Hypothesis Generations via Visual Analysis

There is a particularly strong need in engineering applications to perform automatic optimization of designs using several simulation iterations with suitably varied boundary conditions. The automatic optimization process must have an approximate model of the simulation in order to know how boundary conditions should be adjusted in search for an optimum. Visual analysis can be used to create hypotheses and rules that the automatic optimization can use in its simplified model and also to find out if the optimization misses some families of function graphs while searching for an optimum.

Gaining insight into the current design and setting up hypotheses about its operation via vi-sual analysis has a very important additional advantage over pure numeric optimization. When designing a new component, engineers almost never start from scratch, but the new design evolves from an old one. Because of this iterative nature of design in engineering, the insight gained from the analysis of previous designs can be useful in improving future ones. This also implies that the simulation models of new designs are not radically different from those of the old ones and their results are comparable to some extent, too. By analyzing the relationships between the two, tendencies can be found and extrapolated to improve future designs.

3.5 Chapter Conclusions

The analysis of relationships between families of function graphs is a common task in many application domains. A novel combination of established visualization techniques, linked views and advanced brushing features represents a valuable tool for interactive visual exploration and analysis of data sets that include families of function graphs. Independent and dependent vari-ables in the data set are treated the same, providing improved support for iterative exploration and analysis of the entire data space. Multiple, linked views enable simultaneous viewing of independent and dependent variables with immediate feedback.

Brushing proved to be especially effective, since it allows the interactive exploration of rela-tions between independent and dependent variables. The color gradient improves the visual con-nection of the brushed items to the linked focus+context visualizations. The composite brushing with AND, OR, and SUB operations supports the iterative refinement of information drill-down and the detection or extraction of patterns from the application domain. The line brush technique proves to be especially useful in selecting function graphs. It is intuitive, easy to use and very effective. Figure 3.6 shows how a composition of nearly a dozen line brushes is used to identify a pattern in a family of traffic volume function graphs.

The process of the composite brush construction captures the essence of visual analytics pro-cedures: it is interactive and iterative. The initial brush provides the initial data selection in one view. That selection is immediately displayed in the linked views and analyzed from different perspectives to formulate a hypothesis that is then tested using new brushes. During this iterative

38 CHAPTER 3. VISUAL ANALYSIS OF FAMILIES OF FUNCTION GRAPHS procedure new, possibly unexpected patterns can be found. Figure 3.3 shows a discovery of a pattern inD (constant high occupancy) that indicates a pattern in I (malfunctioning sensors).

Such discoveries are more difficult or even impossible without interactive visual analysis.

Chapter 4

Analysis using Data Aggregation and Derivation

“The important thing in science is not so much to obtain new facts as to discover new ways of thinking about them.”

— Sir William Henry Bragg (1862–1942)¹

Time-series data are regularly collected and analyzed in a wide range of (scientific) domains.

Acquiring values of a physical quantity via simulation or measurement over time produces time-series data. The data can be described as a function of time and it can be represented as a function graph. Multiple simulation runs or multiple measurements of the same physical quantity result in ensembles of function graphs which we call families of function graphs. The analysis of function graphs, (more generally: curves) is extensively studied in mathematics, statistics, and visualization; but less research is focused on the analysis of entire families of function graphs.

Interactive visual analysis in combination with a complex data model, which supports families of function graphs in addition to scalar parameters, represents a premium methodology for such an analysis. In this chapter we describe the three levels of complexity of interactive visual analysis we identified during several case studies from different disciplines. The first two levels represent the current state of the art. The newly introduced third level makes an in-depth analysis of families of function graphs possible. The two essential components of the third level analysis are data derivation and advanced interaction. This is often the only way to extract deeply hidden implicit information from complex data sets. We seamlessly integrate data derivation, advanced interaction, and visual exploration to facilitate interactive visual analysis of families of function graphs. We illustrate the proposed approach with typical analysis patterns identified in two case studies from the automotive industry.

1British physicist, chemist, mathematician, and sportsman. Received the 1915 Nobel Prize in Physics for the analysis of crystal structure using X-ray diffraction.

39

40 CHAPTER 4. ANALYSIS USING DATA AGGREGATION AND DERIVATION

4.1 Motivation

Generating useful knowledge from the information that is often only implicitly available in complex data sets is one of the key challenges in analysis. Interactive visual analysis (IVA) has proven itself, recently, as an important and valuable method of getting insight into, under-standing, and analyzing complex data. However, IVA is still not well integrated into the whole analysis work flow. There is a multitude of powerful methods presented, but, unfortunately, they often remain isolated.

Our work is motivated by case studies we have done with domain experts from different fields including engineering [138, 139, 161] (see also Chapter 7) and medicine [160]. We have realized that many details of the data sets from those very different problem domains can be represented asfamilies of function graphs, introduced in Section 3.2. We could also identify similar procedures in the analysis of such data sets. We suggest that representing function graphs as an atomic type opens new analysis possibilities. We focus on a set of tools for the analysis of data that contains families of function graphs.

The analysis of function graphs is a well-known and extensively researched topic in science and mathematics. However, there is not much research on the analysis of entire families of function graphs. As demonstrated in Chapter 3, IVA offers an effective and efficient opportu-nity to analyze even larger families of function graphs. The state of the art follows the visual information seeking mantra [236]:overview first, zoom and filter, then details-on-demand. This approach has often been proven powerful, but especially when working with families of func-tion graphs, there are cases when zooming and filtering is not sufficient. Our work is in part motivated by curve sketching, a topic all of us are familiar with from high school. We need functionality to extend the data set by computing new attributes and additional derived curves when analyzing families of function graphs; just as we compute new attributes (e.g., extrema) and curves (e.g., first derivative) in curve sketching. Curve sketching helps us in the analysis of single curves. In this chapter, we propose related analysis methods for entire families of function graphs. The proposed ideas are in part suitable for the analysis of families of generic curves, too.

Traditional visualization systems often limit data manipulation to filtering and require more complex pre-processing to be performed in a separate step before the visual analysis. When the pre-processing is designed, one needs to estimate what properties of the data are expected to be of interest. Such a priori knowledge is often not available, in particular not in more in-tricate analysis cases. In this chapter we present a set of tools which extends the conventional approach and facilitates on demand data generation. By allowing the synthetic extension of data by attribute derivation (in addition to filtering, of course) at any time, new analysis possibilities arise. We claim that such an interactive attribute derivation mechanism is useful in particular for experts. An integrated system makes it possible to reveal deeply hidden information in the data without requiring detours or a priori knowledge to design the pre-processing.

The main contribution of this chapter is a set of analysis procedures, cleverly combined in one toolbox, which makes the deep and flexible analysis of complex data containing families of function graphs possible. We argue that a rich set of tightly integrated (general) analysis mechanisms can help in a wide range of application scenarios. We classify the analysis process