / Virtual, Netherlands. ⟨hal-02716136⟩
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To estimate the Hurst exponent of a mono-fractal process, the detrended fluctuation analysis (DFA) is based on the estimation of the trend of the integrated process. The latter is subtracted from the integrated process. The power of the residual is then computed and corresponds to the square of the fluctuation function. Its logarithm is proportional to the Hurst exponent. In the last few years, a few variants of this method have been proposed and differ in the way of estimating the trend. Our contribution in this paper is threefold. First, we introduce a new variant of the DFA, based on a regularized least-square criterion to estimate the trend. Then, the influence of the regularization parameter on the fluctuation function is analyzed in two cases: when the process is wide sense stationary and when it is not. Finally, an application is presented in the field of aeronautics to characterize an attentional impairment: the visual tunneling.
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Jimmy Bondu, Eric Grivel, Audrey Giremus, Pierrick Legrand, Vincent Corretja, et al.. Sea Target Classification Based On An A Priori Motion Model. EUSIPCO 2020 - 28th European Signal Processing Conference, Aug 2020, Amsterdam / Virtual, Netherlands. ⟨10.23919/Eusipco47968.2020.9287480⟩. ⟨hal-02716100⟩
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Target classification can be of real interest for sea surveillance in both civil and military contexts. To address this issue, we present two approaches based on the Singer model. The latter has the advantage of covering a wide range of motions depending on the values of its parameters. Given noisy observations, the first method aims at estimating the motion model parameters by taking advantage of the properties of the correlation function of the estimated acceleration. It is based on a genetic algorithm. The second approach is on-line and consists in deriving a joint tracking and classification (JTC) method. Based on various simulations, we study their respective relevance in different operational settings. The proposed JTC corresponds to the best compromise in terms of performance and number of samples required.
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Uriel Lopez, Leonardo Trujillo, Sara Silva, Leonardo Vanneschi, Pierrick Legrand. Unlabeled Multi-Target Regression with Genetic Programming. GECCO 2020 - The Genetic and Evolutionary Computation Conference, Jul 2020, Cancun, Mexico. ⟨hal-02551154⟩
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Book sections

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Anaïs Gayte-Papon de Lameigné, Pierrick Legrand, Jacques Lévy-Vehel. La modélisation de l'indemnisation du préjudice corporel. Florence G'sell. Le Big Data et le droit, Dalloz, pp.45-60, 2020, 978-2-247-18744-7. ⟨hal-02559847⟩
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Books

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Lhassane Idoumghar, Pierrick Legrand, Arnaud Liefooghe, Evelyne Lutton, Nicolas Monmarché, et al. (Dir.). Artificial Evolution: 14th International Conference, Évolution Artificielle, EA 2019, Mulhouse, France, October 29–30, 2019, Revised Selected Papers. Springer, LNCS - Lecture Notes in Computer Science (12052), pp.219, 2020, Artificial Evolution, 978-3-030-45714-3. ⟨10.1007/978-3-030-45715-0⟩. ⟨hal-03175883⟩
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This book constitutes the thoroughly refereed post-conference proceedings of the 14th International Conference on Artificial Evolution, EA 2019, held in Mulhouses, France, in October 2019. The revised papers were carefully reviewed and selected from the submissions. The papers cover a wide range of topics in the field of artificial evolution, such as evolutionary computation, evolutionary optimization, co-evolution, artificial life, population dynamics, theory, algorithmics and modeling, implementations, application of evolutionary paradigms to the real world (industry, biosciences, ...), other biologically-inspired paradigms (swarm, artificial ants, artificial immune systems, cultural algorithms...), memetic algorithms, multi-objective optimisation, constraint handling, parallel algorithms,, dynamic optimization, machine learning and hybridization with other soft computing techniques.
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2019

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Bastien Berthelot, Patrick Mazoyer, Sarah Egea, Jean-Marc André, Eric Grivel, et al.. Self-affinity of an Aircraft Pilot's Gaze Direction as a Marker of Visual Tunneling. SAE Aerotech, Sep 2019, Bordeaux, France. ⟨hal-02174262⟩
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Bastien Berthelot, Eric Grivel, Pierrick Legrand, Jean-Marc André, Patrick Mazoyer, et al.. Filtering-based Analysis Comparing the DFA with the CDFA for Wide Sense Stationary Processes. EUSIPCO 2019 - 27th European Signal Processing Conference, Sep 2019, A Coruna, Spain. ⟨hal-02147655⟩
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Bastien Berthelot, Eric Grivel, Pierrick Legrand, Marc Donias, Jean-Marc André, et al.. 2D Fourier Transform Based Analysis Comparing the DFA with the DMA. EUSIPCO 2019 - 27th European Signal Processing Conference, Sep 2019, A Coruna, Spain. ⟨hal-02147663⟩
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Bastien Berthelot, Eric Grivel, Pierrick Legrand, Jean-Marc Andre, Patrick Mazoyer, et al.. Interpréter les Fonctions de Fluctuation du DFA et du DMA comme le Résultat d'un Filtrage. GRETSI 2019, Aug 2019, Lille, France. ⟨hal-02145464⟩
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Habilitation à diriger des recherches

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Pierrick Legrand. Artificial evolution, fractal analysis and applications. Artificial Intelligence [cs.AI]. Université de Bordeaux, 2019. ⟨tel-02429815⟩
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This document contains a selection of research works to which I have contributed. It is structured around two themes, artificial evolution and signal regularity analysis and consists of three main parts: Part I: Artificial evolution, Part II: Estimation of signal regularity and Part III: Applications, combination of signal processing, fractal analysis and artificial evolution. In order to set the context and explain the coherence of the rest of the document, this manuscript begins with an introduction, Chapter 1, providing a list of collaborators and of the research projects carried out. Theoretical contributions focus on two areas: evolutionary algorithms and the measurement of signal regularity and are presented in Part I and Part II respectively. These two themes are then exploited and applied to real problems in Part III. Part I, Artificial Evolution, consists of 8 chapters. Chapter 2 contains a brief presentation of various types of evolutionary algorithms (ge-netic algorithms, evolutionary strategies and genetic programming) and presents some contributions in this area, which will be detailed later in the document. Chapter 3, entitled Prediction of Expected Performance for a Genetic Programming Classifier proposes a method to predict the expected performance for a genetic programming (GP) classifier without having to run the program or sample potential solutions in the research space. For a given classification problem, a pre-processing step to simplify the feature extraction process is proposed. Then the step of extracting the characteristics of the problem is performed. Finally, a PEP (prediction of expected performance) model is used, which takes the characteristics of the problem as input and produces the predicted classification error on the test set as output. To build the PEP model, a supervised learning method with a GP is used. Then, to refine this work, an approach using several PEP models is developed, each now becoming a specialized predictors of expected performance (SPEP) specialized for a particular group of problems. It appears that the PEP and SPEP models were able to accurately predict the performance of a GP-classifier and that the SPEP approach gave the best results. Chapter 4, entitled A comparison of fitness-case sampling methods for genetic programming presents an extensive comparative study of four fitness-case sampling methods, namely: Interleaved Sampling, Random Interleaved Sampling, Lexicase Selection and the proposed Keep-Worst Interleaved Sampling. The algorithms are compared on 11 symbolic regression problems and 11 supervised classification problems, using 10 synthetic benchmarks and 12 real-world datasets. They are evaluated based on test performance, overfitting and average program size, comparing them with a standard GP search. The experimental results suggest that fitness-case sampling methods are particularly useful for difficult real-world symbolic regression problems, improving performance, reducing overfitting and limiting code growth. On the other hand, it seems that fitness-case sampling cannot improve upon GP performance when considering supervised binary classification. Chapter 5, entitled Evolving Genetic Programming Classifiers with Novelty Search, deals with a new and unique approach towards search and optimization, the Novelty Search (NS), where an explicit objective function is replaced by a measure of solution novelty. This chapter proposes a NS-based GP algorithm for supervised classification. Results show that NS can solve real-world classification tasks, the algorithm is validated on real-world benchmarks for binary and multiclass problems. Moreover, two new versions of the NS algorithm are proposed, Probabilistic NS (PNS) and a variant of Minimal Criteria NS (MCNS). The former models the behavior of each solution as a random vector and eliminates all of the original NS parameters while reducing the computational overhead of the NS algorithm. The latter uses a standard objective function to constrain and bias the search towards high performance solutions. This chapter also discusses the effects of NS on GP search dynam...
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2018

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Victor R. López-López, Leonardo Trujillo, Pierrick Legrand. Applying Genetic Improvement to a Genetic Programming library in C++. Soft Computing, 2018. ⟨hal-01911943⟩
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A young subfield of Evolutionary Computing that has gained the attention of many researchers in recent years is Genetic Improvement. It uses an automated search method that directly modifies the source code or binaries of a software system tofind improved versions based on some given criteria. Genetic Improvement has achieved notable results and the acceptance of several research communities, namely software engineering and evolutionary computation. Over the past 10 years there has been core publications on the subject, however, we have identified, to the best of our knowledge, that there is no work on applying Genetic Improvement to a meta-heuristic system. In this work we apply the GI framework called GISMO to the Beagle Puppy library version 0.1 in C++, a Genetic Programming system configured to perform symbolic regression on several benchmark and real-world problems. The objective is to improve the processing time while maintaining a similar or better test-fitness of the best individual produced by the unmodified Genetic Programming search. Results show that GISMO can generate individuals that present an improvement on those two key aspects over some problems, while also reducing the effects of bloat, one of the main issues in Genetic Programming.
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José Enrique Hernandez-Beltran, Victor H. Díaz-Ramírez, Leonardo Trujillo, Pierrick Legrand. Design of estimators for restoration of images degraded by haze using genetic programming. Swarm and Evolutionary Computation, 2018. ⟨hal-01909121⟩
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Restoring hazy images is challenging since it must account for several physical factors that are related to the image formation process. Existing analytical methods can only provide partial solutions because they rely on assumptions that may not be valid in practice. This research presents an effective method for restoring hazy images based on genetic programming. Using basic mathematical operators several computer programs that estimate the medium transmission function of hazy scenes are automatically evolved. Afterwards, image restoration is performed using the estimated transmission function in a physics-based restoration model. The proposed estimators are optimized with respect to the mean-absolute-error. Thus, the effects of haze are effectively removed while minimizing overprocessing artifacts. The performance of the evolved GP estimators given in terms of objective metrics and a subjective visual criterion, is evaluated on synthetic and real-life hazy images. Comparisons are carried out with state-of-the-art methods, showing that the evolved estimators can outperform these methods without incurring a loss in efficiency, and in most scenarios achieving improved performance that is statistically significant.
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Leonardo Trujillo, Uriel Lopez, Pierrick Legrand. SOAP: Semantic Outliers Automatic Preprocessing (under review second round). IEEE Transactions on Evolutionary Computation, In press. ⟨hal-01909129⟩
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Uriel Lopez, Leonardo Trujillo, Pierrick Legrand. Filtering Outliers in One Step with Genetic Programming. PPSN 2018 - Fifteenth International Conference on Parallel Problem Solving from Nature (PPSN XV), Sep 2018, Coimbra, Portugal. ⟨10.1007/978-3-319-99253-2_17⟩. ⟨hal-01910433⟩
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Outliers are one of the most difficult issues when dealing with real-world modeling tasks. Even a small percentage of outliers can impede a learning algorithm’s ability to fit a dataset. While robust regression algorithms exist, they fail when a dataset is corrupted by more than 50% of outliers (breakdown point). In the case of Genetic Programming, robust regression has not been properly studied. In this paper we present a method that works as a filter, removing outliers from the target variable (vertical outliers). The algorithm is simple, it uses a randomly generated population of GP trees to determine which target values should be labeled as outliers. The method is highly efficient. Results show that it can return a clean dataset when contamination reaches as high as 90%, and may be able to handle higher levels of contamination. In this study only synthetic univariate benchmarks are used to evaluate the approach, but it must be stressed that no other approaches can deal with such high levels of outlier contamination while requiring such small computational effort.
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Sabrina Machhour, Eric Grivel, Pierrick Legrand, Vincent Corretja, Clément Magnant. A Comparative Study of Orthogonal Moments for Micro-Doppler Classification. EUSIPCO 2018 - 26th European Signal Processing Conference, Sep 2018, Rome, Italy. ⟨hal-01795520⟩
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Víctor López-López, Leonardo Trujillo, Pierrick Legrand. Novelty search for software improvement of a SLAM system. the Genetic and Evolutionary Computation Conference Companion, Jul 2018, Kyoto, Japan. pp.1598-1605, ⟨10.1145/3205651.3208237⟩. ⟨hal-02410785⟩
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Books

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Evelyne Lutton, Pierrick Legrand, Pierre Parrend, Nicolas Monmarché, Marc Schoenauer (Dir.). Artificial Evolution, 13th International Conference, Evolution Artificielle, EA 2017, Paris, France, October 25-27, 2017, Revised Selected Papers. Springer, LNCS - Lecture Notes in Computer Science (10764), 2018, Artificial Evolution, 978-3-319-78132-7. ⟨10.1007/978-3-319-78133-4⟩. ⟨hal-01910443⟩
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This book constitutes the thoroughly refereed post-conference proceedings of the 13th International Conference on Artificial Evolution, EA 2017, held in Paris, France, in October 2017. The 16 revised papers were carefully reviewed and selected from 33 submissions. The papers cover a wide range of topics in the field of artificial evolution, such as evolutionary computation, evolutionary optimization, co-evolution, artificial life, population dynamics, theory, algorithmics and modeling, implementations, application of evolutionary paradigms to the real world (industry, biosciences, ...), other biologically-inspired paradigms (swarm, artificial ants, artificial immune systems, cultural algorithms...), memetic algorithms, multi-objective optimisation, constraint handling, parallel algorithms,, dynamic optimization, machine learning and hybridization with other soft computing techniques.
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Preprints, Working Papers, ...

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Emigdio Z-Flores, Leonardo Trujillo, Pierrick Legrand, Frédérique Faïta-Aïnseba. EEG Feature Extraction using Genetic Programming for the Classification of Mental States (under review GPEM). 2018. ⟨hal-01909128⟩
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2017

Journal articles

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Yuliana Martinez, Enrique Naredo, Leonardo Trujillo, Pierrick Legrand, Uriel Lopez. A comparison of fitness-case sampling methods for genetic programming. Journal of Experimental and Theoretical Artificial Intelligence, 2017. ⟨hal-01389047⟩
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Uriel Lopez, Leonardo Trujillo, Yuliana Martinez, Pierrick Legrand, Enrique Naredo, et al.. RANSAC-GP: Dealing with Outliers in Symbolic Regression with Genetic Programming. Genetic Programming. EuroGP 2017. Lecture Notes in Computer Science, vol 10196. Springer, Cham, Springer, 2017. ⟨hal-01911448⟩
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Genetic programming (GP) has been shown to be a powerful tool for automatic modeling and program induction. It is often used to solve difficult symbolic regression tasks, with many examples in real-world domains. However, the robustness of GP-based approaches has not been substantially studied. In particular, the present work deals with the issue of outliers, data in the training set that represent severe errors in the measuring process. In general, a datum is considered an outlier when it sharply deviates from the true behavior of the system of interest. GP practitioners know that such data points usually bias the search and produce inaccurate models. Therefore, this work presents a hybrid methodology based on the RAndom SAmpling Consensus (RANSAC) algorithm and GP, which we call RANSAC-GP. RANSAC is an approach to deal with outliers in parameter estimation problems, widely used in computer vision and related fields. On the other hand, this work presents the first application of RANSAC to symbolic regression with GP, with impressive results. The proposed algorithm is able to deal with extreme amounts of contamination in the training set, evolving highly accurate models even when the amount of outliers reaches 90%.
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Trujillo Leonardo, Emigdio Z-Flores, Perla S. Juarez Smith, Pierrick Legrand, Sara Silva, et al.. Local Search is Underused in Genetic Programming. Ann Arbor. Genetic Programming Theory and Practice XIV, Springer, 2017. ⟨hal-01388426⟩
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2016

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Enrique Naredo, Leonardo Trujillo, Pierrick Legrand, Sara Silva, Luis Munoz. Evolving Genetic Programming Classifiers with Novelty Search. Information Sciences, 2016, 369, pp.347-367. ⟨10.1016/j.ins.2016.06.044⟩. ⟨hal-01389049⟩
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Novelty Search (NS) is a unique approach towards search and optimization, where an explicit objective function is replaced by a measure of solution novelty. However, NS has been mostly used in evolutionary robotics while its usefulness in classic machine learning problems has not been explored. This work presents a NS-based genetic programming (GP) algorithm for supervised classification. Results show that NS can solve real-world classification tasks, the algorithm is validated on real-world benchmarks for binary and multiclass problems. These results are made possible by using a domain-specific behavior descriptor. Moreover, two new versions of the NS algorithm are proposed, Probabilistic NS (PNS) and a variant of Minimal Criteria NS (MCNS). The former models the behavior of each solution as a random vector and eliminates all of the original NS parameters while reducing the computational overhead of the NS algorithm. The latter uses a standard objective function to constrain and bias the search towards high performance solutions. The paper also discusses the effects of NS on GP search dynamics and code growth. Results show that NS can be used as a realistic alternative for supervised classification, and specifically for binary problems the NS algorithm exhibits an implicit bloat control ability.
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Yuliana Martinez, Leonardo Trujillo, Pierrick Legrand, Edgar Galvan-Lopez. Prediction of Expected Performance for a Genetic Programming Classifier. Genetic Programming and Evolvable Machines, 2016, 17 (4), pp.409-449. ⟨10.1007/s10710-016-9265-9⟩. ⟨hal-01252141⟩
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The study of problem difficulty is an open issue in Genetic Programming (GP). The goal of this work is to generate models that predict the expected performance of a GPbased classifier when it is applied to an unseen task. Classification problems are described using domain-specific features, some of which are proposed in this work, and these features are given as input to the predictive models. These models are referred to as predictors of expected performance (PEPs). We extend this approach by using an ensemble of specialized predictors (SPEP), dividing classification problems into specified groups and choosing the corresponding SPEP. The proposed predictors are trained using 2D synthetic classification problems with balanced datasets. The models are then used to predict the performance of the GP classifier on unseen realworld datasets that are multidimensional and imbalanced. Moreover, as we know, this work is the first to provide a performance prediction of the GP classifier on test data, while previous works focused on predicting training performance. Accurate predictive models are generated by posing a symbolic regression task and solving it with GP. These results are achieved by using highly descriptive features and including a dimensionality reduction stage that simplifies the learning and testing process. The proposed approach could be extended to other classification algorithms and used as the basis of an expert system for algorithm selection.
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Emigdio Z-Flores, Leonardo Trujillo, Arturo Sotelo, Pierrick Legrand, Luis Coria. Regularity and Matching Pursuit Feature Extraction for the Detection of Epileptic Seizures. Journal of Neuroscience Methods, 2016, 266, pp.107-125. ⟨10.1016/j.jneumeth.2016.03.024⟩. ⟨hal-01389051⟩
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Background The neurological disorder known as epilepsy is characterized by involuntary recurrent seizures that diminish a patient's quality of life. Automatic seizure detection can help improve a patient's interaction with her/his environment, and while many approaches have been proposed the problem is still not trivially solved. Methods In this work, we present a novel methodology for feature extraction on EEG signals that allows us to perform a highly accurate classification of epileptic states. Specifically, Hölderian regularity and the Matching Pursuit algorithm are used as the main feature extraction techniques, and are combined with basic statistical features to construct the final feature sets. These sets are then delivered to a Random Forests classification algorithm to differentiate between epileptic and non-epileptic readings. Results Several versions of the basic problem are tested and statistically validated producing perfect accuracy in most problems and 97.6% accuracy on the most difficult case. Comparison with existing methods: A comparison with recent literature, using a well known database, reveals that our proposal achieves state-of-the-art performance. Conclusions The experimental results show that epileptic states can be accurately detected by combining features extracted through regularity analysis, the Matching Pursuit algorithm and simple time-domain statistical analysis. Therefore, the proposed method should be considered as a promising approach for automatic EEG analysis.
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José Enrique Hernandez-Beltran, Victor H. Díaz-Ramírez, Leonardo Trujillo, Pierrick Legrand. Restoration of degraded images using genetic programming. Optics and photonics for information processing X, Aug 2016, San Diego, United States. ⟨hal-01389064⟩
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Victor R. López-López, Leonardo Trujillo, Pierrick Legrand, Gustavo Olague. Genetic Programming: From design to improved implementation. GECCO 2016 - Genetic and Evolutionary Computation Conference, Jun 2016, Denver, United States. ⟨10.1145/2908961.2931693⟩. ⟨hal-01389066⟩
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Genetic programming (GP) is an evolutionary-based search paradigm that is well suited to automatically solve difficult design problems. The general principles of GP have been used to evolve mathematical functions, models, image operators, programs, and even antennas and lenses. Since GP evolves the syntax and structure of a solution, the evolutionary process can be carried out in one environment and the solution can then be ported to another. However, given the nature of GP it is common that the evolved designs are unorthodox compared to traditional approaches used in the problem domain. Therefore, efficiently porting, improving or optimizing an evolved design might not be a trivial task. In this work we argue that the same GP principles used to evolve the solution can then be used to optimize a particular new implementation of the design, following the Genetic Improvement approach. In particular, this paper presents a case study where evolved image operators are ported from Matlab to OpenCV, and then the source code is optimized an improved using Genetic Improvement of Software for Multiple Objectives (GISMOE). In the example we show that functional behavior is maintained (output image) while improving non-functional properties (computation time). Despite the fact that this first example is a simple case, it clearly illustrates the possibilities of using GP principles in two distinct stages of the software development process, from design to improved implementation.
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Proceedings

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Oliver Schuetze, Leonardo Trujillo, Pierrick Legrand, Yazmin Maldonado. NEO 2015 - Numerical and Evolutionary Optimization: Results of the Numerical and Evolutionary Optimization Workshop NEO 2015 held at September 23-25 2015 in Tijuana, Mexico. NEO 2015 - Numerical and Evolutionary Optimization Workshop , Sep 2015, Tijuana, Mexico. Springer, 2016, Studies in Computational Intelligence. ⟨hal-01389071⟩
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This volume comprises a selection of works presented at the Numerical and Evolutionary Optimization (NEO) workshop held in September 2015 in Tijuana, Mexico. The development of powerful search and optimization techniques is of great importance in today’s world that requires researchers and practitioners to tackle a growing number of challenging real-world problems. In particular, there are two well-established and widely known fields that are commonly applied in this area: (i) traditional numerical optimization techniques and (ii) comparatively recent bio-inspired heuristics. Both paradigms have their unique strengths and weaknesses, allowing them to solve some challenging problems while still failing in others. The goal of the NEO workshop series is to bring together people from these and related fields to discuss, compare and merge their complimentary perspectives in order to develop fast and reliable hybrid methods that maximize the strengths and minimize the weaknesses of the underlying paradigms. Through this effort, we believe that the NEO can promote the development of new techniques that are applicable to a broader class of problems. Moreover, NEO fosters the understanding and adequate treatment of real-world problems particularly in emerging fields that affect us all such as health care, smart cities, big data, among many others. The extended papers the NEO 2015 that comprise this book make a contribution to this goal.
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Stephane Bonnevay, Pierrick Legrand, Nicolas Monmarché, Evelyne Lutton, Marc Schoenauer. Artificial Evolution 2015. EA 2015 - 12th International Conference, Evolution Artificielle, Oct 2016, Lyon, France. 9554, Springer, 2016, LNCS - Lecture Notes in Computer Science, ⟨10.1007/978-3-319-31471-6⟩. ⟨hal-01389072⟩
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This book constitutes the thoroughly refereed post-conference proceedings of the 12th International Conference on Artificial Evolution, EA 2015, held in Lyon, France, in October 2015. The 18 revised papers were carefully reviewed and selected from 31 submissions. The focus of the conference is on following topics: Evolutionary Computation, Evolutionary Optimization, Co-evolution, Artificial Life, Population Dynamics, Theory, Algorithmics and Modeling, Implementations, Application of Evolutionary Paradigms to the Real World, Dynamic Optimization, Machine Learning and hybridization with other soft computing techniques.
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2015

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Laurent Vézard, Pierrick Legrand, Marie Chavent, Frédérique Faïta-Aïnseba, Leonardo Trujillo. EEG classification for the detection of mental states. Applied Soft Computing, 2015, 32, pp.113-131. ⟨10.1016/j.asoc.2015.03.028⟩. ⟨hal-01207506⟩
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Conference papers

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Emigdio Z-Flores, Leonardo Trujillo, Oliver Schütze, Pierrick Legrand. A Local Search Approach to Genetic Programming for Binary Classification. Proceedings of the 2015 on Genetic and Evolutionary Computation Conference - GECCO '15, 2015, Madrid, Spain. ⟨10.1145/2739480.2754797⟩. ⟨hal-01207504⟩
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Enrique Naredo, Leonardo Trujillo, Francisco Fernández De Vega, Sara Silva, Pierrick Legrand. Diseñando Problemas Sintéticos de Clasificación con Superficie de Aptitud Deceptiva. MAEB 2015, 2015, Merida, España. ⟨hal-01207507⟩
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Mauro Castelli, Leonardo Trujillo, Leonardo Vanneschi, Sara Silva, Emigdio Z-Flores, et al.. Geometric Semantic Genetic Programming with Local Search. Proceedings of the 2015 on Genetic and Evolutionary Computation Conference - GECCO '15, 2015, Madrid, Spain. ⟨10.1145/2739480.2754795⟩. ⟨hal-01207505⟩
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2014

Conference papers

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Adrien Todeschini, Francois Caron, Marc Fuentes, Pierrick Legrand, Pierre del Moral. Biips software: inference in Bayesian graphical models with sequential Monte Carlo methods. 21st International Conference on Computational Statistics (COMPSTAT 2014), European Regional Section of the IASC, Aug 2014, Genève, Switzerland. ⟨hal-01108399⟩
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The main factor in the success of Markov Chain Monte Carlo Methods is that they can be implemented with little efforts in a large variety of settings. Many softwares have been developped such as BUGS and JAGS, that helped to popularize Bayesian methods. These softwares allow the user to define his statistical model in a so-called BUGS language, then runs MCMC algorithms as a black box. Although sequential Monte Carlo methods have become a very popular class of numerical methods over the last 20 years, there is no such “black box software” for this class of methods. The BiiPS software, which stands for Bayesian Inference with Interacting Particle Systems, aims at bridging this gap. From a graphical model defined in BUGS language, it automatically implements sequential Monte Carlo algorithms and provides summaries of the posterior distributions. In this poster, we will highlight some of the features of the BiiPS software and an illustration of its application to a stochastic volatility model.
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Emigdio Z-Flores, Leonardo Trujillo, Oliver Schuetze, Pierrick Legrand. Effects of local search in genetic programming. EVOLVE 2014, Jul 2014, Beijing, China. ⟨hal-01060315⟩
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Yuliana Martinez, Leonardo Trujillo, Enrique Naredo, Pierrick Legrand. A comparison of fitness-case sampling methods for symbolic regression with genetic programming. EVOLVE 2014, Jul 2014, Beijing, China. pp.201-212, ⟨10.1007/978-3-319-07494-8_14⟩. ⟨hal-01060313⟩
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Adrien Todeschini, Francois Caron, Marc Fuentes, Pierrick Legrand, Pierre del Moral. Recent Developments in Software for MCMC - Round Table Session: Biips software: inference in Bayesian graphical models with sequential Monte Carlo methods. Fifth IMS-ISBA joint meeting MCMSki IV, IMS (Institute of Mathematical Statistics) and ISBA (International Society for Bayesian Analysis), Jan 2014, Chamonix Mont-Blanc, France. ⟨hal-01108393⟩
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The main factor in the success of Markov Chain Monte Carlo Methods is that they can be implemented with little efforts in a large variety of settings. Many softwares have been developped such as BUGS and JAGS, that helped to popularize Bayesian methods. These softwares allow the user to define his statistical model in a so-called BUGS language, then runs MCMC algorithms as a black box. Although sequential Monte Carlo methods have become a very popular class of numerical methods over the last 20 years, there is no such “black box software” for this class of methods. The BiiPS software, which stands for Bayesian Inference with Interacting Particle Systems, aims at bridging this gap. From a graphical model defined in BUGS language, it automatically implements sequential Monte Carlo algorithms and provides summaries of the posterior distributions. In this poster, we will highlight some of the features of the BiiPS software and an illustration of its application to a stochastic volatility model.
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Victor R. López-López, Leonardo Trujillo, Pierrick Legrand, Victor H. Díaz-Ramírez. Evaluation of Local Feature Extraction Methods Generated through Genetic Programming on Visual SLAM. Proceedings of the 2014 IEEE International Autumn Meeting on Power, Electronics and Computing (ROPEC 2014), 2014, Ixtapa, Mexico. ⟨hal-01207508⟩
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Book sections

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Pierrick Legrand, Laurent Vezard, Marie Chavent, Frédérique Faïta, Leonardo Trujillo. Feature extraction and classification of EEG signals. The use of a genetic algorithm for an application on alertness prediction.. Eduardo Miranda; Julien Castet; Benjamin Knapp. Guide to Brain-Computer Music Interfacing, Springer, 2014. ⟨hal-01060317⟩
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Laurent Vezard, Pierrick Legrand, Marie Chavent, Frederique Faita-Ainseba, Julien Clauzel, et al.. Classification of EEG signals by evolutionary algorithm. Guillet, F. and Pinaud, B. and Venturini, G. and Zighed, D.A. Advances in Knowledge Discovery and Management Volume 4, 527, Springer, pp.133-153, 2014, Studies in Computational Intelligence, ISBN 978-3-319-02998-6. ⟨10.1007/978-3-319-02999-3_8⟩. ⟨hal-00939850⟩
resume
The goal of this work is to predict the state of alertness of an individual by analyzing the brain activity through electroencephalographic data (EEG) captured with 58 electrodes. Alertness is characterized here as a binary variable that can be in a "normal" or "relaxed" state. We collected data from 44 subjects before and after a relaxation practice, giving a total of 88 records. After a pre-processing step and data validation, we analyzed each record and discriminate the alertness states using our proposed "slope criterion". Afterwards, several common methods for supervised classification (k nearest neighbors, decision trees (CART), random forests, PLS and discriminant sparse PLS) were applied as predictors for the state of alertness of each subject. The proposed "slope criterion" was further refined using a genetic algorithm to select the most important EEG electrodes in terms of classification accuracy. Results show that the proposed strategy derives accurate predictive models of alertness.
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Proceedings

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Pierrick Legrand, Marc-Michel Corsini, Jin-Kao Hao, Nicolas Monmarché, Evelyne Lutton, et al.. Artificial Evolution, 11th Internatioanl Conference, Evolution Artificielle, EA, 2013, Bordeaux, France, revised selected papers.. Pierrick Legrand; Marc-Michel Corsini; Jin-Kao HAo; Nicolas Monmarché; Evelyne Lutton; Marc Schoenauer. 11th International Conference, Evolution Artificielle, EA 2013, Oct 2013, Bordeaux, France. 8752, Springer, pp.260, 2014, LNCS - Lecture Notes in Computer Science, 978-3-319-11683-9. ⟨10.1007/978-3-319-11683-9⟩. ⟨hal-01060324⟩
resume
This LNCS volume includes the best papers presented at the 11th Biennial International Conference on Artificial Evolution, EA 2 2013, held in Bordeaux (France). Authors had been invited to present original work relevant to Artificial Evolution, including, but not limited to: Evolutionary Computation, Evolutionary Optimization, Co-evolution, Artificial Life, Population Dynamics, Theory, Algorithmics and Modeling, Implementations, Application of Evolutionary Paradigms to the Real World(industry, biosciences,...), other Biologically Inspired Paradigms (Swarm, Artificial Ants, Artificial Immune Systems, Cultural Algorithms...), Memetic Algorithms, Multi-Objective Optimization, Constraint Handling, Parallel Algorithms, Dynamic Optimization, Machine Learning, and hybridization with other soft computing techniques
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Preprints, Working Papers, ...

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Enrique Naredo, Trujillo Leonardo, Pierrick Legrand. Evolving Genetic Programming Classifiers with Novelty Search. 2014. ⟨hal-01111234⟩
resume
Novelty Search (NS) is a unique approach towards search and optimization, where an explicit objective function is replaced by a measure of solution novelty to provide the selective pressure in an artificial evolutionary system. However, NS has been mostly used in evolutionary robotics, while it’s applicability to classic machine learning problems has been mostly unexplored. This work presents a NSbased Genetic Programming (GP) algorithm for supervised classification, with the following noteworthy contributions. It is shown that NS can solve real-world classification tasks, validated over several commonly used benchmarks. These results are made possible by using a domain-specific behavioral descriptor, closely related to the concept of semantics in GP.Moreover, two new variants of the NS algorithm are proposed, Probabilistic NS (PNS) and a variant ofMinimum Criterion NS (MCNS). The former models the behavior of each solution as a random vector, eliminating all the NS parameters and reducing the computational overhead of the traditional NS algorithm; the latter uses a standard objective function to constrain the search and bias the process towards high performance solutions. The paper also discusses the effects of NS on an important GP phenomenon, bloat. In particular, results indicate that some variants of the NS approach can have a beneficial effect on the search process by curtailing code growth.
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Adrien Todeschini, Francois Caron, Marc Fuentes, Pierrick Legrand, Pierre del Moral. Biips: Software for Bayesian Inference with Interacting Particle Systems. 2014. ⟨hal-01096065⟩
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Biips is a software platform for automatic Bayesian inference with interacting particle systems. Biips allows users to define their statistical model in the probabilistic programming BUGS language, as well as to add custom functions or samplers within this language. Then it runs sequential Monte Carlo based algorithms (particle filters, particle independent Metropolis-Hastings, particle marginal Metropolis-Hastings) in a black-box manner so that to approximate the posterior distribution of interest as well as the marginal likelihood. The software is developed in C++ with interfaces with the softwares R, Matlab and Octave.
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Laurent Vezard, Pierrick Legrand, Marie Chavent, Frederique Faita-Ainseba, Trujillo Leonardo. EEG classification for the detection of mental states. 2014. ⟨hal-01111238⟩
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2013

Conference papers

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Laurent Vezard, Pierrick Legrand, Marie Chavent, Frederique Faita-Ainseba, Leonardo Trujillo. Detecting mental states of alertness with genetic algorithm variable selection. IEEE Congress on Evolutionary Computation (CEC) 2013, Jun 2013, Cancun, Mexico. pp.1247 - 1254. ⟨hal-00939851⟩
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Email Print Request Permissions Save to Project The objective of the present work is to develop a method able to automatically determine mental states of vigilance; i.e., a person's state of alertness. Such a task is relevant to diverse domains, where a person is expected or required to be in a particular state. For instance, pilots or medical staffs are expected to be in a highly alert state, and this method could help to detect possible problems. In this paper, an approach is developed to predict the state of alertness ("normal" or "relaxed") from the study of electroencephalographic signals (EEG) collected with a limited number of electrodes. The EEG of 58 participants in the two alertness states (116 records) were collected via a cap with 58 electrodes. After a data validation step, 19 subjects were retained for further analysis. A genetic algorithm was used to select an optimal subset of electrodes. Common spatial pattern (CSP) coupled to linear discriminant analysis (LDA) was used to build a decision rule and thus predict the alertness of the participants. Different subset sizes were investigated and the best result was obtained by considering 9 electrodes (correct classification rate of 73.68%).
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Books

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Oliver Schuetze, Carlos Coello Coello, Alexandru-Adrian Tantar, Emilia Tantar, Pascal Bouvry, et al. (Dir.). EVOLVE - A bridge between Probability , Set Oriented Numerics, and Evolutionary Computation II.. Oliver Schütze; Carlos Coello Coello; Alexandru-Adrian Tantar; Emilia Tantar; Pascal Bouvry; Pierre Del-Moral; Pierrick Legrand. Springer, 175, pp.508, 2013, ⟨10.1007/978-3-642-31519-0⟩. ⟨hal-01060421⟩
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Michael Emmerich, André Deutz, Oliver Schuetze, Thomas Back, Emilia Tantar, et al. (Dir.). EVOLVE - A bridge between Probability , Set Oriented Numerics, and Evolutionary Computation IV.. Michael Emmerich, André Deutz, Oliver Shütze, Thomas Back, Emilia Tantar, Alexandru-Adrian Tantar, Pierre Del Moral, Pierrick Legrand, Pascal Bouvry, Carlos Coello Coello. Springer, 227, pp.300, 2013. ⟨hal-01060389⟩
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Oliver Schuetze, Carlos Coello Coello, Alexandru-Adrian Tantar, Emilia Tantar, Pascal Bouvry, et al. (Dir.). EVOLVE - A bridge between Probability , Set Oriented Numerics, and Evolutionary Computation III.. Oliver Schütze, Carlos Coello Coello, Alexandru-Adrian Tantar, Emilia Tantar, Pascal Bouvry, Pierre Del-Moral, Pierrick Legrand. Springer, 500, pp.300, 2013. ⟨hal-01060418⟩
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Emilia Tantar, Alexandru-Adrian Tantar, Pascal Bouvry, Pierre del Moral, Pierrick Legrand, et al. (Dir.). EVOLVE - A bridge between Probability , Set Oriented Numerics, and Evolutionary Computation.. Emilia Tantar; Alexandru-Adrian Tantar; Pascal Bouvry; Pierre Del-Moral; Pierrick Legrand; Carlos Coello Coello; Oliver Schütze. Springer, 447, pp.412, 2013, 978-3-642-32726-1. ⟨hal-01060424⟩
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The aim of this book is to provide a strong theoretical support for understanding and analyzing the behavior of evolutionary algorithms, as well as for creating a bridge between probability, set-oriented numerics and evolutionary computation.
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2012

Journal articles

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Laurent Vezard, Pierrick Legrand, Marie Chavent, Frederique Faita-Ainseba, Julien Clauzel. Classification de données EEG par algorithme évolutionnaire pour l'étude d'états de vigilance. Revue des Nouvelles Technologies de l'Information, 2012, EGC 2012, 23, pp.459-470. ⟨hal-00643438⟩
resume
L'objectif de ce travail est de prédire l'état de vigilance d'un individu à partir de l'étude de son activité cérébrale (signaux d'électro-encéphalographie EEG). La variable à prédire est binaire (état de vigilance "normal" ou "relaxé"). Des EEG de 44 participants dans les deux états (88 enregistrements), ont été recueillis via un casque à 58 électrodes. Après une étape de prétraitement et de validation des données, un critère nommé "critère des pentes" a été choisi. Des méthodes de classification supervisée usuelles (k plus proches voisins, arbres binaires de décision (CART), forêts aléatoires, PLS et sparse PLS discriminante) ont été appliquées afin de fournir des prédictions de l'état des participants. Le critère utilisé a ensuite été raffiné grâce à un algorithme génétique, ce qui a permis de construire un modèle fiable (taux de bon classement moyen par CART égal à 86.68 +- 1.87%) et de sélectionner une électrode parmi les 58 initiales.
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Yuliana Martínez, Leonardo Trujillo, Edgar Galvan-Lopez, Pierrick Legrand. A comparison of predictive measures of problem difficulty for classification with Genetic Programming. Research in Computing Science, 2012, 59, pp.159-170. ⟨hal-01207509⟩
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Leonardo Trujillo, Pierrick Legrand, Gustavo Olague, Jacques Lévy-Vehel. Evolving Estimators of the Pointwise Holder Exponent with Genetic Programming. Information Sciences, 2012, 209, pp.61-79. ⟨10.1016/j.ins.2012.04.043⟩. ⟨hal-00643387⟩
resume
The analysis of image regularity using Holder exponents can be used to characterize singular structures contained within an image, and provide a compact description of local shape and appearance. However, estimating the Holder exponent is not a trivial task and current methods tend to be slow and complex. Therefore, the goal in this work is to automatically synthesize image operators that can be used to estimate the Holder regularity of an image. We pose this task as an optimization problem and use Genetic Programming (GP) to search for operators that can approximate a traditional estimator, the oscillations method. In our experiments, GP was able to evolve estimators that achieve a low error and a high correlation with the ground truth estimation. Furthermore, most of the GP estimators are faster than the traditional approaches, in some cases their runtime is orders of magnitude smaller. This result allowed us to implement a real-time estimation of the Holder exponent on a live video signal, the first such implementation in current literature. Moreover, the evolved estimators are used to generate local descriptors of salient image regions, a task for which we obtain a stable and robust matching that is comparable with state-of-the-art methods. In conclusion, the evolved estimators produced by GP could help expand the application domain of Holderian regularity within the fields of image analysis and signal processing.
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Conference papers

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Laurent Vezard, Pierrick Legrand, Marie Chavent, Frederique Faita-Ainseba. Sélection de variables par algorithme génétique pour l'étude d'états de vigilance. Journée Évolutionnaire Thématique, 23éme édition, Nov 2012, Paris, France. ⟨hal-00759420⟩
resume
L'objectif de ce travail est de prédire l'état de vigilance (variable binaire, "normal" ou "relaxé") d'un individu à partir de l'étude de son activité cérébrale (signaux d'électro-encéphalographie EEG) recueillie avec un nombre restreint d'électrodes. En effet, la mise en place des électrodes lors de l'acquisition des signaux EEG est coûteuse en temps et ces électrodes sont très corrélées entre elles. Pour notre étude, les EEG de 58 participants dans les deux états (116 enregistrements), ont été recueillis via un casque à 58 électrodes (p=58). Après une étape de validation des données basée sur l'étude de la variation contingente négative (VCN), 19 sujets ont été conservés dans l'étude. Un CSP (Common Spacial Pattern) couplé à une analyse linéaire discriminante ont permis de construire une règle de décision et ainsi prédire l'état de vigilance des participants. Un algorithme génétique a permis de déterminer un sous ensemble d'électrodes de taille p'.
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Leonardo Trujillo, Yuliana Martinez, Edgar Galvan-Lopez, Pierrick Legrand. A comparison of predictive measures of problem difficulty for classification with Genetic Programming. ERA 2012, Nov 2012, Tijuana, Mexico. ⟨hal-00757363⟩
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In the field of Genetic Programming (GP) a question exists that is difficult to solve; how can problem difficulty be determined? In this paper the overall goal is to develop predictive tools that estimate how difficult a problem is for GP to solve. Here we analyse two groups of methods. We call the first group Evolvability Indicators (EI), measures that capture how amendable the fitness landscape is to a GP search. The second are Predictors of Expected Performance (PEP), models that take as input a set of descriptive attributes of a problem and predict the expected performance of a GP system. These predictive variables are domain specific thus problems are described in the context of the problem domain. This paper compares an EI, the Negative Slope Coefficient, and a PEP model for a GP classifier. Results suggest that the EI does not correlate with the performance of GP classifiers. Conversely, the PEP models show a high correlation with GP performance. It appears that while an EI estimates the difficulty of a search, it does not necessarily capture the difficulty of the underlying problem. However, while PEP models treat GP as a computational black-box, they can produce accurate performance predictions.
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Zoé Sigrist, Pierrick Legrand, Eric Grivel, Benoit Alcoverro. Considering the measurement noise for a nonlinear system identification with evolutionary algorithms.. EUSIPCO 2012 - 20th European Signal Processing Conference, Aug 2012, Bucharest, Romania. pp.2114-2118. ⟨hal-00757231⟩
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This paper deals with the identi cation of a nonlinear system modelled by a nonlinear output error (NOE) model when the system output is disturbed by an additive zero-mean white Gaussian noise. In that case, standard on-line or off-line least squares methods may lead to poor results. Here, our approach is based on evolutionary algorithms. Although their computational cost can be higher than the above methods, these algorithms present some advantages, which often lead to an effortless optimisation. Indeed, they do not need an elaborate formalisation of the problem. When their parameters are correctly tuned, they avoid to get stuck at a local optimum. To take into account the in uence of the additive noise, we investigate different approaches and we suggest a whole protocol including the selection of a tness function and a stop rule. Without loss of generality, simulations are provided for two nonlinear systems and various signal-to-noise ratios.
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Laurent Vezard, Pierrick Legrand, Marie Chavent, Frederique Faita-Ainseba, Julien Clauzel. Classification of EEG signals by an evolutionary algorithm. COMPSTAT 2012 - 20th International Conference on Computational Statistics, Aug 2012, Limassol, Cyprus. ⟨hal-00757270⟩
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The goal is to predict the alertness of an individual by analyzing the brain activity through electroencephalographic data (EEG) captured with 58 electrodes. Alertness is characterized as a binary variable that can be in a normal or relaxed state. We collected data from 44 subjects before and after a relaxation practice, giving a total of 88 records. After a pre-processing step and data validation, we analyzed each record and discriminate the alertness states using our proposed slope criterion. Afterwards, several common methods for supervised classification (k nearest neighbors, decision trees -CART-, random forests, PLS and discriminant sparse PLS) were applied as predictors for the state of alertness of each subject. The proposed slope criterion was further refined using a genetic algorithm to select the most important EEG electrodes in terms of classification accuracy. Results shown that the proposed strategy derives accurate predictive models of alertness.
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Leonardo Trujillo, Yuliana Martinez, Edgar Galvan-Lopez, Pierrick Legrand. A Comparative Study of an Evolvability Indicator and a Predictor of Expected Performance for Genetic Programming. GECCO, Jul 2012, Philadelphie, United States. ⟨hal-00757266⟩
resume
One of the main open problems within Genetic Programming (GP) is to meaningfully characterize the difficulty (or hardness) of a problem. The general goal is to develop predictive tools that can allow us to identify how difficult a problem is for a GP system to solve. In this work, we identify and compare two main approaches that address this question. We denote the first group of methods as Evolvability Indicators (EI), which are measures that attempt to capture how amendable the fitness landscape is to a GP search. The best examples of current EIs are the Fitness Distance Correlation (FDC) and the Negative Slope Coefficient (NSC). The second, more recent, group of methods are what we call Predictors of Expected Performance (PEP), which are predictive models that take as input a set of descriptive attributes of a particular problem and produce as output the expected performance of a GP system. The experimental work presented here compares an EI, the NSC, and a PEP model for a GP system applied to data classification. Results suggest that the EI fails at measuring problem difficulty expressed by the performance of the GP classifiers, an unexpected result. On the other hand, the PEP models show a very high correlation with the actual performance of the GP system. It appears that while an EI can correctly estimate the difficulty of a given search, as shown by previous research on this topic, it does not necessarily capture the difficulty of the underlying problem that GP is intended to solve. Conversely, while the PEP models treat the GP system as a computational black-box, they can still provide accurate performance predictions.
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Adrien Todeschini, François Caron, Pierrick Legrand, Pierre del Moral. BiiPS : un logiciel pour l'inférence bayésienne dans les modèles graphiques utilisant des méthodes de Monte Carlo séquentielles. 1ères Rencontres R, Jul 2012, Bordeaux, France. ⟨hal-00717547⟩
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BiiPS : un logiciel pour l'inférence bayésienne dans les modèles graphiques utilisant des méthodes de Monte Carlo séquentielles
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Books

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Jin-Kao Hao, Pierrick Legrand, Pierre Collet, Nicolas Monmarché, Evelyne Lutton, et al. (Dir.). Artificial Evolution 2011 : 10th International Conference, Evolution Artificielle, EA 2011, Angers, France, October 24-26, 2011, Revised Selected Papers. Springer, 7401, 229 p., 2012, Lecture Notes in Computer Science, ⟨10.1007/978-3-642-35533-2_15⟩. ⟨hal-00643404⟩
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Jin-Kao Hao, Pierrick Legrand, Pierre Collet, Nicolas Monmarché, Evelyne Lutton, et al. (Dir.). Artificial Evolution - 10th International Conference, Evolution Artificielle, EA 201. Revised Selected Papers. Springer, 2012, Lecture Notes in Computer Science, 978-3-642-35532-5. ⟨10.1007/978-3-642-35533-2⟩. ⟨hal-03256241⟩
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2011

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Vincent Corretja, Pierrick Legrand, Eric Grivel, Jacques Lévy-Vehel. Relevance of the Hölderian regularity-based interpolation for range-Doppler ISAR image post-processing.. RADAR 2011: 6th International Conference on Radar, Oct 2011, Chengdu, China. ⟨hal-00643369⟩
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In ISAR processing, post-processing of the range Doppler image is useful to help the practitioner for ship recognition. Among the image post-processing tools, interpolation methods can be of interest especially when zooming. In this paper, we study the relevance of the Hölderian regularity-based interpolation. In that case, interpolating consists in adding a new scale in the wavelet transform and the new wavelet coefficients can be estimated from others. In the original method, initially proposed by two of the authors, the image is first interpolated along the rows and then along the columns. Concerning the diagonal pixels, they are estimated as the mean of the adjacent original and interpolated pixels. Here, we propose a variant where the diagonal pixels are estimated by taking into account the local orientation of the image. It has the advantage of conserving local regularity on all interpolated pixels of the image. A comparative study on synthetic data and real range-Doppler images is then carried out with alternative interpolation techniques such as the linear interpolation, the bicubic one, the nearest neighbour interpolation, etc. The simulation results confirm the effectiveness of the approach.
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Leonardo Trujillo, Yuliana Martinez, Edgar Galvan-Lopez, Pierrick Legrand. Predicting Problem Difficulty for Genetic Programming Applied to Data Classification. Gecco 2011, Jul 2011, Dublin, Ireland. pp.1355-1362, ⟨10.1145/2001576.2001759⟩. ⟨hal-00643358⟩
resume
During the development of applied systems, an important problem that must be addressed is that of choosing the correct tools for a given domain or scenario. This general task has been addressed by the genetic programming (GP) community by attempting to determine the intrinsic difficulty that a problem poses for a GP search. This paper presents an approach to predict the performance of GP applied to data classification, one of themost common problems in computer science. The novelty of the proposal is to extract statistical descriptors and complexity descriptors of the problem data, and from these estimate the expected performance of a GP classifier. We derive two types of predictive models: linear regression models and symbolic regression models evolved with GP. The experimental results show that both approaches provide good estimates of classifier performance, using synthetic and real-world problems for validation. In conclusion, this paper shows that it is possible to accurately predict the expected performance of a GP classifier using a set of descriptors that characterize the problem data.
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Laurent Vezard, Marie Chavent, Pierrick Legrand, Frederique Faita-Ainseba, Julien Clauzel. Caractérisation d'états psychophysiologiques par classification de signaux EEG. Intégration de ces résultats dans le projet PSI.. Journée AFIM : électroencéphalographie et composition musicale, Jun 2011, Talence, France. ⟨hal-00649520⟩
resume
Cet exposé avait pour but de présenter un travail qui visait à caractériser l'état de vigilance d'une personne à partir de son électro-encéphalogramme (EEG)
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Leonardo Trujillo, Sara Silva, Pierrick Legrand, Leonardo Vanneschi. An empirical study of functional complexity as an indicator of overfitting in Genetic Programming. EuroGP, Apr 2011, Turin, Italy. pp.262-273, ⟨10.1007/978-3-642-20407-4_23⟩. ⟨hal-00642530⟩
resume
Recently, it has been stated that the complexity of a solution is a good indicator of the amount of overfitting it incurs. However, measuring the complexity of a program, in Genetic Programming, is not a trivial task. In this paper, we study the functional complexity and how it relates with overfitting on symbolic regression problems.We consider two measures of complexity, Slope-based Functional Complexity, inspired by the concept of curvature, and Regularity-based Functional Complexity based on the concept of Holderian regularity. In general, both complexity measures appear to be poor indicators of program overfitting. However, results suggest that Regularity-based Functional Complexity could provide a good indication of overfitting in extreme cases.
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Books

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Jin-Kao Hao, Pierrick Legrand, Pierre Collet, Nicolas Monmarché, Evelyne Lutton, et al. (Dir.). Proceedings of Artificial Evolution. EA - Springer, 2011. ⟨hal-01067820⟩
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2010

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Leonardo Trujillo, Pierrick Legrand, Jacques Lévy Véhel. The estimation of Hölderian regularity using genetic programming. Genetic and Evolutionary Computation Conference (GECCO 2010). Best Paper Award in "Genetic Programming", Jul 2010, Portland Oregon, United States. pp.861-868. ⟨inria-00538943⟩
resume
This paper presents a Genetic Programming (GP) approach to synthesize estimators for the pointwise Hölder exponent in 2D signals. It is known that irregularities and singularities are the most salient and informative parts of a signal. Hence, explicitly measuring these variations can be important in various domains of signal processing. The pointwise Hölder exponent provides a characterization of these types of features. However, current methods for estimation cannot be considered to be optimal in any sense. Therefore, the goal of this work is to automatically synthesize operators that provide an estimation for the Hölderian regularity in a 2D signal. This goal is posed as an optimization problem in which we attempt to minimize the error between a prescribed regularity and the estimated regularity given by an image operator. The search for optimal estimators is then carried out using a GP algorithm. Experiments confirm that the GP-operators produce a good estimation of the Hölder exponent in images of multifractional Brownian motions. In fact, the evolved estimators significantly outperform a traditional method by as much as one order of magnitude. These results provide further empirical evidence that GP can solve difficult problems of applied mathematics.
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Leonardo Trujillo, Pierrick Legrand, Gustavo Olague, Cynthia Pérez. Optimization of the Hölder Image Descriptor using a Genetic Algorithm. GECCO 2010. Best paper award in "Real world applications"., Jul 2010, Portland Oregon, United States. pp.1147-1154. ⟨inria-00534457⟩
resume
Local image features can provide the basis for robust and invariant recognition of objects and scenes. Therefore, compact and distinctive representations of local shape and appearance has become invaluable in modern computer vision. In this work,we study a local descriptor based on the Hölder exponent, a measure of signal regularity. The proposal is to find an optimal number of dimensions for the descriptor using a genetic algorithm (GA). To guide the GA search, fitness is computed based on the performance of the descriptor when applied to standard region matching problems. This criterion is quantified using the F-Measure, derived from recall and precision analysis. Results show that it is possible to reduce the size of the canonical Hölder descriptor without degrading the quality of its performance. In fact, the best descriptor found through the GA search is nearly 70% smaller and achieves similar performance on standard tests.
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Jean Baptiste Burie, Agnes Calonnec, Maud Charron, Pierrick Legrand. Modeling and simulated a fungal disease epidemic over a heterogeneous plot. CMPD 3, May 2010, Bordeaux, France. ⟨inria-00534465⟩
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Pierre Collet, Pierrick Legrand, Nicolas Monmarché, Marc Schoenauer, Evelyne Lutton (Dir.). Artificial Evolution, 9th international Conference, Evolution Artificielles. LNCS - Springer, 2010. ⟨hal-01067814⟩
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Pierre Collet, Nicolas Monmarché, Pierrick Legrand, Marc Schoenauer, Evelyne Lutton (Dir.). Evolution Artificielle 2009. Pierre Collet, Nicolas Monmarché, Pierrick Legrand, Marc Schoenauer, Evelyne Lutton. Springer, LNCS 5975, pp.163, 2010, 978-3-642-14155-3. ⟨hal-00643446⟩
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2009

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Pierrick Legrand. Local Regularity and Multifractal methods for image and signal analysis. Scaling, Fractals and Wavelets, Abry P., Goncalves P., Lévy-Vehel J., 512 p., chapitre 11, 2009. ⟨hal-00294853⟩
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Pierre Collet, Pierrick Legrand, Claire Bourgeois-Republique, Vincent Pean, Bruno Frachet. Using interactive evolutionary algorithms to help fit cochlear implants. Patrick Siarry. Optimization in Signal and Image Processing, Iste-Wiley, pp.329-384, 2009. ⟨hal-00409853⟩
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2008

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Pierrick Legrand. Le réglage par algorithmes évolutionnaires des implants cochléaire. Congrès international JAN09: 9e journée d'Analyse Numérique et d'Optimisation, Dec 2008, Mohammedia, Maroc. ⟨hal-00385739⟩
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Pierrick Legrand. Evolution interactive pour le réglage d'implants cochléaires.. Congrès suisse des audioprothésistes, 2008, Berne, Suisse. ⟨hal-00296788⟩
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M. Cherif, Pierrick Legrand. Sensorless monitoring of CFRP drilling. Proceedings of the 17th International Conference on Manufacturing Systems ICMAS, 2008, France. pp.ISSN 1842-3183. ⟨hal-00297440⟩
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2007

Journal articles

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Pierrick Legrand, Claire Bourgeois-Republique, Vincent Pean, Esther Harboun-Cohen, Jacques Lévy Véhel, et al.. Interactive evolution for cochlear implants fitting. Genetic Programming and Evolvable Machines, 2007, 8 (4), pp.319-354. ⟨hal-00294838⟩
resume
Cochlear implants are devices that become more and more sophisticated and adapted to the need of patients, but at the same time they become more and more difficult to parameterize. After a deaf patient has been surgically implanted, a specialised medical practitioner has to spend hours during months to precisely fit the implant to the patient. This process is a complex one implying two intertwined tasks: the practitioner has to tune the parameters of the device (optimisation) while the patient's brain needs to adapt to the new data he receives (learning). This paper presents a study that intends to make the implant more adaptable to environment (auditive ecology) and to simplify the process of fitting. Real experiments on volunteer implanted patients are presented, that show the efficiency of interactive evolution for this purpose. This work has partially been funded by the French ANR - RNTS HEVEA project 04T550.
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Leonardo Trujillo, Gustavo Olague, Pierrick Legrand, Evelyne Lutton. A new regularity based descriptor computed from local image oscillations.. Optics Express, 2007, 15 (10), pp.6140-6145. ⟨hal-00294862⟩
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This work presents a novel local image descriptor based on the concept of pointwise signal regularity. Local image regions are extracted using either an interest point or an interest region detector, and discriminative feature vectors are constructed by uniformly sampling the pointwise Holderian regularity around each region center. Regularity estimation is performed using local image oscillations, the most straightforward method directly derived from the definition of the Holder exponent. Furthermore, estimating the Holder exponent in this manner has proven to be superior when compared to wavelet based estimation. Our detector shows invariance to illumination change, JPEG compression, image rotation and scale change. Results show that the proposed descriptor is stable with respect to variations in imaging conditions, and reliable performance metrics prove it to be comparable and in some instances better than SIFT, the state-of-the-art in local descriptors.
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Conference papers

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Pierrick Legrand. Ondelettes discrètes pour une interpolation de signaux conservant la régularité Hölderienne. Application à la modélisation du frottement pneumatique-chaussé.. Séminaire TISIC: Traitement de l'Information, Signal, Image, Connaissance n°9: Temps fréquence, temps échelle, 2007, Lyon, France. ⟨hal-00297158⟩
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2006

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Pierrick Legrand, Evelyne Lutton, Gustavo Olague. Evolutionary denoising based on an estimation of Hölder exponents with oscillations.. EvoIASP 2006 - 8th European Workshop on Evolutionary Computation in Image Analysis and Signal Processing, Apr 2006, Budapest, Hungary. pp.520-524, ⟨10.1007/11732242_49⟩. ⟨hal-00294873⟩
resume
In multifractal denoising techniques, the acuracy of the Holder exponents estimations is crucial for the quality of the outputs. In continuity with the method described in [1], where a wavelet decomposition was used, we investigate the use of another H¨older exponent estimation technique, based on the analysis of the local "oscillations" of the signal. The associated inverse problem to be solved, i.e. finding the signal whichis the closest to the initial noisy one but having the prescribed regularity, is then more complex. Moreover, the associated search space is of a different nature as in [J. Levy Vehel and E. Lutton, "Evolutionary signal enhancement based on holder regularity analysis," EVOIASP2001, LNCS 2038, 2001.], which necessitates the design of ad-hoc genetic operators.
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Claire Bourgeois-Republique, P. Collet, Bruno Frachet, Esther Harboun-Cohen, Pierrick Legrand, et al.. Preliminary results on automatic cochlear implant fitting using an interactive evolutionary algorithm. 9th International Conference on Cochlear implants and related Sciences, 2006, Vienne, Austria. ⟨hal-00297457⟩
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Jacques Lévy Véhel, Pierrick Legrand. Hölderian regularity-based image interpolation. ICASSP 06, International Conference on Acoustics, Speech, and Signal Processing, 2006, Toulouse, France. pp.852-855, ⟨10.1109/ICASSP.2006.1660788⟩. ⟨hal-00297218⟩
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We consider the problem of interpolating a signal in IRd known at a given resolution. In our approach, the signal is assumed to belong to a given (large) class of signals. This class is characterized by local regularity constraints, that can be described by a certain inter-scale behaviour of their wavelet coefficients. These constraints allow to predict the scale n coefficients from the ones at lower scales. We investigate some properties of this interpolation scheme. In particular, we give the Holder regularity of the refined signal, and present some asymptotic properties of the method. Finally, numerical experiments are presented. Both the theoretical and numerical results show that our regularity-based scheme allows to obtain good quality interpolated images.
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Book sections

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P. Collet, Pierrick Legrand, Claire Bourgeois-Republique, Vincent Pean, Bruno Frachet. Aide au paramétrage d'implants cochléaires par algorithme évolutionnaire interactif.. Optimisation en traitement du signal et de l'image, Traité IC2, Hermès-Lavoisier, Chapitre 13, 2006. ⟨hal-00294843⟩
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2004

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Jacques Lévy Véhel, Pierrick Legrand. Signal and Image processing with FracLab. FRACTAL04, Complexity and Fractals in Nature, 8th International Multidisciplinary Conference, Apr 2004, Vancouver, Canada. pp.321-322. ⟨inria-00576466⟩
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We describe a software toolbox, called FracLab, for signal and image processing based on fractal and multifractal methods. We illustrate the use of FracLab on a numerical example, and give some new results for estimating fractal parameters in the course of the presentation.
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Pierrick Legrand, Jacques Lévy Véhel, Do Minh Tan. Fractal properties and characterization of road profiles. FRACTAL04, Complexity and Fractals in Nature, 8th International Multidisciplinary Conference, Apr 2004, Vancouver, Canada. pp.189-198. ⟨inria-00576467⟩
resume
A major problem in road engineering is to understand the mechanisms of friction between rubber and the road. We study road profiles obtained using tactile and laser captors. these profiles belong to different category characterized by different friction coefficients. We find that all our profiles indeed display strong fractal behaviour in terms of both correlation exponents and regularization dimension over a large range of scales. However, neither of these fractal parameters seem to be related to friction. We then use a local fractal parameter, namely the pointwise Holder exponent. We show that this exponent does discriminate profiles which have different friction properties.
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Theses

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Pierrick Legrand. Débruitage et interpolation par analyse de la régularité Hölderienne. Application à la modélisation du frottement pneumatique-chaussée.. Traitement du signal et de l'image [eess.SP]. Ecole Centrale de Nantes (ECN); Université de Nantes, 2004. Français. ⟨NNT : ⟩. ⟨tel-00643450⟩
resume
L'utilisation d'ondelettes et d'outils d'analyse fractale est appropriée à l'analyse des signaux irreguliers. On pense que la caractérisation de la régularité locale est importante dans la description de ces signaux. Pour étudier la régularité, on utilise l'exposant de Hölder autour duquel plusieurs outils sont développés. Premièrement, on décrit et on compare des techniques permettant d'estimer cet exposant. Puis nous présentons une méthode d'interpolation de points basée sur la conservation de la régularité Hölderienne. Pour conclure la partie sur l'analyse Hölderienne, de nouvelles méthodes de débruitage avec contrôle de la régularité sont exposées. Ces méthodes, à base d'ondelettes, présentent des taux de convergence asymptotique similaires aux méthodes les plus performantes. Les divers outils développés peuvent être appliqués aux signaux 1D ainsi qu'aux images. Plus particulièrement, dans la deuxième partie de la thèse, on s'intéresse à des profils routiers afin de mieux modéliser le frottement pneumatique-chaussée. Ce travail entre dans le cadre de l'O.R. Adhérence du LCPC, qui a pour but de quantifier le rôle des aspérités de dimensions micrométrique à centimétrique, formant la texture des surfaces de chaussée, dans la génération du frottement. Dans cette partie, nous présentons les travaux menés aux LCPC sur la technique d'indenteur et sa combinaison au modèle de frottement de Stefani. Ensuite on démontre la fractalité des profils routiers puis l'apport des techniques d'interpolation Hölderienne et de débruitage multifractal sur le calcul du frottement. Enfin un modèle multi-echelle de frottement, provenant d'un raffinement du modèle de Stefani, est explicité.
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2003

Conference papers

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Pierrick Legrand, Jacques Lévy Véhel. Local regularity-based image denoising. ICIP03, IEEE International Conference on Image Processing, Sep 2003, Barcelona, Spain. pp.377-380. ⟨inria-00576475⟩
resume
We present an approach for image denoising based on the analysis of the local Hölder regularity. The method takes the point of view that denoising may be performed by increasing the Hölder regularity at each point. Under the assumption that the noise is additive and white, we show that our procedure is asymptotically minimax, provided the original signal belongs to a ball in some Besov space. Such a scheme is well adapted to the case where the image to be recovered is itself very irregular, e.g. nowhere differentiable with rapidly varying local regularity. The method is implemented through a wavelet analysis. We show an application to SAR image denoising where this technique yields good results compared to other algorithms.
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Pierrick Legrand, Jacques Lévy Véhel. Interpolation de signaux par conservation de la régularité Hölderienne. GRETSI03, 19 th GRETSI Symposium on Signal and Image Processing, Sep 2003, Paris, France. ⟨inria-00576477⟩
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On considère le problème de l'interpolation d'un signal dans IRd connu à une certaine résolution. On suppose que le signal appartient à une classe de signaux caractérisée par des contraintes sur la régularité locale, qui peuvent être traduites par un certain comportement interéchelles des coefficients d'ondelette. Ces contraintes permettent de prédire les coefficients de l'échelle n + 1 à partir de ceux des échelles précédentes. Nous donnons quelques propriétés de cette technique d'interpolation, concernant en particulier la régularité Höldérienne du signal raffiné et son comportement asymptotique. Les résultats théoriques et numériques montrent que notre méthode permet d'obtenir des signaux ou des images interpolés de bonne qualité. En particulier, l'aspect visuel de régularité ou d'irrégularité est respecté après interpolation.
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Pierrick Legrand, Jacques Lévy Véhel. Local regularity-based interpolation. WAVELET X, Part of SPIE's Symposium on Optical Science and Technology, SPIE, Aug 2003, San Diego, United States. ⟨inria-00576479⟩
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A ubiquitous problem in signal processing is to obtain data sampled with the best possible resolution. At the acquisition step, the resolution is limited by various factors such as the physical properties of the captors or the cost. It is therefore desirable to seek methods which would allow to increase the resolution after acquisition. This is useful for instance in medical imaging or target recognition. In some applications, one dispose of several low resolution overlapping signals [1]. In more general situations, a single signal is available for superresolution. Interpolation then requires that the available data be supplemented by some a priori information. Two types of methods have been explored: In the rst, "class-based" one, the signal is assumed to belong to some class, with conditions expressed mainly in the time or frequency domain [3, 5, 10]. This puts constraints on the interpolation, which is usually obtained as the minimum of a cost-function. The second type of approaches hypothesizes that the information needed to improve the resolution is local and is present in a class of similar signals [2, 4]. This type of approach could be called "contextual". Both "class-based" and "contextual" approaches use a "model" for interpolation: The "class-based model" is that the signal belongs to an abstract class characterized by a certain mathematical property. The "contextual model" is that the signal will behave locally under a change of resolution in way "similar" to other signals in a given set, for which a high resolution version is known. Both types of techniques have some drawbacks. Roughly speaking, class-based methods generally lead to overly smooth signals, while contextual-based ones, on the contrary, tend to generate spurious details.
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Jacques Lévy Véhel, Pierrick Legrand. Bayesian multifractal signal denoising. ICASSP03, IEEE International Conference on Acoustics, Speech, and Signal Processing, Apr 2003, Hong-Kong, China. ⟨inria-00576482⟩
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This work presents an approach for signal/image denoising in a semi-parametric frame. Our model is a wavelet-based one, which essentially assumes a minimal local regularity. This assumption translates into constraints on the multifractal spectrum of the signals. Such constraints are in turn used in a Bayesian framework to estimate the wavelet coefficients of the original signal from the noisy ones. Our scheme is well adapted to the processing of irregular signals, such as (multi-)fractal ones, and is potentially useful for the processing of e.g. turbulence, bio-medical or seismic data.
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