Performance of the maximum likelihood estimators for the parameters of multivariate generalized Gaussian distributions

International audienceThis paper studies the performance of the maximum likelihood estimators (MLE) for the parameters of multivariate generalized Gaussian distributions. When the shape parameter belongs to ]0,1[, we have proved that the scatter matrix MLE exists and is unique up to a scalar factor. After providing some elements about this proof, an estimation algorithm based on a Newton-Raphson recursion is investigated. Some experiments illustrate the convergence speed of this algorithm. The bias and consistency of the scatter matrix estimator are then studied for different values of the shape parameter. The performance of the shape parameter estimator is finally addressed by comparing its variance to the Cramér-Rao bound

Hypothesis Testing and Model Estimation with Dependent Observations in Heterogeneous Sensor Networks

Advances in microelectronics, communication and signal processing have enabled the development of inexpensive sensors that can be networked to collect vital information from their environment to be used in decision-making and inference. The sensors transmit their data to a central processor which integrates the information from the sensors using a so-called fusion algorithm. Many applications of sensor networks (SNs) involve hypothesis testing or the detection of a phenomenon. Many approaches to data fusion for hypothesis testing assume that, given each hypothesis, the sensors\u27 measurements are conditionally independent. However, since the sensors are densely deployed in practice, their field of views overlap and consequently their measurements are dependent. Moreover, a sensor\u27s measurement samples may be correlated over time. Another assumption often used in data fusion algorithms is that the underlying statistical model of sensors\u27 observations is completely known. However, in practice these statistics may not be available prior to deployment and may change over the lifetime of the network due to hardware changes, aging, and environmental conditions. In this dissertation, we consider the problem of data fusion in heterogeneous SNs (SNs in which the sensors are not identical) collecting dependent data. We develop the expectation maximization algorithm for hypothesis testing and model estimation. Copula distributions are used to model the correlation in the data. Moreover, it is assumed that the distribution of the sensors\u27 measurements is not completely known. we consider both parametric and non-parametric model estimation. The proposed approach is developed for both batch and online processing. In batch processing, fusion can only be performed after a block of data samples is received from each sensor, while in online processing, fusion is performed upon arrival of each data sample. Online processing is of great interest since for many applications, the long delay required for the accumulation of data in batch processing is not acceptable. To evaluate the proposed algorithms, both simulation data and real-world datasets are used. Detection performances of the proposed algorithms are compared with well-known supervised and unsupervised learning methods as well as with similar EM-based methods, which either partially or entirely ignore the dependence in the data

Adaptive Multidimensional Fuzzy Sets for Texture Modeling

The modeling of the perceptual properties of texture plays a fundamental role in tasks where some interaction with subjects is needed. In order to face the imprecision related to these properties, fuzzy sets defined on the domain of computational measures of the corresponding property are usually employed. In this sense, the most interesting approaches show that the combination of different measures as reference sets improve the texture characterization. However, the main drawback of these proposals is that they do not take into account the subjectivity associated with human perception. For example, the perception of a texture property may change depending on the user, and in addition, the image context may influence the global perception of a given property. In this paper, we propose to solve these problems by combining the use of several computational measures in a reference set with adaptation to the subjectivity of human perception. To do this, we propose a generic methodology that automatically transforms any multidimensional fuzzy set modeling a texture property to the particular perception of a new user or to the image context. For this purpose, the information given by the user, or extracted from the textures present in the image, are employed

Modélisation stochastique pour l'analyse d'images texturées (approches Bayésiennes pour la caractérisation dans le domaine des transformées)

Le travail présenté dans cette thèse s inscrit dans le cadre de la modélisation d images texturées à l aide des représentations multi-échelles et multi-orientations. Partant des résultats d études en neurosciences assimilant le mécanisme de la perception humaine à un schéma sélectif spatio-fréquentiel, nous proposons de caractériser les images texturées par des modèles probabilistes associés aux coefficients des sous-bandes. Nos contributions dans ce contexte concernent dans un premier temps la proposition de différents modèles probabilistes permettant de prendre en compte le caractère leptokurtique ainsi que l éventuelle asymétrie des distributions marginales associées à un contenu texturée. Premièrement, afin de modéliser analytiquement les statistiques marginales des sous-bandes, nous introduisons le modèle Gaussien généralisé asymétrique. Deuxièmement, nous proposons deux familles de modèles multivariés afin de prendre en compte les dépendances entre coefficients des sous-bandes. La première famille regroupe les processus à invariance sphérique pour laquelle nous montrons qu il est pertinent d associer une distribution caractéristique de type Weibull. Concernant la seconde famille, il s agit des lois multivariées à copules. Après détermination de la copule caractérisant la structure de la dépendance adaptée à la texture, nous proposons une extension multivariée de la distribution Gaussienne généralisée asymétrique à l aide de la copule Gaussienne. L ensemble des modèles proposés est comparé quantitativement en terme de qualité d ajustement à l aide de tests statistiques d adéquation dans un cadre univarié et multivarié. Enfin, une dernière partie de notre étude concerne la validation expérimentale des performances de nos modèles à travers une application de recherche d images par le contenu textural. Pour ce faire, nous dérivons des expressions analytiques de métriques probabilistes mesurant la similarité entre les modèles introduits, ce qui constitue selon nous une troisième contribution de ce travail. Finalement, une étude comparative est menée visant à confronter les modèles probabilistes proposés à ceux de l état de l art.In this thesis we study the statistical modeling of textured images using multi-scale and multi-orientation representations. Based on the results of studies in neuroscience assimilating the human perception mechanism to a selective spatial frequency scheme, we propose to characterize textures by probabilistic models of subband coefficients.Our contributions in this context consist firstly in the proposition of probabilistic models taking into account the leptokurtic nature and the asymmetry of the marginal distributions associated with a textured content. First, to model analytically the marginal statistics of subbands, we introduce the asymmetric generalized Gaussian model. Second, we propose two families of multivariate models to take into account the dependencies between subbands coefficients. The first family includes the spherically invariant processes that we characterize using Weibull distribution. The second family is this of copula based multivariate models. After determination of the copula characterizing the dependence structure adapted to the texture, we propose a multivariate extension of the asymmetric generalized Gaussian distribution using Gaussian copula. All proposed models are compared quantitatively using both univariate and multivariate statistical goodness of fit tests. Finally, the last part of our study concerns the experimental validation of the performance of proposed models through texture based image retrieval. To do this, we derive closed-form metrics measuring the similarity between probabilistic models introduced, which we believe is the third contribution of this work. A comparative study is conducted to compare the proposed probabilistic models to those of the state-of-the-art.BORDEAUX1-Bib.electronique (335229901) / SudocSudocFranceF

Perception-based fuzzy partitions for visual texture modelling

Visual textures in images are usually described by humans using linguistic terms related to their perceptual properties, like “very coarse”, “low directional”, or “high contrasted”. Computational models with the ability of providing a perceptual texture characterization on the basis of these terms can be very useful in tasks like semantic description of images, content-based image retrieval using linguistic queries, or expert systems design based on low level visual features. In this paper, we address the problem of simulating the human perception of texture, obtaining linguistic labels to describe it in natural language. For this modeling, fuzzy partitions defined on the domain of some of the most representative measures of each property are employed. In order to define the fuzzy partitions, the number of linguistic labels and the parameters of the membership functions are calculated taking into account the relationship between the computational values given by the measures and the human perception of the corresponding property. The performance of each fuzzy partition is analyzed and tested using the human assessments, and a ranking of measures is obtained according to their ability to represent the perception of the property, allowing to identify the most suitable measure

Sustainable Production in Food and Agriculture Engineering

This book is a collection of original research and review papers that report on the state of the art and recent advancements in food and agriculture engineering, such as sustainable production and food technology. Encompassed within are applications in food and agriculture engineering, biosystem engineering, plant and animal production engineering, food and agricultural processing engineering, storing industry, economics and production management and agricultural farms management, agricultural machines and devices, and IT for agricultural engineering and ergonomics in agriculture

An information-theoretic approach to understanding the neural coding of relevant tactile features

Objective: Traditional theories in neuroscience state that tactile afferents present in the glabrous skin of the human hand encode tactile information following a submodality segregation strategy, meaning that each modality (eg. motion, vibration, shape, ... ) is encoded by a different afferent class. Modern theories suggest a submodality convergence instead, in which different afferent classes work together to capture information about the environment through tactile sense. Typically, studies involve electrophysiological recordings of tens of afferents. At the same time, the human hand is filled with around 17.000 afferents. In this thesis, we want to tackle the theoretical gap this poses. Specifically, we aim to address whether the peripheral nervous system relies on population coding to represent tactile information and whether such population coding enables us to disambiguate submodality convergence against the classical segregation. Approach: Understanding the encoding and flow of information in the nervous system is one of the main challenges of modern neuroscience. Neural signals are highly variable and may be non-linear. Moreover, there exist several candidate codes compatible with sensory and behavioral events. For example, they can rely on single cells or populations and also on rate or timing precision. Information-theoretic methods can capture non-linearities while being model independent, statistically robust, and mathematically well-grounded, becoming an ideal candidate to design pipelines for analyzing neural data. Despite information-theoretic methods being powerful for our objective, the vast majority of neural signals we can acquire from living systems makes analyses highly problem-specific. This is so because of the rich variety of biological processes that are involved (continuous, discrete, electrical, chemical, optical, ...). Main results: The first step towards solving the aforementioned challenges was to have a solid methodology we could trust and rely on. Consequently, the first deliverable from this thesis is a toolbox that gathers classical and state-of-the-art information-theoretic approaches and blends them with advanced machine learning tools to process and analyze neural data. Moreover, this toolbox also provides specific guidance on calcium imaging and electrophysiology analyses, encompassing both simulated and experimental data. We then designed an information-theoretic pipeline to analyze large-scale simulations of the tactile afferents that overcomes the current limitations of experimental studies in the field of touch and the peripheral nervous system. We dissected the importance of population coding for the different afferent classes, given their spatiotemporal dynamics. We also demonstrated that different afferent classes encode information simultaneously about very simple features, and that combining classes increases information levels, adding support to the submodality convergence theory. Significance: Fundamental knowledge about touch is essential both to design human-like robots exhibiting naturalistic exploration behavior and prostheses that can properly integrate and provide their user with relevant and useful information to interact with their environment. Demonstrating that the peripheral nervous system relies on heterogeneous population coding can change the designing paradigm of artificial systems, both in terms of which sensors to choose and which algorithms to use, especially in neuromorphic implementations