We propose a three-level classification of complexity in visual analysis tasks. Levels one and two represent the current state of the art. The third level requires advanced interaction and data
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Figure 8.1: Interactive visual analysis on three levels of complexity. The first level is linking and brushing with one brush. On the second level, more views are used and brushes are combined with logical operators. On a third level, advanced interaction (brushing) and attribute derivation are added.
manipulation features so that deeply hidden implicit information from complex data sets can be extracted. Based on our experience gained from several case studies, we present some typical, complex analysis tasks of data sets containing families of function graphs and discuss how the visual analysis framework can support them.
Three Levels of Complexity in Interactive Visual Analysis
Interactive visual analysis is an iterative process. It usually starts with a simple analysis of the original data to gain overview. Then, for a more advanced analysis, the analyst needs to use more complex procedures and can combine findings from earlier stages of the analysis. The need for a more advanced analysis arises as information should be extracted which is more difficult to access. At a certain point it becomes difficult or even impossible to find features of interest by analyzing the original data only using conventional IVA methods. More advanced and complex interaction possibilities are required. Alternatively, or perhaps in addition to that, the data can be enhanced by computing aggregates or first derivatives of time series, for instance. Figure 8.1 illustrates our view on the three levels of complexity in interactive visual analysis.
In a coordinated multiple views system, thefirst level(smallest circle, left in Figure 8.1) can be expressed as simple linking and brushing with one brush. The user interactively selects some items in one view, and they are highlighted consistently in all views. Then a different set of items (anotherfeature of interest) is brushed and the highlighted patterns in the linked views are studied. The user repeats this process, engaging in an iterative IVA loop. This is sufficient in many cases, but we cannot formulate more complex queries, spanning several attributes.
On thesecond level(larger circle in the middle of Figure 8.1) more views are used and sev-eral brushes can be combined with logical operators. Queries can be expressed as combinations of criteria on several (original) data attributes. However, this is insufficient to achieve many analysis goals, for example, selecting those function graphs in a family that are increasing at a given value of the independent variable; or finding curves of some specific shape.
In order to select increasing function graphs, an advanced brush can be designed, which considers the slopes of the lines. Another possibility is to compute the first derivatives of the
122 CHAPTER 8. SUMMARY function graphs, and brush high values of the first derivative to select increasing function graphs.
The combination of complex interaction and on-demand computation of such synthetic,derived attributesconstitutes thethird level(rightmost circle in Figure 8.1) of visual analysis, supporting complex analysis goals. Note that each of the three circles in Figure 8.1 encloses the previous ones from the lower level(s), indicating that a seamless transition between circles (levels of analysis), and also their integration, is possible.
The advantages and drawbacks of the two essential building blocks of complex analysis, advanced interaction and attribute derivation, are complementary. Advanced interaction does not increase the amount of data, nor does it usually require additional views, but the user needs to mentally manage the advanced interaction method. New types of analysis tasks may require new, specialized interaction techniques.
Attribute derivationincreases the amount of data and usually requires additional views. The synthetic data attributes are often exactly the ones that are used in computational analysis, thus experienced analysts are familiar with them. Well-known, simple mechanisms can be used to interact with the data. Due to the step-by-step approach, with a sufficiently rich set of basis operations, a lot of very different derivations are possible, also ones that were not necessarily anticipated at the time when the IVA system is designed.
In open and flexible IVA systems that can be used for a variety of problems, attribute deriva-tion may be preferred. However, in more targeted IVA soluderiva-tions, where similar problems need to be solved repeatedly, advanced interaction can be more time-efficient for the experienced user.
An interesting analogy can be drawn between the three levels of complexity in analysis and the three thresholds of response times in human-computer interaction (refer to Card et al. [41]).
The users’ actions in level one analysis are spontaneous, and instantaneous response is expected from the computer. At level two, the users’ actions are more complex, the pace of action be-comes slower, and response within a second is sufficient to avoid the interruption of the users’
cognitive process. At analysis level three, the users’ decision to request the computation of new, synthetic data attributes reflects elaborate thinking. They are likely to accept longer response times, provided they have some feedback in the form of a progress bar or the visualization being progressively updated.
Complex Analysis of Families of Function Graphs
Based on our previous case studies, we identified some typical, complex analysis tasks asso-ciated with data sets containing families of function graphs. We demonstrate that they can be supported by specialized, advanced interaction techniques, and also by the computation of de-rived data attributes. Our work is in part motivated by curve sketching, where new attributes (e.g., extrema) and curves (e.g., first derivative) are computed to analyze single curves. We pro-pose related analysis methods for entire families of function graphs. The propro-posed ideas are in part suitable for the analysis of families of generic curves, too.
Some of the typical goals in the analysis of families of function graphs can be effectively tackled by computing someaggregate(e.g., minimum, maximum, arithmetic mean, percentile, and integral) of each member curve of the family. A family of function graphs is then represented by a set of scalars, significantly reducing data complexity. Thereby, standard visual analysis tools
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