Optimization of parallel coordinates for visual analytics

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The visualization and interaction of multidimensional data always requires optimized solutions for integrating the display, exploration and analytical reasoning of data into a kind of visual pipeline for human-centered data analysis and interpretation. However, parallel coordinate plot, as one of the most popular multidimensional data visualization techniques, suffers from a visual clutter problem. Although this problem has been addressed in many related studies, computational cost and information loss still hamper the application of these techniques, which leads to large high dimensional data sets. Therefore, the main goal of this thesis is to optimize the visual representation of parallel coordinates based on their geometrical properties. At the first stage, we set out to find optimization methods for permuting data values displayed in parallel coordinate plot to reduce the visual clutter. We divide the dataset into two classifications according to the values and the geometric theory of the parallel coordinate plot: numerical data and non-numerical data, and missing data may exist between them occasionally. We apply Sugiyama’s layered directed graph drawing algorithm into parallel coordinate plot to minimize the number of edge crossing among polygonal lines. The methods are proved to be valuable as it can optimize the order of missing or non-numerical value to tackle clutter reduction. In addition, it is true that optimizing the order is a NP-complete problem, though changing the order of the axis is a straightforward way to address the visual clutter problem. Therefore, we try to propose in the research a new axes re-ordering method in parallel coordinate plot: a similarity-based method, which is based on the combination of Nonlinear Correlation Coefficient (NCC) and Singular Value Decomposition (SVD) algorithms. By using this approach, the first remarkable axis can be selected based on mathematical theory and all axes can be re-ordered in line with the degree of similarities among them. We also propose a measurement of contribution rate of each dimension to reveal the property hidden in the dataset. In the third stage, we put forward a new projection method which is able to visualize more data items in the same display space than the existing parallel coordinate methods. Moreover, it is demonstrated clearly in the research that the new method enjoys some elegant duality properties with parallel coordinate plot and Cartesian orthogonal coordinate representation. Meanwhile, the mean crossing angles and the amount of edge crossing between the neighboring axes are utilized in this research to demonstrate the rationale and effectiveness of our approaches.
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