The focus of this study is the development and evaluation of a new partially supervised learning framework. This framework belongs to an emerging field in machine learning that augments unsupervised learning processes with some elements of supervision. It is based on proximity fuzzy clustering, where an active learning process is designed to query for the domain knowledge required in the supervision. Furthermore, the framework is extended to the parametric optimization of the kernel function in the proximity fuzzy clustering algorithm, where the goal is to achieve interesting non-spherical cluster structures through a non-linear mapping. It is demonstrated that the performance of kernel-based clustering is sensitive to the selection of these kernel parameters. Proximity hints procured from domain knowledge are exploited in the partially supervised framework. The theoretic developments with proximity fuzzy clustering are evaluated in several interesting and practical applications. One such problem is the clustering of a set of graphs based on their structural and semantic similarity. The segmentation of music is a second problem for proximity fuzzy clustering, where the aim is to determine the points in time, i.e. boundaries, of significant structural changes in the music. Finally, a time series prediction problem using a fuzzy rule-based system is established and evaluated. The antecedents of the rules are constructed by clustering the time series using proximity information in order to localize the behavior of the rule consequents in the architecture. Evaluation of these efforts on both synthetic and real-world data demonstrate that proximity fuzzy clustering is well suited for a variety of problems. / Digital Signals and Image Processing

No description available.

In certain areas such as Pharmacokinetic(PK) and Pharmacodynamic(PD), the hazard rate function, denoted by ??, plays a central role in modeling the instantaneous risk of failure time data. In the context of assessing the appropriateness of a given parametric hazard rate model, Huh and Hutmacher [22] showed that their hazard-based visual predictive check is as good as a visual predictive check based on the survival function. Even though Huh and Hutmacher’s visual method is simple to implement and interpret, the final decision reached there depends on the personal experience of the user. In this thesis, our primary aim is to develop nonparametric goodness-ofit tests for hazard rate functions to help bring objectivity in hazard rate model selections or to augment subjective procedures like Huh and Hutmacher’s visual predictive check. Toward that aim two nonparametric goodnessofit (g-o) test statistics are proposed and they are referred to as chi-square g-o test and kernel-based nonparametric goodness-ofit test for hazard rate functions, respectively. On one hand, the asymptotic distribution of the chi-square goodness-ofit test for hazard rate functions is derived under the null hypothesis ??0 : ??(??) = ??0(??) ??? ? R + as well as under the fixed alternative hypothesis ??1 : ??(??) = ??1(??) ??? ? R +. The results as expected are asymptotically similar to those of the usual Pearson chi-square test. That is, under the null hypothesis the proposed test converges to a chi-square distribution and under the fixed alternative hypothesis it converges to a non-central chi-square distribution. On the other hand, we showed that the power properties of the kernel-based nonparametric goodness-ofit test for hazard rate functions are equivalent to those of the Bickel and Rosenblatt test, meaning the proposed kernel-based nonparametric goodness-ofit test can detect alternatives converging to the null at the rate of ???? , ?? < 1/2, where ?? is the sample size. Unlike the latter, the convergence rate of the kernel-base nonparametric g-o test is much greater; that is, one does not need a very large sample size for able to use the asymptotic distribution of the test in practice.

Detection of multiple-lane markings (lane-line) on road surfaces is an essential aspect of autonomous vehicles. Although several approaches have been proposed to detect lanes, detecting multiple lane-lines consistently, particularly across a stream of frames and under varying lighting conditions is still a challenging problem. Since the road's markings are designed to be smooth and parallel, lane-line sampled features tend to be spatially and temporally correlated inside and between frames. In this thesis, we develop novel methods to model these spatial and temporal dependencies in the form of the target tracking problem. In fact, instead of resorting to the conventional method of processing each frame to detect lanes only in the space domain, we treat the overall problem as a Multiple Extended Target Tracking (METT) problem. In the first step, we modelled lane-lines as multiple "independent" extended targets and developed a spline mathematical model for the shape of the targets. We showed that expanding the estimations across the time domain could improve the result of estimation. We identify a set of control points for each spline, which will track over time. To overcome the clutter problem, we developed an integrated probabilistic data association fi lter (IPDAF) as our basis, and formulated a METT algorithm to track multiple splines corresponding to each lane-line.In the second part of our work, we investigated the coupling between multiple extended targets. We considered the non-parametric case and modeled target dependency using the Multi-Output Gaussian Process. We showed that considering dependency between extended targets could improve shape estimation results. We exploit the dependency between extended targets by proposing a novel recursive approach called the Multi-Output Spatio-Temporal Gaussian Process Kalman Filter (MO-STGP-KF). We used MO-STGP-KF to estimate and track multiple dependent lane markings that are possibly degraded or obscured by traffic. Our method tested for tracking multiple lane-lines but can be employed to track multiple dependent rigid-shape targets by using the measurement model in the radial space In the third section, we developed a Spatio-Temporal Joint Probabilistic Data Association Filter (ST-JPDAF). In multiple extended target tracking problems with clutter, sometimes extended targets share measurements: for example, in lane-line detection, when two-lane markings pass or merge together. In single-point target tracking, this problem can be solved using the famous Joint Probabilistic Data Association (JPDA) filter. In the single-point case, even when measurements are dependent, we can stack them in the coupled form of JPDA. In this last chapter, we expanded JPDA for tracking multiple dependent extended targets using an approach called ST-JPDAF. We managed dependency of measurements in space (inside a frame) and time (between frames) using different kernel functions, which can be learned using the trained data. This extension can be used to track the shape and dynamic of dependent extended targets within clutter when targets share measurements. The performance of the proposed methods in all three chapters are quanti ed on real data scenarios and their results are compared against well-known model-based, semi-supervised, and fully-supervised methods. The proposed methods offer very promising results. / Thesis / Doctor of Philosophy (PhD)

Diffusion Tensor MRI can be used to depict the anisotropy of tissue. Translation of this technique to moving objects such as the beating heart has recently become feasible, but remains a challenging task, often leading to high noise levels and limited accuracy. Ultimately, knowledge of the 3D fibre architecture of the myocardium invivo should allow for a better understanding of the cardiac function both in healthy and pathological situations. The main goal of the work presented in this thesis is to overcome the difficulties that such technology presents, by introducing a combination of image processing and analysis approaches. In particular, the characteristic ellipsoidal shape of the left ventricular chamber is used to introduce a shape-based prolate spheroidal coordinate frame that allows for comprehensive, robust and dedicated analysis of diffusion tensor data within the myocardial wall. It is shown that the description of this information is more compact in this coordinate frame. Furthermore, it is demonstrated that the acquisition limitations can be overcome by introducing an approximation scheme based on this coordinate frame. These techniques are tested on ex-vivo datasets to assess their fidelity and sensitivity. Finally, these techniques are applied in-vivo on a group of healthy volunteers, where 2D DTI slices of the LV were acquired at end diastole and end systole, using cardiac dedicated diffusion MR acquisition. Results demonstrate the advantages of using curvilinear coordinates both for the analysis and the approximation of cardiac DTI information. Resulting in-vivo fibre architectures were found to agree with previously reported studies on ex-vivo specimens. The outcome of this work can open the door for clinical applications and cardiac electrophysiology modelling, and improve the understanding of the left ventricular structure and dynamics.

The present Ph.D. thesis, primarily conceived to support and reinforce the relation between academic and industrial worlds, was developed in collaboration with Shell Global Solutions (Amsterdam, The Netherlands) in the endeavour of applying and possibly extending well-established latent variable-based approaches (i.e. Principal Component Analysis - PCA - Partial Least Squares regression - PLS - or Partial Least Squares Discriminant Analysis - PLSDA) for complex problem solving not only in the fields of manufacturing troubleshooting and optimisation, but also in the wider environment of multivariate data analysis. To this end, novel efficient algorithmic solutions are proposed throughout all chapters to address very disparate tasks, from calibration transfer in spectroscopy to real-time modelling of streaming flows of data. The manuscript is divided into the following six parts, focused on various topics of interest: Part I - Preface, where an overview of this research work, its main aims and justification is given together with a brief introduction on PCA, PLS and PLSDA; Part II - On kernel-based extensions of PCA, PLS and PLSDA, where the potential of kernel techniques, possibly coupled to specific variants of the recently rediscovered pseudo-sample projection, formulated by the English statistician John C. Gower, is explored and their performance compared to that of more classical methodologies in four different applications scenarios: segmentation of Red-Green-Blue (RGB) images, discrimination of on-/off-specification batch runs, monitoring of batch processes and analysis of mixture designs of experiments; Part III - On the selection of the number of factors in PCA by permutation testing, where an extensive guideline on how to accomplish the selection of PCA components by permutation testing is provided through the comprehensive illustration of an original algorithmic procedure implemented for such a purpose; Part IV - On modelling common and distinctive sources of variability in multi-set data analysis, where several practical aspects of two-block common and distinctive component analysis (carried out by methods like Simultaneous Component Analysis - SCA - DIStinctive and COmmon Simultaneous Component Analysis - DISCO-SCA - Adapted Generalised Singular Value Decomposition - Adapted GSVD - ECO-POWER, Canonical Correlation Analysis - CCA - and 2-block Orthogonal Projections to Latent Structures - O2PLS) are discussed, a new computational strategy for determining the number of common factors underlying two data matrices sharing the same row- or column-dimension is described, and two innovative approaches for calibration transfer between near-infrared spectrometers are presented; Part V - On the on-the-fly processing and modelling of continuous high-dimensional data streams, where a novel software system for rational handling of multi-channel measurements recorded in real time, the On-The-Fly Processing (OTFP) tool, is designed; Part VI - Epilogue, where final conclusions are drawn, future perspectives are delineated, and annexes are included. / La presente tesis doctoral, concebida principalmente para apoyar y reforzar la relación entre la academia y la industria, se desarrolló en colaboración con Shell Global Solutions (Amsterdam, Países Bajos) en el esfuerzo de aplicar y posiblemente extender los enfoques ya consolidados basados en variables latentes (es decir, Análisis de Componentes Principales - PCA - Regresión en Mínimos Cuadrados Parciales - PLS - o PLS discriminante - PLSDA) para la resolución de problemas complejos no sólo en los campos de mejora y optimización de procesos, sino también en el entorno más amplio del análisis de datos multivariados. Con este fin, en todos los capítulos proponemos nuevas soluciones algorítmicas eficientes para abordar tareas dispares, desde la transferencia de calibración en espectroscopia hasta el modelado en tiempo real de flujos de datos. El manuscrito se divide en las seis partes siguientes, centradas en diversos temas de interés: Parte I - Prefacio, donde presentamos un resumen de este trabajo de investigación, damos sus principales objetivos y justificaciones junto con una breve introducción sobre PCA, PLS y PLSDA; Parte II - Sobre las extensiones basadas en kernels de PCA, PLS y PLSDA, donde presentamos el potencial de las técnicas de kernel, eventualmente acopladas a variantes específicas de la recién redescubierta proyección de pseudo-muestras, formulada por el estadista inglés John C. Gower, y comparamos su rendimiento respecto a metodologías más clásicas en cuatro aplicaciones a escenarios diferentes: segmentación de imágenes Rojo-Verde-Azul (RGB), discriminación y monitorización de procesos por lotes y análisis de diseños de experimentos de mezclas; Parte III - Sobre la selección del número de factores en el PCA por pruebas de permutación, donde aportamos una guía extensa sobre cómo conseguir la selección de componentes de PCA mediante pruebas de permutación y una ilustración completa de un procedimiento algorítmico original implementado para tal fin; Parte IV - Sobre la modelización de fuentes de variabilidad común y distintiva en el análisis de datos multi-conjunto, donde discutimos varios aspectos prácticos del análisis de componentes comunes y distintivos de dos bloques de datos (realizado por métodos como el Análisis Simultáneo de Componentes - SCA - Análisis Simultáneo de Componentes Distintivos y Comunes - DISCO-SCA - Descomposición Adaptada Generalizada de Valores Singulares - Adapted GSVD - ECO-POWER, Análisis de Correlaciones Canónicas - CCA - y Proyecciones Ortogonales de 2 conjuntos a Estructuras Latentes - O2PLS). Presentamos a su vez una nueva estrategia computacional para determinar el número de factores comunes subyacentes a dos matrices de datos que comparten la misma dimensión de fila o columna y dos planteamientos novedosos para la transferencia de calibración entre espectrómetros de infrarrojo cercano; Parte V - Sobre el procesamiento y la modelización en tiempo real de flujos de datos de alta dimensión, donde diseñamos la herramienta de Procesamiento en Tiempo Real (OTFP), un nuevo sistema de manejo racional de mediciones multi-canal registradas en tiempo real; Parte VI - Epílogo, donde presentamos las conclusiones finales, delimitamos las perspectivas futuras, e incluimos los anexos. / La present tesi doctoral, concebuda principalment per a recolzar i reforçar la relació entre l'acadèmia i la indústria, es va desenvolupar en col·laboració amb Shell Global Solutions (Amsterdam, Països Baixos) amb l'esforç d'aplicar i possiblement estendre els enfocaments ja consolidats basats en variables latents (és a dir, Anàlisi de Components Principals - PCA - Regressió en Mínims Quadrats Parcials - PLS - o PLS discriminant - PLSDA) per a la resolució de problemes complexos no solament en els camps de la millora i optimització de processos, sinó també en l'entorn més ampli de l'anàlisi de dades multivariades. A aquest efecte, en tots els capítols proposem noves solucions algorítmiques eficients per a abordar tasques dispars, des de la transferència de calibratge en espectroscopia fins al modelatge en temps real de fluxos de dades. El manuscrit es divideix en les sis parts següents, centrades en diversos temes d'interès: Part I - Prefaci, on presentem un resum d'aquest treball de recerca, es donen els seus principals objectius i justificacions juntament amb una breu introducció sobre PCA, PLS i PLSDA; Part II - Sobre les extensions basades en kernels de PCA, PLS i PLSDA, on presentem el potencial de les tècniques de kernel, eventualment acoblades a variants específiques de la recentment redescoberta projecció de pseudo-mostres, formulada per l'estadista anglés John C. Gower, i comparem el seu rendiment respecte a metodologies més clàssiques en quatre aplicacions a escenaris diferents: segmentació d'imatges Roig-Verd-Blau (RGB), discriminació i monitorització de processos per lots i anàlisi de dissenys d'experiments de mescles; Part III - Sobre la selecció del nombre de factors en el PCA per proves de permutació, on aportem una guia extensa sobre com aconseguir la selecció de components de PCA a través de proves de permutació i una il·lustració completa d'un procediment algorítmic original implementat per a la finalitat esmentada; Part IV - Sobre la modelització de fonts de variabilitat comuna i distintiva en l'anàlisi de dades multi-conjunt, on discutim diversos aspectes pràctics de l'anàlisis de components comuns i distintius de dos blocs de dades (realitzat per mètodes com l'Anàlisi Simultània de Components - SCA - Anàlisi Simultània de Components Distintius i Comuns - DISCO-SCA - Descomposició Adaptada Generalitzada en Valors Singulars - Adapted GSVD - ECO-POWER, Anàlisi de Correlacions Canòniques - CCA - i Projeccions Ortogonals de 2 blocs a Estructures Latents - O2PLS). Presentem al mateix temps una nova estratègia computacional per a determinar el nombre de factors comuns subjacents a dues matrius de dades que comparteixen la mateixa dimensió de fila o columna, i dos plantejaments nous per a la transferència de calibratge entre espectròmetres d'infraroig proper; Part V - Sobre el processament i la modelització en temps real de fluxos de dades d'alta dimensió, on dissenyem l'eina de Processament en Temps Real (OTFP), un nou sistema de tractament racional de mesures multi-canal registrades en temps real; Part VI - Epíleg, on presentem les conclusions finals, delimitem les perspectives futures, i incloem annexos. / Vitale, R. (2017). Novel chemometric proposals for advanced multivariate data analysis, processing and interpretation [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/90442

No description available.

Nous proposons une approche spectrale permettant d'aborder des problèmes d'interpolation à noyaux dont la résolution numérique n'est pas directement envisageable. Un tel cas de figure se produit en particulier lorsque le nombre de données est infini. Nous considérons dans un premier temps le cadre de l'interpolation optimale dans les sous-espaces hilbertiens. Pour un problème donné, un opérateur intégral est défini à partir du noyau sous-jacent et d'une paramétrisation de l'ensemble des données basée sur un espace mesuré. La décomposition spectrale de l'opérateur est utilisée afin d'obtenir une formule de représentation pour l'interpolateur optimal et son approximation est alors rendu possible par troncature du spectre. Le choix de la mesure induit une fonction d'importance sur l'ensemble des données qui se traduit, en cas d'approximation, par une plus ou moins grande précision dans le rendu des données. Nous montrons à titre d'exemple comment cette approche peut être utilisée afin de rendre compte de contraintes de type "conditions aux limites" dans les modèles d'interpolation à noyaux. Le problème du conditionnement des processus gaussiens est également étudié dans ce contexte. Nous abordons enfin dans la dernière partie de notre manuscrit la notion de noyaux conditionnellement positifs. Nous proposons la définition générale de noyaux symétriques conditionnellement positifs relatifs à une espace de référence donné et développons la théorie des sous-espaces semi-hilbertiens leur étant associés. Nous étudions finalement la théorie de l'interpolation optimale dans cette classe d'espaces. / We propose a spectral approach for the resolution of kernel-based interpolation problems of which numerical solution can not be directly computed. Such a situation occurs in particular when the number of data is infinite. We first consider optimal interpolation in Hilbert subspaces. For a given problem, an integral operator is defined from the underlying kernel and a parameterization of the data set based on a measurable space. The spectral decomposition of the operator is used in order to obtain a representation formula for the optimal interpolator and spectral truncation allows its approximation. The choice of the measure on the parameters space introduces a hierarchy onto the data set which allows a tunable precision of the approximation. As an example, we show how this methodology can be used in order to enforce boundary conditions in kernel-based interpolation models. The Gaussian processes conditioning problem is also studied in this context. The last part of this thesis is devoted to the notion of conditionally positive kernels. We propose a general definition of symmetric conditionally positive kernels relative to a given space and exposed the associated theory of semi-Hilbert subspaces. We finally study the optimal interpolation problem in such spaces.

Cette thèse aborde le processus ponctuel déterminantal, un modèle probabiliste qui capture la répulsion entre les points d’un certain espace. Celle-ci est déterminée par une matrice de similarité, la matrice noyau du processus, qui spécifie quels points sont les plus similaires et donc moins susceptibles de figurer dans un même sous-ensemble. Contrairement à la sélection aléatoire uniforme, ce processus ponctuel privilégie les sous-ensembles qui contiennent des points diversifiés et hétérogènes. La notion de diversité acquiert une importante grandissante au sein de sciences comme la médecine, la sociologie, les sciences forensiques et les sciences comportementales. Le processus ponctuel déterminantal offre donc une alternative aux traditionnelles méthodes d’échantillonnage en tenant compte de la diversité des éléments choisis. Actuellement, il est déjà très utilisé en apprentissage automatique comme modèle de sélection de sous-ensembles. Son application en statistique est illustrée par trois articles. Le premier article aborde le partitionnement de données effectué par un algorithme répété un grand nombre de fois sur les mêmes données, le partitionnement par consensus. On montre qu’en utilisant le processus ponctuel déterminantal pour sélectionner les points initiaux de l’algorithme, la partition de données finale a une qualité supérieure à celle que l’on obtient en sélectionnant les points de façon uniforme. Le deuxième article étend la méthodologie du premier article aux données ayant un grand nombre d’observations. Ce cas impose un effort computationnel additionnel, étant donné que la sélection de points par le processus ponctuel déterminantal passe par la décomposition spectrale de la matrice de similarité qui, dans ce cas-ci, est de grande taille. On présente deux approches différentes pour résoudre ce problème. On montre que les résultats obtenus par ces deux approches sont meilleurs que ceux obtenus avec un partitionnement de données basé sur une sélection uniforme de points. Le troisième article présente le problème de sélection de variables en régression linéaire et logistique face à un nombre élevé de covariables par une approche bayésienne. La sélection de variables est faite en recourant aux méthodes de Monte Carlo par chaînes de Markov, en utilisant l’algorithme de Metropolis-Hastings. On montre qu’en choisissant le processus ponctuel déterminantal comme loi a priori de l’espace des modèles, le sous-ensemble final de variables est meilleur que celui que l’on obtient avec une loi a priori uniforme. / This thesis presents the determinantal point process, a probabilistic model that captures repulsion between points of a certain space. This repulsion is encompassed by a similarity matrix, the kernel matrix, which selects which points are more similar and then less likely to appear in the same subset. This point process gives more weight to subsets characterized by a larger diversity of its elements, which is not the case with the traditional uniform random sampling. Diversity has become a key concept in domains such as medicine, sociology, forensic sciences and behavioral sciences. The determinantal point process is considered a promising alternative to traditional sampling methods, since it takes into account the diversity of selected elements. It is already actively used in machine learning as a subset selection method. Its application in statistics is illustrated with three papers. The first paper presents the consensus clustering, which consists in running a clustering algorithm on the same data, a large number of times. To sample the initials points of the algorithm, we propose the determinantal point process as a sampling method instead of a uniform random sampling and show that the former option produces better clustering results. The second paper extends the methodology developed in the first paper to large-data. Such datasets impose a computational burden since sampling with the determinantal point process is based on the spectral decomposition of the large kernel matrix. We introduce two methods to deal with this issue. These methods also produce better clustering results than consensus clustering based on a uniform sampling of initial points. The third paper addresses the problem of variable selection for the linear model and the logistic regression, when the number of predictors is large. A Bayesian approach is adopted, using Markov Chain Monte Carlo methods with Metropolis-Hasting algorithm. We show that setting the determinantal point process as the prior distribution for the model space selects a better final model than the model selected by a uniform prior on the model space.