Scalable multivariate volume visualization and analysis

The article presents and investigates new possibilities of multivariate data visualization and their analytical convenience. We demonstrate elementary principles, algorithms and graphical outputs of modern visualization methods with particular focus on Bertin matrices, RADVIZ, Projection pursuit and parallel coordinates. Illustrative examples show their practical implementation into the process of multivariate data analysis, hence providing the reader with an idea of the wide range of their application.

Over the past decades, parallel coordinates plots (PCPs) have been extensively applied to various tasks of multivariate data visualization. However, a main disadvantage of PCPs is the almost inevitable overlap of polylines, which causes chaotic visual effects when the number of polylines is large and the sequence of parallel coordinates is not conducive to visualization. To tackle this issue, this paper proposed an axis permutation of PCPs based on Laplacian scores (LS), which can be used to enhance the visualization performance of the original PCPs. The enhanced PCP is a combination of an unsupervised feature selection technique (LS) and the visualization of multivariate data. With the new sequence of axes based on the Laplacian scores of the corresponding features, polylines of PCPs are distributed with less clutter and overlap. The experimental results demonstrated that the proposed method made great progress in enhancing the visualization performance of PCPs.

Although simple and based on physical realizable color primaries, the RGB color space cannot allow the direct definition of a topology-preserving, perceptually-compatible inter-color distance. The classical normalized inter-color distances are rather complex to implement and tune. We propose the use of a planar color representation plot, derived from multivariate data visualization using parallel coordinates, which allows the introduction of a luminance-invariant, geometry-based inter-color distance. We show that the new distance is used with good results in the implementation of distance-based color filters and edge detectors.

The curse of dimensionality, i.e., the fact that feature spaces of increasing dimensionality with finite sample sizes tend to be empty, has given incentive to a plethora of research activities in various disciplines and diverse application fields, e.g., statistics or neural networks. Three major application fields are multivariate data classification, data analysis and data visualization. In this contribution, methods for dimensionality reduction from three decades of interdisciplinary research are browsed and their applicability in the above application domains is briefly discussed. Complementing techniques for ensuing interactive data visualization, data navigation and visual exploratory data analysis are presented, which exploit the remarkable human perceptive and associative capabilities for interactive visual exploratory data analysis and systematic recognition system design. The main focus of this paper is on the comparison of feature selection and feature extraction techniques and the potential benefit of their combination. Further, the interesting implications of dimensionality reduction for VLSI design and related area and power consumption are pointed out.

Parallel coordinate plots (PCPs) are commonly used in information visualization to provide insight into multi-variate data. These plots help to spot correlations between variables. PCPs have been successfully applied to unstructured datasets up to a few millions of points. In this paper, we present techniques to enhance the usability of PCPs for the exploration of large, multi-timepoint volumetric data sets, containing tens of millions of points per timestep. The main difficulties that arise when applying PCPs to large numbers of data points are visual clutter and slow performance, making interactive exploration infeasible. Moreover, the spatial context of the volumetric data is usually lost. We describe techniques for preprocessing using data quantization and compression, and for fast GPU-based rendering of PCPs using joint density distributions for each pair of consecutive variables, resulting in a smooth, continuous visualization. Also, fast brushing techniques are proposed for interactive data selection in multiple linked views, including a 3D spatial volume view. These techniques have been successfully applied to three large data sets: Hurricane Isabel (Vis'04 contest), the ionization front instability data set (Vis'08 design contest), and data from a large-eddy simulation of cumulus clouds. With these data, we show how PCPs can be extended to successfully visualize and interactively explore multi-timepoint volumetric datasets with an order of magnitude more data points.

P-Lite: A study of parallel coordinate plot literacy

Multivariate data visualization is a classic topic, for which many solutions have been proposed, each with its own strengths and weaknesses. In standard solutions the structure of the visualization is fixed, we explore how to give the user more freedom to define visualizations. Our new approach is based on the usage of Flexible Linked Axes: The user is enabled to define a visualization by drawing and linking axes on a canvas. Each axis has an associated attribute and range, which can be adapted. Links between pairs of axes are used to show data in either scatter plot- or Parallel Coordinates Plot-style. Flexible Linked Axes enable users to define a wide variety of different visualizations. These include standard methods, such as scatter plot matrices, radar charts, and PCPs [11]; less well known approaches, such as Hyperboxes [1], TimeWheels [17], and many-to-many relational parallel coordinate displays [14]; and also custom visualizations, consisting of combinations of scatter plots and PCPs. Furthermore, our method allows users to define composite visualizations that automatically support brushing and linking. We have discussed our approach with ten prospective users, who found the concept easy to understand and highly promising.

In this paper, we present some graphical techniques for cluster analysis of high-dimensional data. Parallel coordinate plots and parallel coordinate density plots are graphical techniques which map multivariate data into a two-dimensional display. The method has some elegant duality properties with ordinary Cartesian plots so that higher-dimensional mathematical structures can be analyzed. Our high interaction software allows for rapid editing of data to remove outliers and isolate clusters by brushing. Our brushing techniques allow not only for hue adjustment, but also for saturation adjustment. Saturation adjustment allows for the handling of comparatively massive data sets by using the α-channel of the Silicon Graphics workstation to compensate for heavy overplotting.

Interactive labelling of a multivariate dataset for supervised machine learning using linked visualisations, clustering, and active learning

Data visualization is one of the most powerful techniques to analyze and obtain reliable results based on the displayed outputs since it allows humans to improve decision-making by visually analyzing data behavior. Nevertheless, it could be disrupted by high data amounts in the visualization, as is the case with Parallel Coordinate Plot (PCP), where data behavior and associations of volumes of data are difficult to identify. This paper aims to reduce this issue with PCP and take advantage of metaheuristics for optimization problems through a Simulated Annealing (SA) algorithm. The proposed method was developed and tested using air pollution and meteorological variables. The obtained results presented a reduction in data volume, thus helping represent the most relevant data for the final user.KeywordsMetaheuristicParallel coordinates plotFiltering

In the recent years, high-dimensional data visualization has become a challenging task in data science and machine learning. As one of the most effective methods for high-dimensional data visualization, Parallel Coordinates Plots (PCPs) demonstrate dimensional reduction by transforming features of multivariate data into 2D axes. Such approach, however, does not consider the irrelevant or redundant features such that each feature is projected into the axis in a fixed manner. This paper proposed a novel PCP introduced by an unsupervised feature selection called Laplacian Score, which can be used to improve the visualization performance of PCP by ranking the importance of attributes based on their locality preserving power. The experimental results demonstrated that the performance of PCP visualization can be improved by feature selection method. Furthermore, we proposed a flexible user interface based on PCP visualization and Laplacian Score.

Gaining understanding of multivariate and multidimensional data through visualization

This paper describes a minimally immersive interactive system for visualization of multivariate volumetric data. The system, SFA, uses glyph-based volume rendering which does not suffer the initial costs of isosurface rendering or voxel-based volume rendering, while offering the capability of viewing the entire volume. Glyph rendering also allows the simultaneous display of multiple data values per volume location. Two-handed interaction using three-space magnetic trackers and stereoscopic viewing are combined to produce a minimally immersive volumetric visualization system that enhances the user's three-dimensional perception of the data. We describe the usefulness of this system for visualizing volumetric scalar and vector data. SFA allows the three-dimensional volumetric visualization, manipulation, navigation, and analysis of multivariate, time-varying volumetric data, increasing the quantity and clarity of the information conveyed from the visualization system.

This paper describes a minimally immersive interactive system for flow visualization of multivariate volumetric data. The system, SFA, uses perceptually motivated rendering to increase the quantity and clarity of information perceived. Proprioception, stereopsis, perceptually motivated shape visualization, and three-dimensional interaction are combined in SFA to allow the three-dimensional volumetric visualization, manipulation, navigation, and analysis of multivariate, time-varying flow data.

This paper describes a minimally immersive interactive system for visualization of multivariate volumetric data. The system, SFA, uses glyph-based volume rendering which does not suffer the initial costs of isosurface rendering or voxel-based volume rendering, while offering the capability of viewing the entire volume. Glyph rendering also allows the simultaneous display of multiple data values per volume location. Two-handed interaction using three-space magnetic trackers and stereoscopic viewing are combined to produce a minimally immersive volumetric visualization system that enhances the user's three-dimensional perception of the data. We describe the usefulness of this system for visualizing volumetric scalar and vector data. SFA allows the three-dimensional volumetric visualization, manipulation, navigation, and analysis of multivariate, time-varying volumetric data, increasing the quantity and clarity of the information conveyed from the visualization system.