Depth functions as a quality measure and for steering multidimensional projections

Abstract

The analysis of multidimensional data has been a topic of continuous research for many years. This type of data can be found in several different areas of science. A common task while analyzing such data is to investigate patterns by interacting with spatializations of the data in a visual domain. Understanding the relation between the underlying dataset characteristics and the technique used to provide its visual representation is of fundamental importance since it can provide a better intuition on what to expect from the spatialization. In this paper, we propose the usage of concepts from non-parametric statistics, namely depth functions, as a quality measure for spatializations. We evaluate the action of multidimensional projection techniques on such estimates. We apply both qualitative and quantitative analyses on four different multidimensional techniques selected according to the properties they aim to preserve. We evaluate them with datasets of different characteristics: synthetic, real world, high dimensional; and contaminated with outliers. As a straightforward application, we propose to use depth information to guide multidimensional projection techniques which rely on interaction through control point selection and positioning. Even for techniques which do not intend to preserve any centrality measure, interesting results can be achieved by separating regions possibly contaminated with outliers.