Until now a lot of visual analytics predominantly delivers qualitative results-based, for example, on a continuous color map or a detailed spatial encoding. Important target applications, however, such as medical diagnosis and decision making, clearly benefit from quantitative analysis results. In this paper we propose several specific extensions to the well-established concept of linking&brushing in order to make the analysis results more quantitative. We structure the brushing space in order to improve the reproducibility of the brushing operation, e.g., by introducing the percentile grid. We also enhance the linked visualization with overlaid descriptive statistics to enable a more quantitative reading of the resulting focus+context visualization. Additionally, we introduce two novel brushing techniques: the percentile brush and the Mahalanobis brush. Both use the underlying data to support statistically meaningful interactions with the data. We illustrate the use of the new techniques in the context of two case studies, one based on meteorological data and the other one focused on data from the automotive industry where we evaluate a shaft design in the context of mechanical power transmission in cars.
In today's data-driven world, decision makers are facing many conflicting objectives. Since there is usually no solution that optimizes all objectives simultaneously, the aim is to identify a solution with acceptable trade-offs. Interactive multiobjective optimization methods are iterative processes in which a human decision maker repeatedly provides one's preferences to request computing new solutions and compares them. With these methods, the decision maker can learn about the problem and its limitations. However, advanced optimization software usually offer simple visualization tools that can be significantly improved. On the other hand, current approaches for multiobjective optimization from the visualization community provide superior visualization tools but lack advanced optimization. In this paper, we introduce a new term, interactivize, for integrating interactive multiobjective optimization and interactive visualization and present an interactivized approach supporting decision makers in visually steering interactive multiobjective optimization methods. We integrate state-of-the-art interactive visualization with the process of interactive multiobjective optimization in a visual analytics solution that significantly improves the analysis workflow of decision makers, like comparing selected solutions and specifying new preferences during the iterative solution process. To realize the new interactivized approach, we combine a coordinated multiple views system with DESDEO, an open-source software framework for interactive multiobjective optimization. We demonstrate our interactivized approach on a river pollution problem.INDEX TERMS Visual analytics, multiple criteria decision making, interactive optimization.
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