Space-in-Time and Time-in-Space Self-Organizing Maps for Exploring Spatiotemporal Patterns
2010, Andrienko, Gennady L., Andrienko, Natalia, Bremm, S., Schreck, Tobias, Landesberger, Tatiana von, Bak, Peter, Keim, Daniel A.
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.
Regular TreeMap Layouts for Visual Analysis of Hierarchical Data
2006, Schreck, Tobias, Keim, Daniel A., Mansmann, Florian
Hierarchical relationships play an utmost important role in many application domains. The appropriate visualization of hierarchically structured data sets can contribute towards supporting the data analyst in effectively analyzing hierarchic structures using visualization as a user friendly means to communicate information. Information Visualization has contributed a number of useful techniques for visualization of hierarchically structured data sets. Yet, the support for certain regularity requirements as arising from many data element types has to be improved. In this paper, we analyze an existing variant of the popular TreeMap family of hierarchical layout algorithms, and we introduce a novel TreeMap algorithm supporting space efficient layout of hierarchical data sets providing global regular layouts. We detail our algorithm, and we present applications on a real-world data set as well as experiments performed on a synthetic data set, showing its applicability and usefulness.
Importance-Driven Visualization Layouts for Large Time Series Data
2005, Hao, Ming C., Dayal, Umeshwar, Keim, Daniel A., Schreck, Tobias
Time series are an important type of data with applications in virtually every aspect of the real world. Often a large number of time series have to be monitored and analyzed in parallel. Sets of time series may show intrinsic hierarchical relationships and varying degrees of importance among the individual time series. Effective techniques for visually analyzing large sets of time series should encode the relative importance and hierarchical ordering of the time series data by size and position, and should also provide a high degree of regularity in order to support comparability by the analyst. In this paper, we present a framework for visualizing large sets of time series. Based on the notion of inter time series importance relationships, we define a set of objective functions that space-filling layout schemes for time series data should obey. We develop an efficient algorithm addressing the identified problems by generating layouts that reflect hierarchyand importance-based relationships in a regular layout with favorable aspect ratios. We apply our technique to a number of real-world data sets including sales and stock data, and we compare our technique with an aspect ratio aware variant of the well-known TreeMap algorithm. The examples show the advantages and practical usefulness of our layout algorithm.