Projections for Visual Analysis of Multivariate Data: Methods for Identification, Interpretation, and Navigation of Patterns

Dimensionality Reduction, in particular, projection-based methods transform the data to a lower-dimensional space, yet preserving its main structure. A scatterplot typically depicts the results, presenting a means to make the data space visually accessible to the user. This abstract representation of complex data enables exploration, however, brings in challenges about the analysis and interpretation of patterns because the data is often large-scale, comprises many attributes, or evolves. The present thesis aims to integrate the user into the analysis process using interactive data visualization, and centers around the research question: How to support people to identify, interpret, and navigate patterns in multivariate projection spaces? This thesis makes two main computer science contributions to tackle this question based on the assessment of related work concerning the interactive visual analysis of projections of multivariate data. First, the development and evaluation of interactive visual analysis methods to foster the identification and interpretation of patterns in multivariate data spaces using projections. A user study together with domain experts untrained in advanced statistics shows the effectiveness of projections. The experts mastered the abundance of attribute combinations (subspaces), and thus patterns, by manually deciding on interesting attributes. This behavior motivated the development of novel methods to analyze structural pattern changes among different subspaces visually and to support the interpretation of identified patterns. Patterns can not only change among subspaces but also over time, posing a challenge to identify patterns in general. This thesis proposes sequential one-dimensional projections that make temporal patterns visible, as well as means to interpret identified patterns. Different use cases showcase the usefulness of the methods, including the analysis of survey, crime and computer network data. Second, the development and investigation of off-screen visualization for context-aware navigation in information spaces spanned by projections. The depiction of a multivariate projection can result in a large information space that is challenging to navigate effectively. Users apply zooming and panning operations to explore the space at a global but also local scale depending on the task at hand. As a result, the users face the inherent trade-off between overview and detail. This work proposes a data-driven overview by surrounding the viewport with a dedicated border region that preserves the relations between off-screen located data objects. Aggregation, thereby, plays a key component to overcome the challenges regarding the visualization of vast amounts of data. Several techniques and use cases are presented in this context. Furthermore, results of a study show that the border can be designed adaptively to improve the awareness of the data space dimensions without negatively influencing the overview perception. The results of the study also suggest projecting off-screen located objects to the border region using the orthographic over the radial strategy. The present thesis systematically discusses the benefits and challenges of the proposed methods and outlines future directions.