Proposing a Pareto-VIKOR Ranking Method for Enhancing Parallel Coordinates Visualization

Abstract

Data visualization is an essential step in data science to get better interpretation to analyse data. The parallel coordinates plot (PCP) is a well-known method to visualize high-dimensional $(D \gt 3)$ data without dimension reduction. In large-scale datasest, PCP may fail because of many clutters and crossing lines in the plot. The order of coordinates is one of the parameters in PCP which can affect on the performance of this method. Finding the best order can be considered as a multi-criteria comparison task based on different metrics such as minimizing the number of crossing lines between adjacent coordinates and the maximizing the pairwise correlation coefcient values. In order to improve the visualization of data using PCP, this paper presents a multi-metric Pareto-VIKOR ranking (PVRPCP), a new method which determines the best order of coordinates based on optimizing two or more metrics. The method consists of evaluating all possible coordinates permutations based on evaluation metrics and applying non-dominated sorting algorithm (NDS) to obtain the Pareto-front ranks (PF). The solutions on each Pareto front are then ranked by VIKOR, a multi-criteria decision making measure. In order to evaluate the effectiveness of the the proposed method in data visualization, we also designed several multi-dimensional benchmarks to represent the effect of ordering in PCP. In addition to author-created benchmarks, several multi-objective function benchmarks and real-world datasets are utilized to evaluate the proposed method. The experimental results show that the PVRPCP offers improved PCP visualization compared to the original order in terms of both utilized metrics.