Grafická analýza vícerozměrných dat

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.

Preserving all multidimensional data in two-dimensional visualization is a long-standing problem in Visual Analytics, Machine Learning/Data Mining, and Multiobjective Pareto Optimization. While Parallel and Radial (Star) coordinates preserve all n-D data in two dimensions, they are not sufficient to address visualization challenges of all possible datasets such as occlusion. More such methods are needed. Recently, the concepts of lossless General Line Coordinates that generalize Parallel, Radial, Cartesian, and other coordinates were proposed with initial exploration and application of several subclasses of General Line Coordinates such as Collocated Paired Coordinates and Star Collocated Paired Coordinates. This article explores and enhances benefits of General Line Coordinates. It shows the ways to increase expressiveness of General Line Coordinates including decreasing occlusion and simplifying visual pattern while preserving all n-D data in two dimensions by adjusting General Line Coordinates for given n-D datasets. The adjustments include relocating, rescaling, and other transformations of General Line Coordinates. One of the major sources of benefits of General Line Coordinates relative to Parallel Coordinates is twice less number of point and lines in visual representation of each n-D points. This article demonstrates the benefits of different General Line Coordinates for real data visual analysis such as health monitoring and benchmark Iris data classification compared with results from Parallel Coordinates, Radvis, and Support Vector Machine. The experimental part of the article presents the results of the experiment with about 70 participants on efficiency of visual pattern discovery using Star Collocated Paired Coordinates, Parallel, and Radial Coordinates. It shows advantages of visual discovery of n-D patterns using General Line Coordinates subclass Star Collocated Paired Coordinates with n = 160 dimensions.

Exploratory analysis of multivariate data: Applications of parallel coordinates in ecology

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.

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.

This article discusses a procedure for the exploration of options in preliminary design. The procedure is based on the application of morphing procedures, which are typical of animation software, to building parametric analyses. The procedure is based on partially overlapping sequences of evaluations targeted on dynamic ad-hoc test-models and is aimed at the creation of data fields for the representation of the performance consequences of competing design sceneries. This representation is necessarily multidimensional and is based on parallel coordinates plots. The implementation of a specific test procedure of the kind described above is also discussed. The procedure has been supported by the use of contemporary analytical and representational systems and tools; namely, ESP-r, Radiance, Ggobi, and an extensible tool for the dynamic morphing of models through user-specified criteria, named OPTS, by the author.

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.

P-Lite: A study of parallel coordinate plot literacy

Multivariate data analysis for Raman imaging of a model pharmaceutical tablet

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.

John J. MillerEdward J. WegmanCenter for Computational StatisticsGeorge Mason UniversityFairfax, VA 22030ABSTRACTThe graphical representation of high dimensional data may be accomplished by usingthe parallel coordinate plotting system. In such a representation points in Euclidian n-space aremapped into line segments in Euclidian 2-space by a projective transformation. Thisrepresentation preserves much of the geometric structure found in hyperspace but not easilyrepresentable by other methods. In large data set applications, the graphical displays may beheavily overplotted like ordinary scatterplots yielding uninterpretable displays. In this paper,we suggest replacing the raw data display with a density plot. In order to define densities forlines sensibly, we introduce the notion of line densities and develop their basic construction.We illustrate with theoretical parallel coordinate density plots for the normal and the uniformcases. Finally we illustrate sample density plots with 4-dimensional spheres.1. Introduction.The graphical display of high dimensional data is a challenging and difficult task. Anumber of interesting techniques including rotating three-dimensional scatterplots, thescatterplot matrix with brushing, the grand tour and other related graphical and computationalmethodologies have been invented with the ambition of seeing structural relationships amongrandom variables in three, four and more dimensions. One such technique is the parallelcoordinate display. This has been exposited by Inselberg (1985) as a tool for computationalgeometry and by Bolorforoush and Wegman (1988) and Wegman (1990) as a tool forexploratory data analysis. Recognizing the basic weakness of Cartesian plots as an inability tohave more than three orthogonal coordinate axes, the parallel coordinate idea is to give uporthogonality in favor of a system of parallel coordinate axes drawn in the 2-plane. Of course,as many parallel axes as one likes can be drawn in the 2-plane so that there is no inherentdimensionality limit. The idea then is to label each axis with an appropriate variable name andto connect points on adjacent axes with straight line segments. Figure 1.1 illustrates the basicidea.

Parallel coordinate is a popular tool for visualizing high-dimensional data and analyzing multivariate data. With the rapid growth of data size and complexity, data clutter in parallel coordinates is a major issue for Big Data visualization. This has given rise to three problems, 1) how to rearrange the parallel axes without the loss of data patterns, 2) how to shrink data attributes on each axis without the loss of data trends, 3) how to visualize the structured and unstructured data patterns for Big Data analysis. In this paper, we introduce the 5Ws dimensions as the parallel axes and establish the 5Ws sending density and receiving density as additional axes for Big Data visualization. Our model not only demonstrates Big Data attributes and patterns, but also reduces data over-lapping by up to 80 percent without the loss of data patterns. Experiments show that this new model can be efficiently used for Big Data analysis and visualization.

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

It is well known that the correlation matrix has a central role in the analysis of multivariate data. The inverse of the correlation matrix, however, also has important interpretations. An exposition of some of the properties connected with the inverse of the correlation matrix is provided and its use in the analysis of multivariate data is described.

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.