A Disc-based Approach to Data Summarization and Privacy Preservation

Data summarization has been recognized as a fundamental operation in database systems and data mining with important applications such as data compression and privacy preservation. While the existing methods such as CF-values and DataBubbles may perform reasonably well, they cannot provide any guarantees on the quality of their results. In this paper, we introduce a summarization approach for numerical data based on discs formalizing the notion of quality. Our objective is to find a minimal set of discs, i.e. spheres satisfying a radius and a significance constraint, covering the given dataset. Since the proposed problem is NP-complete, we design two different approximation algorithms. These algorithms have a quality guarantee, but they do not scale well to large databases. However, the machinery from approximation algorithms allows a precise characterization of a further, heuristic algorithm. This heuristic, efficient algorithm exploits multi-dimensional index structures and can be well-integrated with database systems. The experiments show that our heuristic algorithm generates summaries that outperform the state-of-the-art data bubbles in terms of internal measures as well as in terms of external measures when using the data summaries as input for clustering methods