Clustering Visualizations of Multidimensional Data

This paper describes an R package which produces tours of multivariate data. The package includes functions for creating different types of tours, including grand, guided, and little tours, which project multivariate data (p-D) down to 1, 2, 3, or, more generally, d (≤ p) dimensions. The projected data can be rendered as densities or histograms, scatterplots, anaglyphs, glyphs, scatterplot matrices, parallel coordinate plots, time series or images, and viewed using an R graphics device, passed to GGobi, or saved to disk. A tour path can be stored for visualisation or replay. With this package it is possible to quickly experiment with different, and new, approaches to tours of data. This paper contains animations that can be viewed using the Adobe Acrobat PDF viewer.

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.

The first step is to analyze the statistical graphics in use, so we examine the descriptive statistics. Next is the boxplot, the Q-Q plot, the histogram, the regressogram, the barchart, the dotchart, the piechart, the 2D-scatterplot, the 2D-contour plot, the scatterplot matrix, the 3D-scatterplot, the 3D-contour plot, the Chernoff faces and the parallel coordinate plot. We use some of the tools of XploRe to examine the Berlin housing dataset which use the plots mentioned above. Finally we state that two kinds of windows are necessary, one which can draw points, lines and areas, another which can draw glyphs windows, i.e. the Chernoff faces, star diagrams and so on.

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.

Traditional multidimensional visualization techniques, such as glyphs, parallel coordinates and scatterplot matrices, suffer from clutter at the display level and difficult user navigation among dimensions when visualizing high dimensional datasets. In this paper, we propose a new multidimensional visualization technique named a value and relation (VaR) display, together with a rich set of navigation and selection tools, for interactive exploration of datasets with up to hundreds of dimensions. By explicitly conveying the relationships among the dimensions of a high dimensional dataset, the VaR display helps users grasp the associations among dimensions. By using pixel-oriented techniques to present values of the data items in a condensed manner, the VaR display reveals data patterns in the dataset using as little screen space as possible. The navigation and selection tools enable users to interactively reduce clutter, navigate within the dimension space, and examine data value details within context effectively and efficiently. The VaR display scales well to datasets with large numbers of data items by employing sampling and texture mapping. A case study on a real dataset, as well as the VaR displays of multiple real datasets throughout the paper, reveals how our proposed approach helps users interactively explore high dimensional datasets with large numbers of data items

We explore how to rigorously evaluate multidimensional visualizations for their ability to support decision making. We first define multi-attribute choice tasks, a type of decision task commonly performed with such visualizations. We then identify which of the existing multidimensional visualizations are compatible with such tasks, and set out to evaluate three elementary visualizations: parallel coordinates, scatterplot matrices and tabular visualizations. Our method consists in first giving participants low-level analytic tasks, in order to ensure that they properly understood the visualizations and their interactions. Participants are then given multi-attribute choice tasks consisting of choosing holiday packages. We assess decision support through multiple objective and subjective metrics, including a decision accuracy metric based on the consistency between the choice made and self-reported preferences for attributes. We found the three visualizations to be comparable on most metrics, with a slight advantage for tabular visualizations. In particular, tabular visualizations allow participants to reach decisions faster. Thus, although decision time is typically not central in assessing decision support, it can be used as a tie-breaker when visualizations achieve similar decision accuracy. Our results also suggest that indirect methods for assessing choice confidence may allow to better distinguish between visualizations than direct ones. We finally discuss the limitations of our methods and directions for future work, such as the need for more sensitive metrics of decision support.

Multidimensional projections are an increasingly popular technique for visualizing large datasets containing observations having tens or even hundreds of dimensions. Compared to other techniques such as parallel coordinates, tables, and scatterplot matrices, they support tasks such as finding groups of related observations and outliers in simpler, more effective, ways. The authors discuss here the advantages of multidimensional projections, how to compute them, and recent advances that enhance them by visual explanatory techniques, so as to make them efficient and effective instruments that should be part of the toolkit of any scientist interested in high-dimensional data exploration.

Discovering and extracting linear trends and correlations in datasets is very important for analysts to understand multivariate phenomena. However, current widely used multivariate visualization techniques, such as parallel coordinates and scatterplot matrices, fail to reveal and illustrate such linear relationships intuitively, especially when more than 3 variables are involved or multiple trends coexist in the dataset. We present a novel multivariate model parameter space visualization system that helps analysts discover single and multiple linear patterns and extract subsets of data that fit a model well. Using this system, analysts are able to explore and navigate in model parameter space, interactively select and tune patterns, and refine the model for accuracy using computational techniques. We build connections between model space and data space visually, allowing analysts to employ their domain knowledge during exploration to better interpret the patterns they discover and their validity. Case studies with real datasets are used to investigate the effectiveness of the visualizations.

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

In this work, we present an effective and scalable system for multivariate volume data visualization and analysis with a novel Transfer Function (TF) interface design that tightly couples parallel coordinates plots (PCP) and MDS-based dimension projection plots. In our system, the PCP visualizes the data distribution of each variate and the MDS plots project features. Together, they are integrated seamlessly to provide flexible feature classification without context switching between different data presentations during the user interaction. The proposed interface enables users to identify relevant correlation clusters and assign optical properties on them. To further support large scale multivariate volume data visualization and analysis, we develop three integrated parallel systems to accelerate the rendering of PCP, the layout of MDS, as well as parallel rendering of multivarite volume data. Our experiments show that the system is effective in multivariate volume data visualization and its performance is scalable for data sets with different sizes and number of variates.

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.

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.

Visual analytics of multidimensional multivariate data is a challenging task because of the difficulty in understanding metrics in attribute spaces with more than three dimensions. Frequently, the analysis goal is not to look into individual records but to understand the distribution of the records at large and to find clusters of records with similar attribute values. A large number of (typically hierarchical) clustering algorithms have been developed to group individual records to clusters of statistical significance. However, only few visualization techniques exist for further exploring and understanding the clustering results. We propose visualization and interaction methods for analyzing individual clusters as well as cluster distribution within and across levels in the cluster hierarchy. We also provide a clustering method that operates on density rather than individual records. To not restrict our search for clusters, we compute density in the given multidimensional multivariate space. Clusters are formed by areas of high density. We present an approach that automatically computes a hierarchical tree of high density clusters. To visually represent the cluster hierarchy, we present a 2D radial layout that supports an intuitive understanding of the distribution structure of the multidimensional multivariate data set. Individual clusters can be explored interactively using parallel coordinates when being selected in the cluster tree. Furthermore, we integrate circular parallel coordinates into the radial hierarchical cluster tree layout, which allows for the analysis of the overall cluster distribution. This visual representation supports the comprehension of the relations between clusters and the original attributes. The combination of the 2D radial layout and the circular parallel coordinates is used to overcome the overplotting problem of parallel coordinates when looking into data sets with many records. We apply an automatic coloring scheme based on the 2D radial layout of the hierarchical cluster tree encoding hue, saturation, and value of the HSV color space. The colors support linking the 2D radial layout to other views such as the standard parallel coordinates or, in case data is obtained from multidimensional spatial data, the distribution in object space.

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.