Neighborhood Graphs, Stripes and Shadow Plots for Cluster Visualization

Centroid-based partitioning cluster analysis is a popular method for segmenting data into more homogeneous subgroups. Visualization can help tremendously to understand the positions of these subgroups relative to each other in higher dimensional spaces and to assess the quality of partitions. In this paper we present several improvements on existing cluster displays using neighborhood graphs with edge weights based on cluster separation and convex hulls of inner and outer cluster regions. A new display called shadow-stars can be used to diagnose pairwise cluster separation with respect to the distribution of the original data. Artificial data and two case studies with real data are used to demonstrate the techniques

Medoid-based shadow value validation and visualization

A silhouette index is a well-known measure of an internal criteria validation for the clustering algorithm results. While it is a medoid-based validation index, a centroid-based validation index that is called a centroid-based shadow value (CSV) has been developed.  Although both are similar, the CSV has an additional unique property where an image of a 2-dimensional neighborhood graph is possible. A new internal validation index is proposed in this article in order to create a medoid-based validation that has an ability to visualize the results in a 2-dimensional plot. The proposed index behaves similarly to the silhouette index and produces a network visualization, which is comparable to the neighborhood graph of the CSV. The network visualization has a multiplicative parameter (c) to adjust its edges visibility. Due to the medoid-based, in addition, it is more an appropriate visualization technique for any type of data than a neighborhood graph of the CSV

Spectral Embedding Norm: Looking Deep into the Spectrum of the Graph Laplacian

The extraction of clusters from a dataset which includes multiple clusters and a significant background component is a non-trivial task of practical importance. In image analysis this manifests for example in anomaly detection and target detection. The traditional spectral clustering algorithm, which relies on the leading $K$ eigenvectors to detect $K$ clusters, fails in such cases. In this paper we propose the {\it spectral embedding norm} which sums the squared values of the first $I$ normalized eigenvectors, where $I$ can be significantly larger than $K$. We prove that this quantity can be used to separate clusters from the background in unbalanced settings, including extreme cases such as outlier detection. The performance of the algorithm is not sensitive to the choice of $I$, and we demonstrate its application on synthetic and real-world remote sensing and neuroimaging datasets

Shape and Topology Constrained Image Segmentation with Stochastic Models

The central theme of this thesis has been to develop robust algorithms for the task of image segmentation. All segmentation techniques that have been proposed in this thesis are based on the sound modeling of the image formation process. This approach to image partition enables the derivation of objective functions, which make all modeling assumptions explicit. Based on the Parametric Distributional Clustering (PDC) technique, improved variants have been derived, which explicitly incorporate topological assumptions in the corresponding cost functions. In this thesis, the questions of robustness and generalizability of segmentation solutions have been addressed in an empirical manner, giving comprehensive example sets for both problems. It has been shown, that the PDC framework is indeed capable of producing highly robust image partitions. In the context of PDC-based segmentation, a probabilistic representation of shape has been constructed. Furthermore, likelihood maps for given objects of interest were derived from the PDC cost function. Interpreting the shape information as a prior for the segmentation task, it has been combined with the likelihoods in a Bayesian setting. The resulting posterior probability for the occurrence of an object of a specified semantic category has been demonstrated to achieve excellent segmentation quality on very hard testbeds of images from the Corel gallery

Interactive Visualization Lenses:: Natural Magic Lens Interaction for Graph Visualization

Information visualization is an important research field concerned with making sense and inferring knowledge from data collections. Graph visualizations are specific techniques for data representation relevant in diverse application domains among them biology, software-engineering, and business finance. These data visualizations benefit from the display space provided by novel interactive large display environments. However, these environments also cause new challenges and result in new requirements regarding the need for interaction beyond the desktop and according redesign of analysis tools. This thesis focuses on interactive magic lenses, specialized locally applied tools that temporarily manipulate the visualization. These may include magnification of focus regions but also more graph-specific functions such as pulling in neighboring nodes or locally reducing edge clutter. Up to now, these lenses have mostly been used as single-user, single-purpose tools operated by mouse and keyboard. This dissertation presents the extension of magic lenses both in terms of function as well as interaction for large vertical displays. In particular, this thesis contributes several natural interaction designs with magic lenses for the exploration of graph data in node-link visualizations using diverse interaction modalities. This development incorporates flexible switches between lens functions, adjustment of individual lens properties and function parameters, as well as the combination of lenses. It proposes interaction techniques for fluent multi-touch manipulation of lenses, controlling lenses using mobile devices in front of large displays, and a novel concept of body-controlled magic lenses. Functional extensions in addition to these interaction techniques convert the lenses to user-configurable, personal territories with use of alternative interaction styles. To create the foundation for this extension, the dissertation incorporates a comprehensive design space of magic lenses, their function, parameters, and interactions. Additionally, it provides a discussion on increased embodiment in tool and controller design, contributing insights into user position and movement in front of large vertical displays as a result of empirical investigations and evaluations.Informationsvisualisierung ist ein wichtiges Forschungsfeld, das das Analysieren von Daten unterstützt. Graph-Visualisierungen sind dabei eine spezielle Variante der Datenrepräsentation, deren Nutzen in vielerlei Anwendungsfällen zum Einsatz kommt, u.a. in der Biologie, Softwareentwicklung und Finanzwirtschaft. Diese Datendarstellungen profitieren besonders von großen Displays in neuen Displayumgebungen. Jedoch bringen diese Umgebungen auch neue Herausforderungen mit sich und stellen Anforderungen an Nutzerschnittstellen jenseits der traditionellen Ansätze, die dadurch auch Anpassungen von Analysewerkzeugen erfordern. Diese Dissertation befasst sich mit interaktiven „Magischen Linsen“, spezielle lokal-angewandte Werkzeuge, die temporär die Visualisierung zur Analyse manipulieren. Dabei existieren zum Beispiel Vergrößerungslinsen, aber auch Graph-spezifische Manipulationen, wie das Anziehen von Nachbarknoten oder das Reduzieren von Kantenüberlappungen im lokalen Bereich. Bisher wurden diese Linsen vor allem als Werkzeug für einzelne Nutzer mit sehr spezialisiertem Effekt eingesetzt und per Maus und Tastatur bedient. Die vorliegende Doktorarbeit präsentiert die Erweiterung dieser magischen Linsen, sowohl in Bezug auf die Funktionalität als auch für die Interaktion an großen, vertikalen Displays. Insbesondere trägt diese Dissertation dazu bei, die Exploration von Graphen mit magischen Linsen durch natürliche Interaktion mit unterschiedlichen Modalitäten zu unterstützen. Dabei werden flexible Änderungen der Linsenfunktion, Anpassungen von individuellen Linseneigenschaften und Funktionsparametern, sowie die Kombination unterschiedlicher Linsen ermöglicht. Es werden Interaktionstechniken für die natürliche Manipulation der Linsen durch Multitouch-Interaktion, sowie das Kontrollieren von Linsen durch Mobilgeräte vor einer Displaywand vorgestellt. Außerdem wurde ein neuartiges Konzept körpergesteuerter magischer Linsen entwickelt. Funktionale Erweiterungen in Kombination mit diesen Interaktionskonzepten machen die Linse zu einem vom Nutzer einstellbaren, persönlichen Arbeitsbereich, der zudem alternative Interaktionsstile erlaubt. Als Grundlage für diese Erweiterungen stellt die Dissertation eine umfangreiche analytische Kategorisierung bisheriger Forschungsarbeiten zu magischen Linsen vor, in der Funktionen, Parameter und Interaktion mit Linsen eingeordnet werden. Zusätzlich macht die Arbeit Vor- und Nachteile körpernaher Interaktion für Werkzeuge bzw. ihre Steuerung zum Thema und diskutiert dabei Nutzerposition und -bewegung an großen Displaywänden belegt durch empirische Nutzerstudien

Generalization, Combination and Extension of Functional Clustering Algorithms: The R Package funcy

Clustering functional data is mostly based on the projection of the curves onto an adequate basis and building random effects models of the basis coefficients. The parameters can be fitted with an EM algorithm. Alternatively, distance models based on the coefficients are used in the literature. Similar to the case of clustering multidimensional data, a variety of derivations of different models has been published. Although their calculation procedure is similar, their implementations are very different including distinct hyperparameters and data formats as input. This makes it difficult for the user to apply and particularly to compare them. Furthermore, they are mostly limited to specific basis functions. This paper aims to show the common elements between existing models in highly cited articles, first on a theoretical basis. Later their implementation is analyzed and it is illustrated how they could be improved and extended to a more general level. A special consideration is given to those models designed for sparse measurements. The work resulted in the R package funcy which was built to integrate the modified and extended algorithms into a unique framework