Analyzing the quality of local and global multidimensional projections using performance evaluation planning

Abstract

Among the challenges of the big data era, the analysis of high-dimensional data is still an open research area. As a result, several multidimensional projection techniques have been developed to reduce data dimensionality, becoming important visualization and visual analytics tools. In order to ensure the quality of projections, it is necessary to assess the low-dimensional embeddings by using different dataset configurations as input and analyzing evaluation metrics. However, it is not clear to the user how factors such as the number of dimensions, instances, or clusters, can affect the projection mapping and its quality regarding different projection techniques and assessment metrics. The research reported in this paper aims to clarify how much these factors affect each response variable via performance evaluation planning. We present an evaluation approach, supported by factorial design, that carries out a complete analysis, in the sense of measuring all possible combinations of all the input factors. The results of the analyses of local and global structure preservation in the projections yield a better understanding of how distinct dataset properties can influence the choice of projections based on quality metrics results.