Sound Multi-objective Feature Space Transformation for Clustering

In this work we propose a novel, generalized framework for feature space transformation in unsupervised knowledge discovery settings. Unsupervised feature space transformation inherently is a multi-objective optimization problem. In order to facilitate data exploration, transformations should increase the quality of the result and should still preserve as much of the original data set information as possible. We exemplify this relationship on the problem of data clustering. First, we show that existing approaches to multi-objective unsupervised feature selection do not pose the optimization problem in an appropriate way. Furthermore, using feature selection only is often not sufficient for real-world knowledge discovery tasks. We propose a new, generalized framework based on the idea of information preservation. This framework enables feature selection as well as feature construction for unsupervised learning. We compare our method against existing approaches on several real world data sets.