Markov Chain Driven Multi-Dimensional Visual Pattern Analysis with Parallel Coordinates

Abstract

Parallel coordinates is a widely used visualization technique for presenting, analyzing and exploring multidimensional data. However, like many other visualizations, it can suffer from an overplotting problem when rendering large data sets. Until now, quite a few methods are proposed to discover and illustrate the major data trends in cluttered parallel coordinates. Among them, frequency-based approaches using binning and histograms are widely adopted. The traditional binning method, which records line-segment frequency, only considers data in a two-dimensional subspace, as a result, the multi-dimensional features are not taken into account for trend and outlier analysis. Obtaining a coherent binned representation in higher dimensions is challenging because multidimensional binning can suffer from the curse of dimensionality. In this paper, we utilize the Markov Chain model to compute an n-dimensional joint probability for each data tuple based on a two-dimensional binning method. This probability value can be utilized to guide the user for selection and brushing. We provide various interaction techniques for the user to control the parameters during the brushing process. Filtered data with a high probability measure often explicitly illustrates major data trends. In order to scale to large data sets, we also propose a more precise angular representation for angular histograms to depict the density of the brushed data trends. We demonstrate our methods and evaluate the results on a wide variety of data sets, including real-world, high-dimensional biological data.