Explanatory visualization of multidimensional prejections - Martins, Rafael Messias (2016)
Visual analytics tools play an important role in the scenario of big data solutions, combining data analysis and interactive visualization techniques in effective ways to support the incremental exploration of large data collections from a wide range of domains. One particular challenge for visual analytics is the analysis of multidimensional datasets, which consist of many observations, each being described by a large number of dimensions, or attributes. Finding and understanding data-related patterns present in such spaces, such as trends, correlations, groups of related observations, and outliers, is hard. Dimensionality reduction methods, or projections, can be used to construct low (two or three) dimensional representations of high-dimensional datasets. The resulting representation can then be used as a proxy for the visual interpretation of the high-dimensional space to efficiently and effectively support the above-mentioned data analysis tasks. Projections have important advantages over other visualization techniques for multidimensional data, such as visual scalability, high degree of robustness to noise and low computational complexity. However, a major obstacle to the effective practical usage of projections relates to their difficult interpretation. Two main types of interpretation challenges for projections are studied in this thesis. First, while projection techniques aim to preserve the so-called structure of the original dataset in the final produced layout, and effectively achieve the proxy effect mentioned earlier, they may introduce a certain amount of errors that influence the interpretation of their results. However, it is hard to convey to users where such errors occur in the projection, how large they are, and which specific data-interpretation aspects they affect. Secondly, interpreting the visual patterns that appear in the projection space is far from trivial, beyond the projections ability to show groups of similar observations. In particular, it is hard to explain these patterns in terms of the meaning of the original data dimensions. In this thesis we focus on the design and development of novel visual explanatory techniques to address the two interpretation challenges of multidimensional projections outlined above. We propose several methods to quantify, classify, and visually represent several types of projection errors, and how their explicit depiction helps interpreting data patterns. Next we show how projections can be visually explained in terms of the highdimensional data attributes, both in a global and a local way. Our proposals are designed to be easily added, and used with, any projection technique, and in any application context using such techniques. Their added value is demonstrated by presenting several exploration scenarios involving various types of multidimensional datasets, ranging from measurements, scientific simulations, software quality metrics, software system structure, and networks.