On the effect of clustering on quality assessment measures for dimensionality reduction
Bassam Mokbel, Andrej Gisbrecht, Barbara Hammer · PUB – Publications at Bielefeld University (Bielefeld University) · 2010
Visualization techniques constitute important interfaces between the rapidly increasing digital information available today and the human user. In this context, numerous dimensionality reduction models have been proposed in the literature, see, e.g., [1, 2]. This fact recently motivated the development of frameworks for a reliable and automatic quality assessment of the produced results [3, 2]. These specialized measurements represent a means to objectively assess an overall qualitative change under spatial transformation. The rapidly increasing size of the data sets, however, causes the need to not only map given data points to low dimensionality, but to priorly compress the available information, e.g., by means of clustering techniques. While a standard evaluation measure for clustering is given by the quantization error, its counterpart, the reconstruction error, is usually infeasible for dimensionality reduction, such that one has to rely on alternatives. In this paper, we investigate in how far two existing quality measures used for dimensionality reduction are appropriate to evaluate the quality of clustering outputs, such that only one quality measure can be used for the full visualization process in the context of large data sets. In this contribution, we present empirical results from different basic clustering scenarios as a first study to analyze how structural characteristics of the data are reflected in the quality assessment.