Geometric and Statistical Summaries for Big Data Visualization

In recent times, the visualization and data analysis paradigm is adapting fast to keep up with the rapid growth in computing power and data size. Modern scientific simulations run at massive scale to produce huge datasets, which must be analyzed and visualized by the domain experts to continue innovation. In the presence of large-scale data, it is important to identify and extract the informative regions at an early stage so that the following analysis algorithms, which are usually memory and compute-intensive, can focus only on those regions. Transforming the raw data to a compact yet meaningful representation also helps to maintain the interactivity of the query and visualization of analysis results. In this dissertation, we propose a novel and general-purpose framework suitable for exploring large-scale data. We propose to use importance-based data summaries, which can substitute for the raw data to answer queries and drive visual exploration. Since the definition of importance is dependent on the nature of the data and the task at hand, we propose to use suitable statistical and geometric measures or combination of various measures to quantify importance and perform data reduction on scalar and vector field data. Our research demonstrates two instances of the proposed framework. The first instance applies to large number of streamlines computed from vector fields. We make the visual exploration of such data much easier compared to navigating through a cluttered 3D visualization of the raw data. In this case, we introduce a fractal dimension based metric called box counting ratio, which quantifies the geometric complexity of