Ranking Gradients in Multi-Dimensional Spaces

Business organizations must pay attention to interesting changes in customer behavior in order to anticipate their needs and act accordingly with appropriated business actions. Tracking customer’s commercial paths through the products they are interested in is an essential technique to improve business and increase customer satisfaction. Data warehousing (DW) allows us to do so, giving the basic means to record every customer transaction based on the different business strategies established. Although managing such huge amounts of records may imply business advantage, its exploration, especially in a multi-dimensional space (MDS), is a nontrivial task. The more dimensions we want to explore, the more are the computational costs involved in multi-dimensional data analysis (MDA). To make MDA practical in real world business problems, DW researchers have been working on combining data cubing and mining techniques to detect interesting changes in MDS. Such changes can also be detected through gradient queries. While those studies have provided the basis for future research in MDA, just few of them points to preference query selection in MDS. Thus, not only the exploration of changes in MDS is an essential task, but also even more important is ranking most interesting gradients. In this chapter, the authors investigate how to mine and rank the most interesting changes in a MDS applying a TOP-K gradient strategy. Additionally, the authors also propose a gradient-based cubing method to evaluate interesting gradient regions in MDS. So, the challenge is to find maximum gradient regions (MGRs) that maximize the task of raking gradients in a MDS. The authors’ evaluation study demonstrates that the proposed method presents a promising strategy for ranking gradients in MDS.