In this thesis, we study time-dependent empirical processes, which extend the classical empirical processes to have a time parameter; for example the empirical process for a sequence of independent stochastic processes {Yi : i ∈ N}: (1) ν_n(t, y) = n^(−1/2 )Sigma[1_(Y i(t)¬<=y) – P(Yi(t) <= y)] from i=1 to n, t ∈ E, y ∈ R. In the case of independent identically distributed samples (that is {Yi(t) : i ∈ N} are iid), Kuelbs et al. (2013) proved a Central Limit Theorem for ν_n(t, y) for a large class of stochastic processes. In Chapter 3, we give a sufficient condition for the weak convergence of the weighted empirical process for iid samples from a uniform process: (2) α_n(t, y) := n^(−1/2 )Sigma[w(y)(1_(X (t)<=y) – y)] from i=1 to n, t ∈ E, y ∈ [0, 1] where {X (t), X1(t), X2(t), • • • } are independent and identically distributed uniform processes (for each t ∈ E, X (t) is uniform on (0, 1)) and w(x) is a “weight” function satisfying some regularity properties. Then we give an example when X (t) := Ft(Bt) : t ∈ E = [1, 2], where Bt is a Brownian motion and Ft is the distribution function of Bt. In Chapter 4, we investigate the weak convergence of the empirical processes for non-iid samples. We consider the weak convergence of the empirical process: (3) β_n(t, y) := n^(−1/2 )Sigma[(1_(Y (t)<=y) – Fi(t,y))] from i=1 to n, t ∈ E ⊂ R, y ∈ R where {Yi(t) : i ∈ N} are independent processes and Fi(t, y) is the distribution function of Yi(t). We also prove that the covariance function of the empirical process for non-iid samples indexed by a uniformly bounded class of functions necessarily uniformly converges to the covariance function of the limiting Gaussian process for a CLT.

La production d’énergie, et en particulier la production d’électricité, est la principale responsable de l’émission de gaz à effet de serre au niveau mondial. Le secteur résidentiel étant le plus consommateur d’énergie, il est essentiel d’agir au niveau personnel afin de réduire ces émissions. Avec le développement de l’informatique ubiquitaire, il est désormais aisé de récolter des données de consommation d’électricité des appareils électriques d’un logement. Cette possibilité a permis le développement des technologies eco-feedback, dont l’objectif est de fournir aux consommateurs un retour sur leur consommation dans le but de la diminuer. Dans cette thèse nous proposons une méthode de visualisation de données temporelles personnelles basée sur une interaction what if, qui signifie que les utilisateurs peuvent appliquer des changements de comportement de manière virtuelle. En particulier notre méthode permet de simuler une modification de l’utilisation des appareils électriques d’un logement, puis d’évaluer visuellement l’impact de ces modifications sur les données. Cette méthode a été implémentée dans le système Activelec, que nous avons évalué avec des utilisateurs sur des données réelles. Nous synthétisons les éléments de conception indispensables aux systèmes eco-feedback dans un état de l’art. Nous exposons également les limitations de ces technologies, la principale étant la difficulté rencontrée par les utilisateurs pour trouver des modifications de comportement pertinentes leur permettant de consommer moins d’énergie.Nous présentons ensuite trois contributions. La première contribution est la conception d’une méthode what if appliquée à l’eco-feedback ainsi que son implémentation dans le système Activelec. La seconde contribution est l’évaluation de notre méthode grâce à deux expérimentations menées en laboratoire. Dans ces expérimentations nous évaluons si des participants utilisant notre méthode trouvent des modifications qui économisent de l’énergie et qui nécessitent suffisamment peu d’efforts pour être appliquées en vrai. Enfin la troisième contribution est l’évaluation in-situ du système Activelec dans des logements personnels pour une durée d’environ un mois. Activelec a été déployé dans trois appartements privés afin de permettre l’évaluation de notre méthode en contexte domestique réel. Dans ces trois expérimentations, les participants ont pu trouver des modifications d’utilisation des appareils qui économiseraient une quantité d’énergie significative, et qui ont été jugées faciles à appliquer en réalité. Nous discutons également de l’application de notre méthode what if au-delà des données de consommation électrique au domaine de la visualisation personnelle, qui est définie comme l’analyse visuelle des données personnelles. Nous présentons ainsi plusieurs applications possibles à d’autres données temporelles personnelles, par exemple concernant l’activité physique ou les transports. Cette thèse ouvre de nouvelles perspectives pour l’utilisation d’un paradigme d’interaction what if pour la visualisation personnelle. / The production of energy, in particular the production of electricity, is the main responsible for the emission of greenhouse gases at world scale. The residential sector being the most energy consuming, it is essential to act at a personal scale to reduce these emissions. Thanks to the development of ubiquitous computing, it is now easy to collect data about the electricity consumption of electrical appliances of a housing. This possibility has allowed the development of eco-feedback technologies, whose objective is to provide to consumers a feedback about their consumption with the aim to reduce it. In this thesis we propose a personal visualization method for time-dependent data based on a what if interaction, which means that users can apply modifications in their behavior in a virtual way. Especially our method allows to simulate the modification of the usage of electrical appliances of a housing, and then to evaluate visually the impact of the modifications on data. This approach has been implemented in the Activelec system, which we have evaluated with users on real data.We synthesize the essential elements of conception for eco-feedback systems in a state of the art. We also outline the limitations of these technologies, the main one being the difficulty faced by users to find relevant modifications in their behavior to decrease their energy consumption. We then present three contributions. The first contribution is the development of a what if approach applied to eco-feedback as well as its implementation in the Activelec system. The second contribution is the evaluation of our approach with two laboratory studies. In these studies we assess if participants using our method manage to find modifications that save energy and which require a sufficiently low effort to be applied in reality. Finally the third contribution is the in-situ evaluation of the Activelec system. Activelec has been deployed in three private housings and used for a duration of approximately one month. This in-situ experiment allows to evaluate the usage of our approach in a real domestic context. In these three studies, participants managed to find modifications in the usage of appliances that would savea significant amount of energy, while being judged easy to be applied in reality.We also discuss of the application of our what if approach to the domain of personal visualization, beyond electricity consumption data, which is defined as the visual analysis of personal data. We hence present several potential applications to other types of time-dependent personal data, for example related to physical activity or to transportation. This thesis opens new perspectives for using a what if interaction paradigm for personal visualization.

<p dir="ltr">The emergence of time-dependent data provides researchers with unparalleled opportunities to investigate disaggregated levels of safety performance on roadway infrastructures. A disaggregated crash risk analysis uses both time-dependent data (e.g., hourly traffic, speed, weather conditions and signal controls) and fixed data (e.g., geometry) to estimate hourly crash probability. Despite abundant research on crash risk analysis, coordinated signalized intersections continue to require further investigation due to both the complexity of the safety problem and the relatively small number of past studies that investigated the risk factors of coordinated signalized intersections. This dissertation aimed to develop robust crash risk prediction models to better understand the risk factors of coordinated signalized intersections and to identify practical safety countermeasures. The crashes first were categorized into three types (same-direction, opposite-direction, and right-angle) within several crash-generating scenarios. The data needed were organized in hourly observations and included the following factors: road geometric features, traffic movement volumes, speeds, weather precipitation and temperature, and signal control settings. Assembling hourly observations for modeling crash risk was achieved by synchronizing and linking data sources organized at different time resolutions. Three different non-crash sampling strategies were applied to the following three statistical models (Conditional Logit, Firth Logit, and Mixed Logit) and two machine learning models (Random Forest and Penalized Support Vector Machine). Important risk factors, such as the presence of light rain, traffic volume, speed variability, and vehicle arrival pattern of downstream, were identified. The Firth Logit model was selected for implementation to signal coordination practice. This model turned out to be most robust based on its out-of-sample prediction performance and its inclusion of important risk factors. The implementation examples of the recommended crash risk model to building daily risk profiles and to estimating the safety benefits of improved coordination plans demonstrated the model’s practicality and usefulness in improving safety at coordinated signals by practicing engineers.</p>

The analysis of the immensity of data in space and time is a challenging task. For this thesis, the time-dependent data has been explored in various directions. The studies focused on data visualization, feature extraction, and data classification. The data that has been used in the studies comes from various well-recognized archives and has been the basis of numerous researches. The data characteristics ranged from the univariate time series to multivariate time series, from hand gestures to unconstrained views of general human movements. The experiments covered more than one hundred datasets. In addition, we also discussed the applications of visual analytics to video data. Two approaches were proposed to create a feature vector for time-dependent data classification. One is designed especially for a bio-inspired model for human motion recognition and the other is a subspace-based approach for arbitrary data characteristics. The extracted feature vectors of the proposed approaches can be easily visualized in two-dimensional space. For the classification, we experimented with various known models and offered a simple model using data in subspaces for light-weight computation. Furthermore, this method allows a data analyst to inspect feature vectors and detect an anomaly from a large collection of data simultaneously. Various classification techniques were compared and the findings were summarized. Hence, the studies can assist a researcher in picking an appropriate technique when setting up a corresponding model for a given characteristic of temporal data, and offer a new perspective for analyzing the time series data. This thesis is comprised of two parts. The first part gives an overview of time-dependent data and of this thesis with its focus on classification; the second part covers the collection of seven publications.

Large, strongly connected amounts of data, as collected in knowledge bases or those occurring when describing software, are often read slowly and with difficulty by humans when they are represented as spreadsheets or text. Graphical representations can help people to understand facts more intuitively and offer a quick overview. The electronic representation offers means that are beyond the possibilities of print such as unlimited zoom and hyperlinks. This paper addresses a framework for visualizing connected information in 3D-space taking into account the techniques of media design to build visualization structures and map information to graphical properties. / Große, stark vernetzte Datenmengen, wie sie in Wissensbasen oder Softwaremodellen vorkommen, sind von Menschen oft nur langsam und mühsam zu lesen, wenn sie als Tabellen oder Text dargestellt werden. Graphische Darstellungen können Menschen helfen, Tatsachen intuitiver zu verstehen und bieten einen schnellen Überblick. Die elektronische Darstellung bietet Mittel, welche über die Möglichkeiten von Print hinausgehen, wie z.B. unbegrenzten Zoom und Hyperlinks. Diese Arbeit stellt ein Framework für die Visualisierung vernetzter Informationen im 3D-Raum vor, welches Techniken der Gestaltung zur Erstellung von graphischen Strukturen und zur Abbildung von Informationen auf graphische Eigenschaften berücksichtigt.

Large, strongly connected amounts of data, as collected in knowledge bases or those occurring when describing software, are often read slowly and with difficulty by humans when they are represented as spreadsheets or text. Graphical representations can help people to understand facts more intuitively and offer a quick overview. The electronic representation offers means that are beyond the possibilities of print such as unlimited zoom and hyperlinks. This paper addresses a framework for visualizing connected information in 3D-space taking into account the techniques of media design to build visualization structures and map information to graphical properties.:1 EINFÜHRUNG S. 9 1.1 Zusammenfassung des Gestaltungsentwurfs S. 9 1.2 Ziel des Belegs S. 10 1.3 Interdisziplinäres Projekt S. 10 2 VORGEHEN S. 12 2.1 Ablauf S. 12 2.2 Konkrete Beispielinhalte S. 13 2.3 Beispielimplementierung S. 13 3 DATENMODELL S. 15 3.1 Ontologien S. 15 3.2 Ontologie Konstruktion S. 15 3.3 Analyse der Domain Design S. 18 3.8 Erstes Ordnen S. 19 3.9 Verwendete Ontologie-Struktur S. 21 3.10 Design-Ontologien S. 23 3.11 Schwierigkeiten bei der Ontologiekonstruktion S. 28 3.12 Einpflegen der Daten mit Protégé S. 29 3.13 Facetten S. 29 3.14 Filter S. 32 4 DATENVISUALISIERUNG S. 35 4.1 Visualisierung zeitlicher Daten S. 35 4.2 Hyperhistory S. 35 4.3 Graphisches Vokabular - graphische Dimensionen S. 37 4.4 Mapping S. 39 5 FRAMEWORK UND GESTALTUNG DES MEDIUMS S. 43 5.1 Technologien und Werkzeuge S. 44 5.2 Architektur S. 46 5.3 Konfiguration S. 51 5.4 DataBackendManager S. 52 5.5 Mapping im Framework S. 53 5.6 atomicelements S. 54 5.7 Appearance Bibliothek S. 55 5.8 TransformationUtils S. 56 5.9 Structures S. 57 5.10 LOD S. 64 5.11 Häufung von Einträgen [+] S. 66 5.12 Darstellung von Relationen [+] S. 69 5.13 Head Up Display [+] S. 71 5.14 Navigation S. 72 5.15 Performanz S. 73 5.16 Gestaltung des Mediums S. 74 6 AUSBLICK S. 80 7 FAZIT S. 81 8 ANHANG A – Installation S. 82 8.1 Vorraussetzungen S. 82 8.2 Programmaufruf S. 82 8.3 Stereoskopie S. 82 9 ANHANG B – Beispielimplementierung zur Visualisierung des Themas „Geschichte des Designs in Deutschland im 19. und 20. Jh.“ S. 84 9.1 Eingrenzung des Umfangs S. 84 9.2 Überblick zur deutschen Designgeschichte S. 84 9.3 Vorgehen S. 85 9.4 Unscharfe Datumsangaben S. 85 9.5 Kontextereignisse S. 85 9.6 Ursache-Wirkung-Beziehungen S. 86 9.7 Mehrsprachigkeit S. 86 9.8 Quellenangaben S. 86 9.9 Bildmaterial S. 87 LITERATURVERZEICHNIS S. 88 GLOSSAR S. 90 ABBILDUNGSVERZEICHNIS S. 91 / Große, stark vernetzte Datenmengen, wie sie in Wissensbasen oder Softwaremodellen vorkommen, sind von Menschen oft nur langsam und mühsam zu lesen, wenn sie als Tabellen oder Text dargestellt werden. Graphische Darstellungen können Menschen helfen, Tatsachen intuitiver zu verstehen und bieten einen schnellen Überblick. Die elektronische Darstellung bietet Mittel, welche über die Möglichkeiten von Print hinausgehen, wie z.B. unbegrenzten Zoom und Hyperlinks. Diese Arbeit stellt ein Framework für die Visualisierung vernetzter Informationen im 3D-Raum vor, welches Techniken der Gestaltung zur Erstellung von graphischen Strukturen und zur Abbildung von Informationen auf graphische Eigenschaften berücksichtigt.:1 EINFÜHRUNG S. 9 1.1 Zusammenfassung des Gestaltungsentwurfs S. 9 1.2 Ziel des Belegs S. 10 1.3 Interdisziplinäres Projekt S. 10 2 VORGEHEN S. 12 2.1 Ablauf S. 12 2.2 Konkrete Beispielinhalte S. 13 2.3 Beispielimplementierung S. 13 3 DATENMODELL S. 15 3.1 Ontologien S. 15 3.2 Ontologie Konstruktion S. 15 3.3 Analyse der Domain Design S. 18 3.8 Erstes Ordnen S. 19 3.9 Verwendete Ontologie-Struktur S. 21 3.10 Design-Ontologien S. 23 3.11 Schwierigkeiten bei der Ontologiekonstruktion S. 28 3.12 Einpflegen der Daten mit Protégé S. 29 3.13 Facetten S. 29 3.14 Filter S. 32 4 DATENVISUALISIERUNG S. 35 4.1 Visualisierung zeitlicher Daten S. 35 4.2 Hyperhistory S. 35 4.3 Graphisches Vokabular - graphische Dimensionen S. 37 4.4 Mapping S. 39 5 FRAMEWORK UND GESTALTUNG DES MEDIUMS S. 43 5.1 Technologien und Werkzeuge S. 44 5.2 Architektur S. 46 5.3 Konfiguration S. 51 5.4 DataBackendManager S. 52 5.5 Mapping im Framework S. 53 5.6 atomicelements S. 54 5.7 Appearance Bibliothek S. 55 5.8 TransformationUtils S. 56 5.9 Structures S. 57 5.10 LOD S. 64 5.11 Häufung von Einträgen [+] S. 66 5.12 Darstellung von Relationen [+] S. 69 5.13 Head Up Display [+] S. 71 5.14 Navigation S. 72 5.15 Performanz S. 73 5.16 Gestaltung des Mediums S. 74 6 AUSBLICK S. 80 7 FAZIT S. 81 8 ANHANG A – Installation S. 82 8.1 Vorraussetzungen S. 82 8.2 Programmaufruf S. 82 8.3 Stereoskopie S. 82 9 ANHANG B – Beispielimplementierung zur Visualisierung des Themas „Geschichte des Designs in Deutschland im 19. und 20. Jh.“ S. 84 9.1 Eingrenzung des Umfangs S. 84 9.2 Überblick zur deutschen Designgeschichte S. 84 9.3 Vorgehen S. 85 9.4 Unscharfe Datumsangaben S. 85 9.5 Kontextereignisse S. 85 9.6 Ursache-Wirkung-Beziehungen S. 86 9.7 Mehrsprachigkeit S. 86 9.8 Quellenangaben S. 86 9.9 Bildmaterial S. 87 LITERATURVERZEICHNIS S. 88 GLOSSAR S. 90 ABBILDUNGSVERZEICHNIS S. 91