Tran Van Long

A framework for exploring multidimensional data with 3D projections

Visualization of high‐dimensional data requires a mapping to a visual space. Whenever the goal is to preserve similarity relations a frequent strategy is to use 2D projections, which afford intuitive interactive exploration, e.g., by users locating and selecting groups and gradually drilling down to individual objects. In this paper, we propose a framework for projecting high‐dimensional data to 3D visual spaces, based on a generalization of the Least‐Square Projection (LSP). We compare projections to 2D and 3D visual spaces both quantitatively and through a user study considering certain exploration tasks. The quantitative analysis confirms that 3D projections outperform 2D projections in terms of precision. The user study indicates that certain tasks can be more reliably and confidently answered with 3D projections. Nonetheless, as 3D projections are displayed on 2D screens, interaction is more difficult. Therefore, we incorporate suitable interaction functionalities into a framework that supports 3D transformations, predefined optimal 2D views, coordinated 2D and 3D views, and hierarchical 3D cluster definition and exploration. For visually encoding data clusters in a 3D setup, we employ color coding of projected data points as well as four types of surface renderings. A second user study evaluates the suitability of these visual encodings. Several examples illustrate the frameworks applicability for both visual exploration of multidimensional abstract (non‐spatial) data as well as the feature space of multi‐variate spatial data.

Multiclustertree: interactive visual exploration of hierarchical clusters in multidimensional multivariate data

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.

SmoothViz: Visualization of Smoothed Particles Hydrodynamics Data

Smoothed particle hydrodynamics (SPH) is a completely mesh-free method to simulate fluid flow (Gingold & Monaghan, 1977; Lucy, 1977). Rather than representing the physical variables on a fixed grid, the fluid is represented by freely moving interpolation centers (“particles”). Apart from their position and velocity these particles carry information about the physical quantities of the considered fluid, such as temperature, composition, chemical potentials, etc. As the method is completely Lagrangian and particles follow the motion of the flow, the particles represent an unstructured data set at each point in time, i.e., the particles do not exhibit a regular spatial arrangement nor a fixed connectivity. For a recent detailed review of modern formulations of the SPH method see Rosswog (2009). For the analysis of the simulation results, data visualization plays an important role. However, visualization methods need to account for the highly adaptive, unstructured data representation in SPH simulations. Reconstructing the entire data field over a regular grid is not an option, as it would either use grids of immense sizes that cannot be handled efficiently anymore or it inevitably would introduce significant interpolation errors. Such errors should be avoided, especially as they would occur most prominently in areas of high particle density, i.e., areas of highest importance are undersampled. Adaptive grids may be an option as interpolation errors can be kept low, but the adaptivity requires special treatments during the visualization process. In this chapter, we introduce visualization methods that operate directly on the particle data, i.e., on unstructured point-based volumetric data. Section 3 introduces an approach to directly extract isosurfaces from a scalar field of the SPH simulation. Isosurfaces extraction is a common visualization concept and is suitable for SPH data visualization, as one is often interested in seeing boundaries of certain features. Because of the use of radial kernel functions in SPH computations (which is crucial for exact conservation of energy, momentum, and angular momentum) together with a poor a resolution, one can observe that the extracted isosurfaces may be bumpy, especially in regions of low particle density. We approach this issue by introducing level-set methods for 1

Reordering dimensions for Radial Visualization of multidimensional data — A Genetic Algorithms approach

In this paper, we propose a Genetic Algorithm (GA) for solving the problem of dimensional ordering in Radial Visualization (Radviz) systems. The Radviz is a non-linear projection of high-dimensional data set onto two dimensional space. The order of dimension anchors in the Radviz system is crucial for the visualization quality. We conducted experiments on five common data sets and compare the quality of solutions found by GA and those found by the other well-known methods. The experimental results show that the solutions found by GA for these tested data sets are very competitive having better cost values than almost all solutions found by other methods. This suggests that GA could be a good approach to solve the problem of dimensional ordering in Radviz.

Efficient Reordering of Parallel Coordinates and Its Application to Multidimensional Biological Data Visualization

Multidimensional data visualization is a challenging research field with many applications in various fields of sciences. Parallel coordinate plots are one of the most common information visualization techniques for visualizing multidimensional data. Unfortunately, the effectiveness of parallel coordinates depends heavily on the order of the data dimensions and different orders exhibit different information about the structures in the multidimensional data. In this paper, we propose a method that supports an automatic dimension reordering and spacing of the axes in parallel coordinate plots. The underlying idea of our method is to find an asymptotic for the optimization of the permutation based on data dimension similarity. We present our method with two kinds of similarities, namely, Pearson’s correlation similarity for unclassified data and class distance consistency for classified data. We present results on well-known multidimensional data sets to show how our method improves the parallel coordinate plots and to prove its efficiency. Finally, we demonstrate how our approach can be applied to the visualization of bivariate structures in biological data.

A new metric on parallel coordinates and its application for high-dimensional data visualization

High-dimensional data visualization is a changing task with many applications in a various fields of sciences. Parallel coordinates is one of the most widely used information visualization technique for multivariate data analysis and high-dimensional geometry. The dimension ordering is an original problem for exploring structures in a high-dimensional data space. In this paper, we propose a new metric for measuring distance between two line-segment on the parallel coordinates. The metric is suitable and effective on the parallel coordinates. We use our metric distance for finding an optimal dimension ordering on the parallel coordinates. Finally, we demonstrate our method can be applied to visualize clusters in high-dimensional data on the parallel coordinates.

iSPLOM: Interactive with Scatterplot Matrix for Exploring Multidimensional Data

The scatterplot matrix is one of the most common methods for multidimensional data visualization. The scatterplot matrix is usually used to display all pairwise of data dimensions, that is organized a matrix. In this paper, we propose an interactive technique with scatterplot matrix to explore multidimensional data. The multidimensional data is projected into all pairwise orthogonal sections and display with scatterplot matrix. A user can select a subset of data set that separates from the rest of data set. A subset of the data set organized as a hierarchy cluster structure. The hierarchy cluster structure is display as a radial tree cluster. The user can select a cluster in the radial tree and all data points in this cluster are display on scatterplot matrix. The user is repeated this process to identify clusters. One of the most useful of our method can be identify the structure of multidimensional data set in an intuition fashion.

Laplacian star coordinates for visualizing multidimensional data

Multidimensional data visualization is an interesting research field with many applications in ubiquitous all fields of sciences. Star coordinates are one of the most common information visualization techniques for visualizing multidimensional data. A star coordinate system is a linear transformation that maps a multidimensional data space into a two-dimensional visual space, unfortunately, involving a loss of information. In this paper, we proposed to improve standard star coordinates by developing the concept of Laplacian star coordinates for visualizing multidimensional data. The Laplacian star coordinate system is based on dimension axes placement according to their similarity, which improves the quality of data representation. We prove the efficiency and robustness of our methods by measuring the quality of the representations for several data sets.

iRadviz: an inversion radviz for class visualization of multivariate data visualization

Multivariate data visualization is an interesting research field with many applications in ubiquitous fields of sciences. Radial visualization (Radviz) is one of the most common information visualization techniques for visualizing multivariate data. Unfortunately, Radviz display different information about structures of multivariate data on the different the order of the data dimensions and all points with different scale maps into the same point in the visual space. In this paper, we propose a method that improve the Radviz layout for class visualization of multivariate data. The basic idea of our method is finding a good corner viewing of a hypercube. Our method provides an improvement visualizing class structures of multivariate data sets on the Radviz. We present our method with two kinds of quality measurement. We prove the efficiency of our method for several data sets.

An optimal radial layout for high dimensional data class visualization

Multivariate data visualization is an interesting research field with many applications in ubiquitous fields of sciences. Radial visualization is one of the most common information visualization techniques for visualizing multivariate data. Unfortunately, Radial visualization display different information about structures of multivariate data on the different positions of dimensional anchors on the unit circle. In this paper, we propose a method that improve the Radviz layout for class visualization of high-dimensional data. We apply the differential evolution algorithm to find the optimal dimensional anchors of the RadViz such that maximum the quality of Radial visualization for classifier data. We use the k nearest neighbors classifier for quality measurement. Our method provides an improvement visualizing class structures of high-dimensional data sets on the RadViz. We demonstrate the efficiency of our method for some data sets.