Dimensionality-Reduction Algorithms for Progressive Visual Analytics

Visual analysis of high dimensional data is a challenging process. Direct visualizations work well for a few dimensions but do not scale to the hundreds or thousands of dimensions that have become increasingly common in current data analytics problems. Visual analytics is the science of analytical reasoning facilitated by interactive visual interfaces, and it has been proven as an effective tool for high dimensional data analysis. In visual analytics systems, several visualizations are jointly analyzed in order to discover patterns in the data. One of the fundamental tools that has been integrated in visual analytics, is nonlinear dimensionality-reduction; a tool for the indirect visualization aimed at the discovery and analysis of non-linear patterns in the high-dimensional data. However, the computational complexity of non-linear dimensionality-reduction techniques does not allow direct employment in interactive systems. This limitation makes the analytic process a time-consuming task that can take hours, days or even weeks to be performed. In this thesis, we present novel algorithmic solutions that enable integration of non-linear dimensionality-reduction techniques in visual analytics systems. Our proposed algorithms are, not only much faster than existing solutions, but provide richer insights into the data at hand. This result, is achieved by introducing new data processing and optimization techniques and by embracing the recently introduced concept of Progressive Visual Analytics; a computational paradigm that enables the interactivity of complex analytics techniques by means of visualization as well as interaction with intermediate results. Moreover, we present several applications that are designed to provide unprecedented analytical capabilities in several domains. These applications are powered by the algorithms introduced in this dissertation and led to several discoveries in areas ranging from the biomedical research field, to social-network data analysis and machine-learning models interpretability.Comp Graphics & Visualisatio