Visual Analytics for Complex Multivariate Data: Techniques for Soil Science, Temporal Networks, and Interactive 3D Visualization

In an era of exponential data growth, the ability to effectively visualize and analyze complex multivariate data is crucial for scientific discovery and decision-making across numerous disciplines. This dissertation addresses key challenges in current visualization techniques for high-dimensional spatial, temporal, and network data through innovative visual analytics approaches. The research tackles three main issues: (1) the inadequacy of traditional visualization methods in representing high-dimensional spatial data, (2) the difficulty in detecting and analyzing anomalies in multivariate time series, and (3) the challenge of visualizing evolving relationships in dynamic network data. To address these challenges, this dissertation proposes: 1. A high-dimensional spatial data visualization framework that integrates computational geometry with dimensionality reduction techniques. This novel approach combines multiple visualization methods to provide comprehensive views of spatial and temporal variations in complex datasets. 2. A dual-view framework for multivariate time series data, designed to highlight abnormal patterns through feature extraction and interactive filtering. 3. A temporal graph visualization method for evolving network relationships, incorporating quantitative metrics to track changing node importance over time. Methodologically, this research employs a combination of computational geometry, dimensionality reduction, network analysis, and interactive visualization techniques. All proposed approaches are implemented as web-based, scalable tools capable of handling large-scale, complex datasets. The effectiveness of these visualization techniques is demonstrated through multiple case studies. These include applications in soil science for analyzing elemental compositions, genomics for exploring gene relationship evolution, and time series analysis for detecting anomalies in various global datasets. These diverse applications highlight the wide applicability of the developed visualization methodologies across different domains with orthogonal data paradigms. This research contributes to advancing the field of visual analytics by providing researchers with powerful tools to uncover intricate patterns and relationships in multivariate data. The proposed techniques have the potential to accelerate scientific discovery across various disciplines, from environmental science to genomics and beyond.