Spatiotemporal data pose serious challenges to analysts in geographic and other domains. Owing to the complexity of the geospatial and temporal components, this kind of data cannot be analyzed by fully automatic methods but require the involvement of the human analyst's expertise. For a comprehensive analysis, the data need to be considered from two complementary perspectives: (1) as spatial distributions (situations) changing over time and (2) as profiles of local temporal variation distributed over space. In order to support the visual analysis of spatiotemporal data, we suggest a framework based on the "Self-Organizing Map" (SOM) method combined with a set of interactive visual tools supporting both analytic perspectives. SOM can be considered as a combination of clustering and dimensionality reduction. In the first perspective, SOM is applied to the spatial situations at different time moments or intervals. In the other perspective, SOM is applied to the local temporal evolution profiles. The integrated visual analytics environment includes interactive coordinated displays enabling various transformations of spatiotemporal data and post-processing of SOM results. The SOM matrix display offers an overview of the groupings of data objects and their two-dimensional arrangement by similarity. This view is linked to a cartographic map display, a time series graph, and a periodic pattern view. The linkage of these views supports the analysis of SOM results in both the spatial and temporal contexts. The variable SOM grid coloring serves as an instrument for linking the SOM with the corresponding items in the other displays. The framework has been validated on a large dataset with real city traffic data, where expected spatiotemporal patterns have been successfully uncovered. We also describe the use of the framework for discovery of previously unknown patterns in 41-years time series of 7 crime rate attributes in the states of the USA.

Traditionally, the visual analysis of hierarchies, respectively, trees, is conducted by focusing on one given hierarchy. However, in many research areas multiple, differing hierarchies need to be analyzed simultaneously in a comparative way - in particular to highlight differences between them, which sometimes can be subtle. A prominent example is the analysis of so-called phylogenetic trees in biology, reflecting hierarchical evolutionary relationships among a set of organisms. Typically, the analysis considers multiple phylogenetic trees, either to account for statistical significance or for differences in derivation of such evolutionary hierarchies; for example, based on different input data, such as the 16S ribosomal RNA and protein sequences of highly conserved enzymes. The simultaneous analysis of a collection of such trees leads to more insight into the evolutionary process. We introduce a novel visual analytics approach for the comparison of multiple hierarchies focusing on both global and local structures. A new tree comparison score has been elaborated for the identification of interesting patterns. We developed a set of linked hierarchy views showing the results of automatic tree comparison on various levels of details. This combined approach offers detailed assessment of local and global tree similarities. The approach was developed in close cooperation with experts from the evolutionary biology domain. We apply it to a phylogenetic data set on bacterial ancestry, demonstrating its application benefit

The analysis of high-dimensional data is an important, yet inherently difficult problem. Projection techniques such as PCA, MDS, and SOM can be used to map high-dimensional data to 2D display space. However, projections typically incur a loss in information. Often uncertainty exists regarding the precision of the projection as compared with its original data characteristics. While the output quality of these projection techniques can be discussed in terms of algorithmic assessment, visualization is often helpful for better understanding the results. We address the visual assessment of projection precision by an approach integrating an appropriately designed projection precision measure directly into the projection visualization. To this end, a flexible projection precision measure is defined that allows the user to balance the degree of locality at which the measure is evaluated. Several visual mappings are designed for integrating the precision measure into the projection visualization at various levels of abstraction. The techniques are implemented in a fully interactive system which is practically applied on several data sets. We demonstrate the usefulness of the approach for visual analysis of classified and clustered high-dimensional data sets. We thereby show how our novel interactive precision quality visualization system helps to examine preservation of closeness of the data in original space into the low-dimensional space

We focus on visual analysis of space- and time-referenced categorical data, which describe possible states of spatial (geographical) objects or locations and their changes over time. The analysis of these data is difficult as there are only limited possibilities to analyze the three aspects (location, time and category) simultaneously. We present a new approach which interactively combines (a) visualization of categorical changes over time; (b) various spatial data displays; (c) computational techniques for task-oriented selection of time steps. They provide an expressive visualization with regard to either the overall evolution over time or unusual changes. We apply our approach on two use cases demonstrating its usefulness for a wide variety of tasks. We analyze data from movement tracking and meteorologic areas. Using our approach, expected events could be detected and new insights were gained

The analysis of high-dimensional data is an important, yet inherently difficult problem. Projection techniques such as Principal Component Analysis, Multi-dimensional Scaling and Self-Organizing Map can be used to map high-dimensional data to 2D display space. However, projections typically incur a loss in information. Often, uncertainty exists regarding the precision of the projection as compared with its original data characteristics. While the output quality of these projection techniques can be discussed in terms of aggregate numeric error values, visualization is often helpful for better understanding the projection results. We address the visual assessment of projection precision by an approach integrating an appropriately designed projection precision measure directly into the projection visualization. To this end, a flexible projection precision measure is defined that allows the user to balance the degree of locality at which the measure is evaluated. Several visual mappings are designed for integrating the precision measure into the projection visualization at various levels of abstraction. The techniques are implemented in an interactive system, including methods supporting the user in finding appropriate settings of relevant parameters. We demonstrate the usefulness of the approach for visual analysis of classified and unclassified high-dimensional data sets. We show how our interactive precision quality visualization system helps to examine the preservation of original data properties in projected space.