Interactive Visual Analysis of Families of Function Graphs

Abstract

The analysis and exploration of multidimensional and multivariate data is still one of the most challenging areas in the field of visualization. In this paper, we describe an approach to visual analysis of an especially challenging set of problems that exhibit a complex internal data structure. We describe the interactive visual exploration and analysis of data that includes several (usually large) families of function graphs fi (x, t). We describe analysis procedures and practical aspects of the interactive visual analysis specific to this type of data (with emphasis on the function graph characteristic of the data). We adopted the well-proven approach of multiple, linked views with advanced interactive brushing to assess the data. Standard views such as histograms, scatterplots, and parallel coordinates are used to jointly visualize data. We support iterative visual analysis by providing means to create complex, composite brushes that span multiple views and that are constructed using different combination schemes. We demonstrate that engineering applications represent a challenging but very applicable area for visual analytics. As a case study, we describe the optimization of a fuel injection system in diesel engines of passenger cars.

Visualizing Flow Trajectories Using Locality-based Rendering and Warped Curve Plots

“…Konyha et al used families of function graphs to help steer the visual analysis process [4]. Families of function graphs are visualized by plotting each function graph curve onto the same plot.…”

“…Various kinds of curve plots have also been used in other visualization systems as a selection tool [4,10], so we will first describe the construction of a typical pathline plot. Let L = {l 1 , l 2 ,...l n } be the set of trajectories and X = {x 1 , x 2 ,...x m } be the attributes associated with each trajectory.…”

Evolutional Insights from UML and Source Code Versions using Information Visualization and Visual Analysis

“…The mixture of function graphs and scalars is particularly challenging. We have used a combination of the curves view and conventional views in [6] in order to analyze similarly structured data sets.…”

“…The lower view provides a curve view [6], a family of 8,537 curves, each representing a class over a sequence of 72 versions (from 1. 1.2 012 to 1.6.0).…”

“…The availability of large number of Java SDK source code versions (72 versions) provides an excellent opportunity to explore changes in the code using the UML design diagram as a reference point. A plethora of information visualization techniques and views is provided by the previously developed ComVis information visualization tool [6]. ComVis includes conventional views like 2D and 3D scatter plots, parallel coordinates, histogram, as well as other curve views used for displaying function graphs.…”