Optimization of parallel coordinates for visual analytics

University of Technology Sydney. Faculty of Engineering and Information Technology.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

Measuring Visual Complexity of Cluster-Based Visualizations

Handling visual complexity is a challenging problem in visualization owing to the subjectiveness of its definition and the difficulty in devising generalizable quantitative metrics. In this paper we address this challenge by measuring the visual complexity of two common forms of cluster-based visualizations: scatter plots and parallel coordinatess. We conceptualize visual complexity as a form of visual uncertainty, which is a measure of the degree of difficulty for humans to interpret a visual representation correctly. We propose an algorithm for estimating visual complexity for the aforementioned visualizations using Allen's interval algebra. We first establish a set of primitive 2-cluster cases in scatter plots and another set for parallel coordinatess based on symmetric isomorphism. We confirm that both are the minimal sets and verify the correctness of their members computationally. We score the uncertainty of each primitive case based on its topological properties, including the existence of overlapping regions, splitting regions and meeting points or edges. We compare a few optional scoring schemes against a set of subjective scores by humans, and identify the one that is the most consistent with the subjective scores. Finally, we extend the 2-cluster measure to k-cluster measure as a general purpose estimator of visual complexity for these two forms of cluster-based visualization

Information visualization for DNA microarray data analysis: A critical review

Graphical representation may provide effective means of making sense of the complexity and sheer volume of data produced by DNA microarray experiments that monitor the expression patterns of thousands of genes simultaneously. The ability to use ldquoabstractrdquo graphical representation to draw attention to areas of interest, and more in-depth visualizations to answer focused questions, would enable biologists to move from a large amount of data to particular records they are interested in, and therefore, gain deeper insights in understanding the microarray experiment results. This paper starts by providing some background knowledge of microarray experiments, and then, explains how graphical representation can be applied in general to this problem domain, followed by exploring the role of visualization in gene expression data analysis. Having set the problem scene, the paper then examines various multivariate data visualization techniques that have been applied to microarray data analysis. These techniques are critically reviewed so that the strengths and weaknesses of each technique can be tabulated. Finally, several key problem areas as well as possible solutions to them are discussed as being a source for future work

Two axes re-ordering methods in parallel coordinates plots

© 2015 Elsevier Ltd. Visualization and interaction of multidimensional data are challenges in visual data analytics, which requires optimized solutions to integrate the display, exploration and analytical reasoning of data into one visual pipeline for human-centered data analysis and interpretation. Even though it is considered to be one of the most popular techniques for visualization and analysis of multidimensional data, parallel coordinate visualization is also suffered from the visual clutter problem as well as the computational complexity problem, same as other visualization methods in which visual clutter occurs where the volume of data needs to be visualized to be increasing. One straightforward way to address these problems is to change the ordering of axis to reach the minimal number of visual clutters. However, the optimization of the ordering of axes is actually a NP-complete problem. In this paper, two axes re-ordering methods are proposed in parallel coordinates visualization: (1) a contribution-based method and (2) a similarity-based method.The contribution-based re-ordering method is mainly based on the singular value decomposition (SVD) algorithm. It can not only provide users with the mathmetical theory for the selection of the first remarkable axis, but also help with visualizing detailed structure of the data according to the contribution of each data dimension. This approach reduces the computational complexity greatly in comparison with other re-ordering methods. A similarity-based re-ordering method is based on the combination of nonlinear correlation coefficient (NCC) and SVD algorithms. By using this approach, axes are re-ordered in line with the degree of similarities among them. It is much more rational, exact and systemic than other re-ordering methods, including those based on Pearson's correlation coefficient (PCC). Meanwhile, the paper also proposes a measurement of contribution rate of each dimension to reveal the property hidden in the dataset. At last, the rationale and effectiveness of these approaches are demonstrated through case studies. For example, the patterns of Smurf and Neptune attacks hidden in KDD 1999 dataset are visualized in parallel coordinates using contribution-based re-ordering method; NCC re-ordering method can enlarge the mean crossing angles and reduce the amount of polylines between the neighboring axes