Approach to Interactive Visual Exploration of Two-Dimensional Time Dependent Data . 148

In our approach for the exploratory visual analysis of the data, we rely on effective interactive data visualization.

The visualization techniques for two-dimensional time series are usually based on scatterplots and employ an-imation and trajectoryvisualization in 2D and 3D. We employ both animation and trajectory techniques while concentrating on 2D display of the data which is more familiar to the analysts than the 3D presentation (see Fig-ure4.7left). We employ in both visualizations interactive functions to support the analysis. Interactive functions include, in addition to view transformations, filtering and thresholding (dynamic queries).

Animation is well-suited for visualization of a broad class of time-dependent data, wherein “most promis-ing uses of animation seem to convey real-time changes and reorientations in time and space” [TMB02]. For example, in financial analysis, animation can help to analyze development of financial indicators over time.

When using animation,perceptionplays an important role for the efficiency of the visualization. In order to study the effects of animation setting on the awareness of dynamic changes in a dataset, we conduct aperception study. Our study is inspired by the main issues of interest of financial analysts – revealing similarity/dissimilarity in the development of financial indicators. In instrumental terms, the similarity is deemed to be detected due to a coherent motion of a glyph subset. The task appears, however, non-trivial because of a large number of data items (i.e. stocks) along with idiosyncratic movement of visualized items.

We wish to find out whether there is an effect of animation velocity and the size of direction change on the detection of the direction change by the user (see Figure4.7right). In a laboratory experiment, we employ a simplified alteration of an animated scatterplot of time-dependent financial data used for exploration of the two-dimensional time dependent data space while changing data and visualization parameters. The results will provide guidelines for setting-up of animation parameters in the visualization.

Visualization Study of animation techniques

y

perception

Animation Velocity

Trajectories Angle of change change

Figure 4.7.: Approach to visual exploration of two-dimensional time-dependent data. Left: The two main visual-ization techniques used: point animation and display of trajectories. Right: The study of animation perception with the animation parameters in focus.

Trajectory shows the path of a point in two-dimensional space (scatterplot). While animation is good for understanding general movements in the data (shown in our study in [TVK08]), it is however difficult to follow

4.3. New Approaches to Visual Analysis of Two-Dimensional Time-Dependent Data

exact movements of individual items over longer time periods. Therefore, alternatively, we use trajectories for showing the exact paths of the items.

4.3.2. Approach to Visual Analysis of Two-Dimensional Time Dependent with Grouping of Entities

In this section, we concentrate on thevisual analysis of groups of time-dependent two-dimensional data entities⁵. We assume a constant grouping of entities according to predefined grouping criteria.

In our approach, we combine algorithmic data analysis with interactive data visualization of dynamic point clouds (see Figure4.8). In many application areas,point cloud visualization can be an effective tool for data analysis. The visualization of point cloud data for their exploration has been used in geography [PSKN06,HK98], microarray data [CK03] or database exploration [PKJ^∗07]. In our work, various data visualizations using hulls and path traces are offered for the exploration of the data set. On the analytical side, we extend the approach of Wilkinson et al. [WAG05] foralgorithmic analysisof single group static two-dimensional data into multi-group time-dependent data.

When algorithmically analyzing time-dependent 2D point clouds, several aspects need to be taken into con-sideration. In particular, we consider time-dependent features (i.e., indicators, characteristics) of

• points within groups(e.g., velocity, position within group, etc.),

• each group(e.g., changes in point density, point cloud movements, etc.),

• multiple groups(e.g., overlap, distance, etc.).

In the case of asingle entity in a group, the movement and the position of the point within the group is relevant (also with respect to the group movement). For example, it is relevant whether the entity is an outlier in the group, lies in the center or at the border of the group. For the dynamics of the entity, the change of these indicators, such as the value and change of movement directions, and the length of movement is very interesting for the analysis.

Fora group of entities, the distribution of entities within the group, the center, size and shape of the point cloud are the indicators of main interest. For time-dependent point clouds, the changes in these indicators as well as changes in the absolute position of the cloud are relevant. The size and shape of the cloud can be represented by enclosing hulls (alpha, convex, butterfly, circle, etc.) which can be visualized and for which we can calculate various descriptors (area, convexity, direction, etc.). Mid-points of entity groups and their movement serve as an additional indicator of group position and its change over time.

Multiple groups can be characterized by their relative position to each other (e.g., number of overlapping points, the relative overlapping area, number of overlapping point clouds) and by their dynamics (co-movements) characterized by the dynamics of the mid point.

The proposed features are calculated and visualized (see Figure4.8. These time-dependent characteristics are used for the determination of interesting data views. This is especially useful when analyzing large amounts of data (with respect to either time-dimension or number of objects). The features can indicate time-periods and data elements which are deemed useful for further detailed visual inspection (see Figure4.9for an illustration).

For the details on the indicators used in the analysis, we refer to Section4.6.2.

5In the further text also referred to as time-dependent/dynamic groups, time-dependent/dynamic point clouds, or time-dependent/dynamic data classes

Raw Data

Entities in Individual Multiple-group

Raw Data Entities in

groups

Individual groups

Multiple-group relationship

Calculated features

Figure 4.8.: Approach to visual analysis of groups of two-dimensional time-dependent entities using feature mon-itoring. The data is visualized and algorithmically analyzed on three levels: the development of in-dividual entities within groups, of inin-dividual groups and of relationships between inin-dividual groups over time. The extracted features are visualized and explored. These results reveal interesting parts of the data set, which can be visually analyzed in more detail on demand.

Figure 4.9.: Illustration of visual analysis of groups of two-dimensional time dependent entities. Left: State-of-the art visualization of the grouped data using convex hull trace visualization showing an over-crowded display that is difficult to explore. Right: The new feature-based visual analysis revealing interesting views on the data. These interesting views are in the focus.

4.3. New Approaches to Visual Analysis of Two-Dimensional Time-Dependent Data

4.3.3. Approach to Visual Analysis of Two-Dimensional Time Dependent Data Using