Quantitative Approach on Parallel Coordinates and Scatter Plots for Multidimensional-Data Visual Analytics

Parallel coordinates and scatter plots are two well-known visualization techniques for multidimensional data analytics and often employed cooperatively for flexibility increase in exploration of such data. Existing approaches approximately consider qualitative issues and single attribute comparison, which might face statistic challenges in case of quantitative requirement. This paper introduces a new quantitative approach for visual enhancement of parallel coordinates and scatter plots in term of multiple attribute comparison. The method is based on the visual integration of interactive stacked bars and visual queries on parallel axes and scatter charts. The parallel coordinates play the role of a context view while the scatter charts are for focus details. Using the technique, users could not only quantitatively analyze multivariate data, but also flexibly compare multiple target attributes. Moreover, further investigation is enabled for deep understanding of desired information. The characteristics and usefulness of our approach are demonstrated via a case study with two typical use cases

Implicit Multidimensional Projection of Local Subspaces

We propose a visualization method to understand the effect of multidimensional projection on local subspaces, using implicit function differentiation. Here, we understand the local subspace as the multidimensional local neighborhood of data points. Existing methods focus on the projection of multidimensional data points, and the neighborhood information is ignored. Our method is able to analyze the shape and directional information of the local subspace to gain more insights into the global structure of the data through the perception of local structures. Local subspaces are fitted by multidimensional ellipses that are spanned by basis vectors. An accurate and efficient vector transformation method is proposed based on analytical differentiation of multidimensional projections formulated as implicit functions. The results are visualized as glyphs and analyzed using a full set of specifically-designed interactions supported in our efficient web-based visualization tool. The usefulness of our method is demonstrated using various multi- and high-dimensional benchmark datasets. Our implicit differentiation vector transformation is evaluated through numerical comparisons; the overall method is evaluated through exploration examples and use cases

Doctor of Philosophy

dissertationCorrelation is a powerful relationship measure used in many fields to estimate trends and make forecasts. When the data are complex, large, and high dimensional, correlation identification is challenging. Several visualization methods have been proposed to solve these problems, but they all have limitations in accuracy, speed, or scalability. In this dissertation, we propose a methodology that provides new visual designs that show details when possible and aggregates when necessary, along with robust interactive mechanisms that together enable quick identification and investigation of meaningful relationships in large and high-dimensional data. We propose four techniques using this methodology. Depending on data size and dimensionality, the most appropriate visualization technique can be provided to optimize the analysis performance. First, to improve correlation identification tasks between two dimensions, we propose a new correlation task-specific visualization method called correlation coordinate plot (CCP). CCP transforms data into a powerful coordinate system for estimating the direction and strength of correlations among dimensions. Next, we propose three visualization designs to optimize correlation identification tasks in large and multidimensional data. The first is snowflake visualization (Snowflake), a focus+context layout for exploring all pairwise correlations. The next proposed design is a new interactive design for representing and exploring data relationships in parallel coordinate plots (PCPs) for large data, called data scalable parallel coordinate plots (DSPCP). Finally, we propose a novel technique for storing and accessing the multiway dependencies through visualization (MultiDepViz). We evaluate these approaches by using various use cases, compare them to prior work, and generate user studies to demonstrate how our proposed approaches help users explore correlation in large data efficiently. Our results confirmed that CCP/Snowflake, DSPCP, and MultiDepViz methods outperform some current visualization techniques such as scatterplots (SCPs), PCPs, SCP matrix, Corrgram, Angular Histogram, and UntangleMap in both accuracy and timing. Finally, these approaches are applied in real-world applications such as a debugging tool, large-scale code performance data, and large-scale climate data

Interactive Visualization of High-Dimensional Petascale Ocean Data

We describe an application for interactive visualization of 5 petabytes of time-varying multivariate data from a high-resolution global ocean circulation model. The input data are 10311 hourly (ocean time) time steps of various 2D and 3D fields from a 22-billion point 1/48- degree lat-lon cap configuration of the MIT General Circulation Model (MITgcm). We map the global horizontal model domain onto our 128-screen (8x16) tiled display wall to produce a canonical tiling with approximately one MITgcm grid point per display pixel, and using this tiling we encode the entire time series for multiple native and computed scalar quantities at a collection of ocean depths. We reduce disk bandwidth requirements by converting the models floating point data to 16-bit fixed point values, and compressing those values with a lossless video encoder, which together allow synchronized playback at 24 time steps per second across all 128 displays. The application allows dynamic assignment of any two encoded tiles to any display, and has multiple interfaces for quickly specifying various orderly arrangements of tiles. All subsequent rendering is done on the fly, with run time control of colormaps, transfer functions, histogram equalization, and labeling. The two data streams on each screen can be rendered independently and combined in various ways, including blending, differencing, horizontal/ vertical wipes, and checkerboarding. The two data streams on any screen can optionally be displayed as a scatterplot in their joint attribute space. All scatterplots and map-view plots from the same x/y location and depth are linked so they all show the current brushable selection. Ocean scientists have used the system, and have found previously unidentified features in the data

A parallel algorithm for computing the flow complex: theory and applications

Wir präsentieren einen parallelen Algorithmus zur Berechnung des Hasse-Diagramms des Flow-Komplexes einer Punktwolke im euklidischen Raum. Bekannte Algorithmen in zwei und drei Dimensionen berechnen zunächst dessen geometrische Realisierung und müssen vorher die Delaunay-Triangulierung berechnen. Unser Algorithmus berechnet nur das Hasse-Diagramm des Flow-Komplexes, welches, mit ausreichend geometrischen Informationen versehen, die selbe topologische Multiskalenanalyse ermöglicht wie die Alpha-Shape Filtration. Wir zeigen mit experimentelle Ergebnissen für mittlere Dimensionen, dass unser Algorithmus gut mit der Anzahl der verfügbaren Kerne auf einer Mehrkern-Architektur skaliert. Wir wenden unseren Algorithmus an, um den Träger eines wahrscheinlichkeitsmaßes auf Basis von Punkten zu skizzieren, welche aus dem euklidischen Raum gezogen wurden. Des Weiteren wenden wir unseren Algorithmus auf Streudiagramme an, welche zur Korrelationsanalyse verwendet werden, aber auch ein nützliches Werkzeug sind, um die Verteilung hochdimensionaler Punktwolken zu verstehen

Cognitive Foundations for Visual Analytics

In this report, we provide an overview of scientific/technical literature on information visualization and VA. Topics discussed include an update and overview of the extensive literature search conducted for this study, the nature and purpose of the field, major research thrusts, and scientific foundations. We review methodologies for evaluating and measuring the impact of VA technologies as well as taxonomies that have been proposed for various purposes to support the VA community. A cognitive science perspective underlies each of these discussions

Flow-based scatterplots for sensitivity analysis

Visualization of multi-dimensional data is challenging due to the number of complex correlations that may be present in the data but that are difficult to be visually identified. One of the main causes for this problem is the inherent loss of information that occurs when high-dimensional data is projected into 2D or 3D. Although 2D scatterplots are ubiquitous due to its simplicity and familiarity, there are not a lot of variations on its basic metaphor. In this paper, we present a new way of visualizing multidimensional data using scatterplots. We extend 2D scatterplots using sensitivity coefficients to highlight local variation of one variable with respect to another. When applied to a scatterplot, these sensitivities can be understood as velocities, and the resulting visualization resembles a flow field. We also present a number of operations, based on flow-field analysis, that help users navigate, select and cluster points in an efficient manner. We show the flexibility and generality of this approach using a number of multidimensional data sets across different domains