Applying machine learning methods to avalanche forecasting

Avalanche forecasting is a complex process involving the assimilation of multiple data sources to make predictions over varying spatial and temporal resolutions. Numerically assisted forecasting often uses nearest neighbour methods (NN), which are known to have limitations when dealing with high dimensional data. We apply Support Vector Machines to a dataset from Lochaber, Scotland to assess their applicability in avalanche forecasting. Support Vector Machines (SVMs) belong to a family of theoretically based techniques from machine learning and are designed to deal with high dimensional data. Initial experiments showed that SVMs gave results which were comparable with NN for categorical and probabilistic forecasts. Experiments utilising the ability of SVMs to deal with high dimensionality in producing a spatial forecast show promise, but require further work.

Modelling ecological niches with support vector machines

1. The ecological niche is a fundamental biological concept. Modelling species' niches is central to numerous ecological applications, including predicting species invasions, identifying reservoirs for disease, nature reserve design and forecasting the effects of anthropogenic and natural climate change on species' ranges. 2. A computational analogue of Hutchinson's ecological niche concept (the multidimensional hyperspace of species' environmental requirements) is the support of the distribution of environments in which the species persist. Recently developed machine-learning algorithms can estimate the support of such high-dimensional distributions. We show how support vector machines can be used to map ecological niches using only observations of species presence to train distribution models for 106 species of woody plants and trees in a montane environment using up to nine environmental covariates. 3. We compared the accuracy of three methods that differ in their approaches to reducing model complexity. We tested models with independent observations of both species presence and species absence. We found that the simplest procedure, which uses all available variables and no pre-processing to reduce correlation, was best overall. Ecological niche models based on support vector machines are theoretically superior to models that rely on simulating pseudo-absence data and are comparable in empirical tests. 4. Synthesis and applications. Accurate species distribution models are crucial for effective environmental planning, management and conservation, and for unravelling the role of the environment in human health and welfare. Models based on distribution estimation rather than classification overcome theoretical and practical obstacles that pervade species distribution modelling. In particular, ecological niche models based on machine-learning algorithms for estimating the support of a statistical distribution provide a promising new approach to identifying species' potential distributions and to project changes in these distributions as a result of climate change, land use and landscape alteration.

Machine learning for geospatial data : algorithms, software tools and case studies

Résumé Cette thèse est consacrée à l'analyse, la modélisation et la visualisation de données environnementales à référence spatiale à l'aide d'algorithmes d'apprentissage automatique (Machine Learning). L'apprentissage automatique peut être considéré au sens large comme une sous-catégorie de l'intelligence artificielle qui concerne particulièrement le développement de techniques et d'algorithmes permettant à une machine d'apprendre à partir de données. Dans cette thèse, les algorithmes d'apprentissage automatique sont adaptés pour être appliqués à des données environnementales et à la prédiction spatiale. Pourquoi l'apprentissage automatique ? Parce que la majorité des algorithmes d'apprentissage automatiques sont universels, adaptatifs, non-linéaires, robustes et efficaces pour la modélisation. Ils peuvent résoudre des problèmes de classification, de régression et de modélisation de densité de probabilités dans des espaces à haute dimension, composés de variables informatives spatialisées (« géo-features ») en plus des coordonnées géographiques. De plus, ils sont idéaux pour être implémentés en tant qu'outils d'aide à la décision pour des questions environnementales allant de la reconnaissance de pattern à la modélisation et la prédiction en passant par la cartographie automatique. Leur efficacité est comparable au modèles géostatistiques dans l'espace des coordonnées géographiques, mais ils sont indispensables pour des données à hautes dimensions incluant des géo-features. Les algorithmes d'apprentissage automatique les plus importants et les plus populaires sont présentés théoriquement et implémentés sous forme de logiciels pour les sciences environnementales. Les principaux algorithmes décrits sont le Perceptron multicouches (MultiLayer Perceptron, MLP) - l'algorithme le plus connu dans l'intelligence artificielle, le réseau de neurones de régression généralisée (General Regression Neural Networks, GRNN), le réseau de neurones probabiliste (Probabilistic Neural Networks, PNN), les cartes auto-organisées (SelfOrganized Maps, SOM), les modèles à mixture Gaussiennes (Gaussian Mixture Models, GMM), les réseaux à fonctions de base radiales (Radial Basis Functions Networks, RBF) et les réseaux à mixture de densité (Mixture Density Networks, MDN). Cette gamme d'algorithmes permet de couvrir des tâches variées telle que la classification, la régression ou l'estimation de densité de probabilité. L'analyse exploratoire des données (Exploratory Data Analysis, EDA) est le premier pas de toute analyse de données. Dans cette thèse les concepts d'analyse exploratoire de données spatiales (Exploratory Spatial Data Analysis, ESDA) sont traités selon l'approche traditionnelle de la géostatistique avec la variographie expérimentale et selon les principes de l'apprentissage automatique. La variographie expérimentale, qui étudie les relations entre pairs de points, est un outil de base pour l'analyse géostatistique de corrélations spatiales anisotropiques qui permet de détecter la présence de patterns spatiaux descriptible par une statistique. L'approche de l'apprentissage automatique pour l'ESDA est présentée à travers l'application de la méthode des k plus proches voisins qui est très simple et possède d'excellentes qualités d'interprétation et de visualisation. Une part importante de la thèse traite de sujets d'actualité comme la cartographie automatique de données spatiales. Le réseau de neurones de régression généralisée est proposé pour résoudre cette tâche efficacement. Les performances du GRNN sont démontrées par des données de Comparaison d'Interpolation Spatiale (SIC) de 2004 pour lesquelles le GRNN bat significativement toutes les autres méthodes, particulièrement lors de situations d'urgence. La thèse est composée de quatre chapitres : théorie, applications, outils logiciels et des exemples guidés. Une partie importante du travail consiste en une collection de logiciels : Machine Learning Office. Cette collection de logiciels a été développée durant les 15 dernières années et a été utilisée pour l'enseignement de nombreux cours, dont des workshops internationaux en Chine, France, Italie, Irlande et Suisse ainsi que dans des projets de recherche fondamentaux et appliqués. Les cas d'études considérés couvrent un vaste spectre de problèmes géoenvironnementaux réels à basse et haute dimensionnalité, tels que la pollution de l'air, du sol et de l'eau par des produits radioactifs et des métaux lourds, la classification de types de sols et d'unités hydrogéologiques, la cartographie des incertitudes pour l'aide à la décision et l'estimation de risques naturels (glissements de terrain, avalanches). Des outils complémentaires pour l'analyse exploratoire des données et la visualisation ont également été développés en prenant soin de créer une interface conviviale et facile à l'utilisation. Machine Learning for geospatial data: algorithms, software tools and case studies Abstract The thesis is devoted to the analysis, modeling and visualisation of spatial environmental data using machine learning algorithms. In a broad sense machine learning can be considered as a subfield of artificial intelligence. It mainly concerns with the development of techniques and algorithms that allow computers to learn from data. In this thesis machine learning algorithms are adapted to learn from spatial environmental data and to make spatial predictions. Why machine learning? In few words most of machine learning algorithms are universal, adaptive, nonlinear, robust and efficient modeling tools. They can find solutions for the classification, regression, and probability density modeling problems in high-dimensional geo-feature spaces, composed of geographical space and additional relevant spatially referenced features. They are well-suited to be implemented as predictive engines in decision support systems, for the purposes of environmental data mining including pattern recognition, modeling and predictions as well as automatic data mapping. They have competitive efficiency to the geostatistical models in low dimensional geographical spaces but are indispensable in high-dimensional geo-feature spaces. The most important and popular machine learning algorithms and models interesting for geo- and environmental sciences are presented in details: from theoretical description of the concepts to the software implementation. The main algorithms and models considered are the following: multi-layer perceptron (a workhorse of machine learning), general regression neural networks, probabilistic neural networks, self-organising (Kohonen) maps, Gaussian mixture models, radial basis functions networks, mixture density networks. This set of models covers machine learning tasks such as classification, regression, and density estimation. Exploratory data analysis (EDA) is initial and very important part of data analysis. In this thesis the concepts of exploratory spatial data analysis (ESDA) is considered using both traditional geostatistical approach such as_experimental variography and machine learning. Experimental variography is a basic tool for geostatistical analysis of anisotropic spatial correlations which helps to understand the presence of spatial patterns, at least described by two-point statistics. A machine learning approach for ESDA is presented by applying the k-nearest neighbors (k-NN) method which is simple and has very good interpretation and visualization properties. Important part of the thesis deals with a hot topic of nowadays, namely, an automatic mapping of geospatial data. General regression neural networks (GRNN) is proposed as efficient model to solve this task. Performance of the GRNN model is demonstrated on Spatial Interpolation Comparison (SIC) 2004 data where GRNN model significantly outperformed all other approaches, especially in case of emergency conditions. The thesis consists of four chapters and has the following structure: theory, applications, software tools, and how-to-do-it examples. An important part of the work is a collection of software tools - Machine Learning Office. Machine Learning Office tools were developed during last 15 years and was used both for many teaching courses, including international workshops in China, France, Italy, Ireland, Switzerland and for realizing fundamental and applied research projects. Case studies considered cover wide spectrum of the real-life low and high-dimensional geo- and environmental problems, such as air, soil and water pollution by radionuclides and heavy metals, soil types and hydro-geological units classification, decision-oriented mapping with uncertainties, natural hazards (landslides, avalanches) assessments and susceptibility mapping. Complementary tools useful for the exploratory data analysis and visualisation were developed as well. The software is user friendly and easy to use.

Spatial prediction of monthly wind speeds in complex terrain with adaptive general regression neural networks

This paper presents the general regression neural networks (GRNN) as a nonlinear regression method for the interpolation of monthly wind speeds in complex Alpine orography. GRNN is trained using data coming from Swiss meteorological networks to learn the statistical relationship between topographic features and wind speed. The terrain convexity, slope and exposure are considered by extracting features from the digital elevation model at different spatial scales using specialised convolution filters. A database of gridded monthly wind speeds is then constructed by applying GRNN in prediction mode during the period 1968-2008. This study demonstrates that using topographic features as inputs in GRNN significantly reduces cross-validation errors with respect to low-dimensional models integrating only geographical coordinates and terrain height for the interpolation of wind speed. The spatial predictability of wind speed is found to be lower in summer than in winter due to more complex and weaker wind-topography relationships. The relevance of these relationships is studied using an adaptive version of the GRNN algorithm which allows to select the useful terrain features by eliminating the noisy ones. This research provides a framework for extending the low-dimensional interpolation models to high-dimensional spaces by integrating additional features accounting for the topographic conditions at multiple spatial scales. Copyright (c) 2012 Royal Meteorological Society.

Fuzzy Principal Components Analysis

Due to the large number of characteristics, there is a need to extract the most relevant characteristicsfrom the input data, so that the amount of information lost in this way is minimal, and the classification realized with the projected data set is relevant with respect to the original data. In order to achieve this feature extraction, different statistical techniques, as well as the principal components analysis (PCA) may be used. This thesis describes an extension of principal components analysis (PCA) allowing the extraction ofa finite number of relevant features from high-dimensional fuzzy data and noisy data. PCA finds linear combinations of the original measurement variables that describe the significant variation in the data. The comparisonof the two proposed methods was produced by using postoperative patient data. Experiment results demonstrate the ability of using the proposed two methods in complex data. Fuzzy PCA was used in the classificationproblem. The classification was applied by using the similarity classifier algorithm where total similarity measures weights are optimized with differential evolution algorithm. This thesis presents the comparison of the classification results based on the obtained data from the fuzzy PCA.

COMPASS identifies T-cell subsets correlated with clinical outcomes.

Advances in flow cytometry and other single-cell technologies have enabled high-dimensional, high-throughput measurements of individual cells as well as the interrogation of cell population heterogeneity. However, in many instances, computational tools to analyze the wealth of data generated by these technologies are lacking. Here, we present a computational framework for unbiased combinatorial polyfunctionality analysis of antigen-specific T-cell subsets (COMPASS). COMPASS uses a Bayesian hierarchical framework to model all observed cell subsets and select those most likely to have antigen-specific responses. Cell-subset responses are quantified by posterior probabilities, and human subject-level responses are quantified by two summary statistics that describe the quality of an individual's polyfunctional response and can be correlated directly with clinical outcome. Using three clinical data sets of cytokine production, we demonstrate how COMPASS improves characterization of antigen-specific T cells and reveals cellular 'correlates of protection/immunity' in the RV144 HIV vaccine efficacy trial that are missed by other methods. COMPASS is available as open-source software.

Adaptive MCMC methods with applications in environmental and geophysical models

This work presents new, efficient Markov chain Monte Carlo (MCMC) simulation methods for statistical analysis in various modelling applications. When using MCMC methods, the model is simulated repeatedly to explore the probability distribution describing the uncertainties in model parameters and predictions. In adaptive MCMC methods based on the Metropolis-Hastings algorithm, the proposal distribution needed by the algorithm learns from the target distribution as the simulation proceeds. Adaptive MCMC methods have been subject of intensive research lately, as they open a way for essentially easier use of the methodology. The lack of user-friendly computer programs has been a main obstacle for wider acceptance of the methods. This work provides two new adaptive MCMC methods: DRAM and AARJ. The DRAM method has been built especially to work in high dimensional and non-linear problems. The AARJ method is an extension to DRAM for model selection problems, where the mathematical formulation of the model is uncertain and we want simultaneously to fit several different models to the same observations. The methods were developed while keeping in mind the needs of modelling applications typical in environmental sciences. The development work has been pursued while working with several application projects. The applications presented in this work are: a winter time oxygen concentration model for Lake Tuusulanjärvi and adaptive control of the aerator; a nutrition model for Lake Pyhäjärvi and lake management planning; validation of the algorithms of the GOMOS ozone remote sensing instrument on board the Envisat satellite of European Space Agency and the study of the effects of aerosol model selection on the GOMOS algorithm.

Error models in hydrogeology applications

Notre consommation en eau souterraine, en particulier comme eau potable ou pour l'irrigation, a considérablement augmenté au cours des années. De nombreux problèmes font alors leur apparition, allant de la prospection de nouvelles ressources à la remédiation des aquifères pollués. Indépendamment du problème hydrogéologique considéré, le principal défi reste la caractérisation des propriétés du sous-sol. Une approche stochastique est alors nécessaire afin de représenter cette incertitude en considérant de multiples scénarios géologiques et en générant un grand nombre de réalisations géostatistiques. Nous rencontrons alors la principale limitation de ces approches qui est le coût de calcul dû à la simulation des processus d'écoulements complexes pour chacune de ces réalisations. Dans la première partie de la thèse, ce problème est investigué dans le contexte de propagation de l'incertitude, oú un ensemble de réalisations est identifié comme représentant les propriétés du sous-sol. Afin de propager cette incertitude à la quantité d'intérêt tout en limitant le coût de calcul, les méthodes actuelles font appel à des modèles d'écoulement approximés. Cela permet l'identification d'un sous-ensemble de réalisations représentant la variabilité de l'ensemble initial. Le modèle complexe d'écoulement est alors évalué uniquement pour ce sousensemble, et, sur la base de ces réponses complexes, l'inférence est faite. Notre objectif est d'améliorer la performance de cette approche en utilisant toute l'information à disposition. Pour cela, le sous-ensemble de réponses approximées et exactes est utilisé afin de construire un modèle d'erreur, qui sert ensuite à corriger le reste des réponses approximées et prédire la réponse du modèle complexe. Cette méthode permet de maximiser l'utilisation de l'information à disposition sans augmentation perceptible du temps de calcul. La propagation de l'incertitude est alors plus précise et plus robuste. La stratégie explorée dans le premier chapitre consiste à apprendre d'un sous-ensemble de réalisations la relation entre les modèles d'écoulement approximé et complexe. Dans la seconde partie de la thèse, cette méthodologie est formalisée mathématiquement en introduisant un modèle de régression entre les réponses fonctionnelles. Comme ce problème est mal posé, il est nécessaire d'en réduire la dimensionnalité. Dans cette optique, l'innovation du travail présenté provient de l'utilisation de l'analyse en composantes principales fonctionnelles (ACPF), qui non seulement effectue la réduction de dimensionnalités tout en maximisant l'information retenue, mais permet aussi de diagnostiquer la qualité du modèle d'erreur dans cet espace fonctionnel. La méthodologie proposée est appliquée à un problème de pollution par une phase liquide nonaqueuse et les résultats obtenus montrent que le modèle d'erreur permet une forte réduction du temps de calcul tout en estimant correctement l'incertitude. De plus, pour chaque réponse approximée, une prédiction de la réponse complexe est fournie par le modèle d'erreur. Le concept de modèle d'erreur fonctionnel est donc pertinent pour la propagation de l'incertitude, mais aussi pour les problèmes d'inférence bayésienne. Les méthodes de Monte Carlo par chaîne de Markov (MCMC) sont les algorithmes les plus communément utilisés afin de générer des réalisations géostatistiques en accord avec les observations. Cependant, ces méthodes souffrent d'un taux d'acceptation très bas pour les problèmes de grande dimensionnalité, résultant en un grand nombre de simulations d'écoulement gaspillées. Une approche en deux temps, le "MCMC en deux étapes", a été introduite afin d'éviter les simulations du modèle complexe inutiles par une évaluation préliminaire de la réalisation. Dans la troisième partie de la thèse, le modèle d'écoulement approximé couplé à un modèle d'erreur sert d'évaluation préliminaire pour le "MCMC en deux étapes". Nous démontrons une augmentation du taux d'acceptation par un facteur de 1.5 à 3 en comparaison avec une implémentation classique de MCMC. Une question reste sans réponse : comment choisir la taille de l'ensemble d'entrainement et comment identifier les réalisations permettant d'optimiser la construction du modèle d'erreur. Cela requiert une stratégie itérative afin que, à chaque nouvelle simulation d'écoulement, le modèle d'erreur soit amélioré en incorporant les nouvelles informations. Ceci est développé dans la quatrième partie de la thèse, oú cette méthodologie est appliquée à un problème d'intrusion saline dans un aquifère côtier. -- Our consumption of groundwater, in particular as drinking water and for irrigation, has considerably increased over the years and groundwater is becoming an increasingly scarce and endangered resource. Nofadays, we are facing many problems ranging from water prospection to sustainable management and remediation of polluted aquifers. Independently of the hydrogeological problem, the main challenge remains dealing with the incomplete knofledge of the underground properties. Stochastic approaches have been developed to represent this uncertainty by considering multiple geological scenarios and generating a large number of realizations. The main limitation of this approach is the computational cost associated with performing complex of simulations in each realization. In the first part of the thesis, we explore this issue in the context of uncertainty propagation, where an ensemble of geostatistical realizations is identified as representative of the subsurface uncertainty. To propagate this lack of knofledge to the quantity of interest (e.g., the concentration of pollutant in extracted water), it is necessary to evaluate the of response of each realization. Due to computational constraints, state-of-the-art methods make use of approximate of simulation, to identify a subset of realizations that represents the variability of the ensemble. The complex and computationally heavy of model is then run for this subset based on which inference is made. Our objective is to increase the performance of this approach by using all of the available information and not solely the subset of exact responses. Two error models are proposed to correct the approximate responses follofing a machine learning approach. For the subset identified by a classical approach (here the distance kernel method) both the approximate and the exact responses are knofn. This information is used to construct an error model and correct the ensemble of approximate responses to predict the "expected" responses of the exact model. The proposed methodology makes use of all the available information without perceptible additional computational costs and leads to an increase in accuracy and robustness of the uncertainty propagation. The strategy explored in the first chapter consists in learning from a subset of realizations the relationship between proxy and exact curves. In the second part of this thesis, the strategy is formalized in a rigorous mathematical framework by defining a regression model between functions. As this problem is ill-posed, it is necessary to reduce its dimensionality. The novelty of the work comes from the use of functional principal component analysis (FPCA), which not only performs the dimensionality reduction while maximizing the retained information, but also allofs a diagnostic of the quality of the error model in the functional space. The proposed methodology is applied to a pollution problem by a non-aqueous phase-liquid. The error model allofs a strong reduction of the computational cost while providing a good estimate of the uncertainty. The individual correction of the proxy response by the error model leads to an excellent prediction of the exact response, opening the door to many applications. The concept of functional error model is useful not only in the context of uncertainty propagation, but also, and maybe even more so, to perform Bayesian inference. Monte Carlo Markov Chain (MCMC) algorithms are the most common choice to ensure that the generated realizations are sampled in accordance with the observations. Hofever, this approach suffers from lof acceptance rate in high dimensional problems, resulting in a large number of wasted of simulations. This led to the introduction of two-stage MCMC, where the computational cost is decreased by avoiding unnecessary simulation of the exact of thanks to a preliminary evaluation of the proposal. In the third part of the thesis, a proxy is coupled to an error model to provide an approximate response for the two-stage MCMC set-up. We demonstrate an increase in acceptance rate by a factor three with respect to one-stage MCMC results. An open question remains: hof do we choose the size of the learning set and identify the realizations to optimize the construction of the error model. This requires devising an iterative strategy to construct the error model, such that, as new of simulations are performed, the error model is iteratively improved by incorporating the new information. This is discussed in the fourth part of the thesis, in which we apply this methodology to a problem of saline intrusion in a coastal aquifer.

Identification and visualization of multidimensional antigen-specific T-cell populations in polychromatic cytometry data.

An important aspect of immune monitoring for vaccine development, clinical trials, and research is the detection, measurement, and comparison of antigen-specific T-cells from subject samples under different conditions. Antigen-specific T-cells compose a very small fraction of total T-cells. Developments in cytometry technology over the past five years have enabled the measurement of single-cells in a multivariate and high-throughput manner. This growth in both dimensionality and quantity of data continues to pose a challenge for effective identification and visualization of rare cell subsets, such as antigen-specific T-cells. Dimension reduction and feature extraction play pivotal role in both identifying and visualizing cell populations of interest in large, multi-dimensional cytometry datasets. However, the automated identification and visualization of rare, high-dimensional cell subsets remains challenging. Here we demonstrate how a systematic and integrated approach combining targeted feature extraction with dimension reduction can be used to identify and visualize biological differences in rare, antigen-specific cell populations. By using OpenCyto to perform semi-automated gating and features extraction of flow cytometry data, followed by dimensionality reduction with t-SNE we are able to identify polyfunctional subpopulations of antigen-specific T-cells and visualize treatment-specific differences between them.

Resultados preliminares en la caracterización geométrica 3D de un litosoma arenoso de progradación deltaica mediante Georadar (GPR) (Fm. Arenisca de Roda, Eoceno, Cuenca de Graus-Tremp).

A set of GPR profiles have been recorded in order to determine the 3D geometry of a prograding delta-front sandbody (Roda sandstone formation, Eocene, Graus-Tremp basin). Common Mid Points (CMP) also have been recorded to obtain the velocity of the electromagnetic wave in ground. In order to build the topsurface of a 3D prism a set of topographic points have been acquired. Most of the GPR profiles are oriented parallel to the progradation direction (NNE-SSW) and show the expected geometries. The 3D prism has been built from the individual profiles, which shows the three dimensional geometry of the sandy lithosome.

Computing the diameter of Coxeter groups

This thesis addresses the problem of computing the minimal and maximal diameter of the Cayley graph of Coxeter groups. We first present and assert relevant parts of polytope theory and related Coxeter theory. After this, a method of contracting the orthogonal projections of a polytope from Rd onto R2 and R3, d ¸ 3 is presented. This method is the Equality Set Projection algorithm that requires a constant number of linearprogramming problems per facet of the projection in the absence of degeneracy. The ESP algorithm allows us to compute also projected geometric diameters of high-dimensional polytopes. A representation set of projected polytopes is presented to illustrate the methods adopted in this thesis.

Radiaalikompressorin juoksupyörän virtauskanavan suunnittelu

Diplomityössä on tutkittu radiaalikompressorin juoksupyörän virtauskanavan suunnittelua ja esitelty yleisesti käytetyt suunnittelumenetelmät. Virtauskanavan muodon vaikutukset virtauskenttään on esitetty. Työssä on kehitetty uusi tietokoneohjelma juoksupyörän kolmiulotteisen geometrian luomiseen, yksiulotteisesta suunnittelusta saatujen päämittojen pohjalta. Ohjelmalla luotua juoksupyörän geometriaa voidaan käyttää virtaus- ja lujuusanalyyseissä. Ohjelmaan on myös liitetty kaksiulotteinen kokoonpuristuvan viskoosittoman virtauksen ratkaisija.

Evaluating multidimensional visualization techniques in data mining tasks

Visual data mining (VDM) tools employ information visualization techniques in order to represent large amounts of high-dimensional data graphically and to involve the user in exploring data at different levels of detail. The users are looking for outliers, patterns and models – in the form of clusters, classes, trends, and relationships – in different categories of data, i.e., financial, business information, etc. The focus of this thesis is the evaluation of multidimensional visualization techniques, especially from the business user’s perspective. We address three research problems. The first problem is the evaluation of projection-based visualizations with respect to their effectiveness in preserving the original distances between data points and the clustering structure of the data. In this respect, we propose the use of existing clustering validity measures. We illustrate their usefulness in evaluating five visualization techniques: Principal Components Analysis (PCA), Sammon’s Mapping, Self-Organizing Map (SOM), Radial Coordinate Visualization and Star Coordinates. The second problem is concerned with evaluating different visualization techniques as to their effectiveness in visual data mining of business data. For this purpose, we propose an inquiry evaluation technique and conduct the evaluation of nine visualization techniques. The visualizations under evaluation are Multiple Line Graphs, Permutation Matrix, Survey Plot, Scatter Plot Matrix, Parallel Coordinates, Treemap, PCA, Sammon’s Mapping and the SOM. The third problem is the evaluation of quality of use of VDM tools. We provide a conceptual framework for evaluating the quality of use of VDM tools and apply it to the evaluation of the SOM. In the evaluation, we use an inquiry technique for which we developed a questionnaire based on the proposed framework. The contributions of the thesis consist of three new evaluation techniques and the results obtained by applying these evaluation techniques. The thesis provides a systematic approach to evaluation of various visualization techniques. In this respect, first, we performed and described the evaluations in a systematic way, highlighting the evaluation activities, and their inputs and outputs. Secondly, we integrated the evaluation studies in the broad framework of usability evaluation. The results of the evaluations are intended to help developers and researchers of visualization systems to select appropriate visualization techniques in specific situations. The results of the evaluations also contribute to the understanding of the strengths and limitations of the visualization techniques evaluated and further to the improvement of these techniques.

Mapping financial stability

The ongoing global financial crisis has demonstrated the importance of a systemwide, or macroprudential, approach to safeguarding financial stability. An essential part of macroprudential oversight concerns the tasks of early identification and assessment of risks and vulnerabilities that eventually may lead to a systemic financial crisis. Thriving tools are crucial as they allow early policy actions to decrease or prevent further build-up of risks or to otherwise enhance the shock absorption capacity of the financial system. In the literature, three types of systemic risk can be identified: i ) build-up of widespread imbalances, ii ) exogenous aggregate shocks, and iii ) contagion. Accordingly, the systemic risks are matched by three categories of analytical methods for decision support: i ) early-warning, ii ) macro stress-testing, and iii ) contagion models. Stimulated by the prolonged global financial crisis, today's toolbox of analytical methods includes a wide range of innovative solutions to the two tasks of risk identification and risk assessment. Yet, the literature lacks a focus on the task of risk communication. This thesis discusses macroprudential oversight from the viewpoint of all three tasks: Within analytical tools for risk identification and risk assessment, the focus concerns a tight integration of means for risk communication. Data and dimension reduction methods, and their combinations, hold promise for representing multivariate data structures in easily understandable formats. The overall task of this thesis is to represent high-dimensional data concerning financial entities on lowdimensional displays. The low-dimensional representations have two subtasks: i ) to function as a display for individual data concerning entities and their time series, and ii ) to use the display as a basis to which additional information can be linked. The final nuance of the task is, however, set by the needs of the domain, data and methods. The following ve questions comprise subsequent steps addressed in the process of this thesis: 1. What are the needs for macroprudential oversight? 2. What form do macroprudential data take? 3. Which data and dimension reduction methods hold most promise for the task? 4. How should the methods be extended and enhanced for the task? 5. How should the methods and their extensions be applied to the task? Based upon the Self-Organizing Map (SOM), this thesis not only creates the Self-Organizing Financial Stability Map (SOFSM), but also lays out a general framework for mapping the state of financial stability. This thesis also introduces three extensions to the standard SOM for enhancing the visualization and extraction of information: i ) fuzzifications, ii ) transition probabilities, and iii ) network analysis. Thus, the SOFSM functions as a display for risk identification, on top of which risk assessments can be illustrated. In addition, this thesis puts forward the Self-Organizing Time Map (SOTM) to provide means for visual dynamic clustering, which in the context of macroprudential oversight concerns the identification of cross-sectional changes in risks and vulnerabilities over time. Rather than automated analysis, the aim of visual means for identifying and assessing risks is to support disciplined and structured judgmental analysis based upon policymakers' experience and domain intelligence, as well as external risk communication.

Chaos in a Two-Degree of Freedom Duffing Oscillator

High dimensional dynamical systems has intricate behavior either on temporal or on spatial evolution properties. Nevertheless, most of the work on chaotic dynamics has been concentrated on temporal behavior of low-dimensional systems. This contribution is concerned with the chaotic response of a two-degree of freedom Duffing oscillator. Since the equations of motion are associated with a five-dimensional system, the analysis is performed by considering two Duffing oscillators, both with single-degree of freedom, coupled by a spring-dashpot system. With this assumption, it is possible to analyze the transmissibility of motion between the two oscillators.