Adaptive Strategies for Mining the Positive Border of Interesting Patterns: Application to Inclusion Dependencies in Databases

Abstract

Given the theoretical framework of Mannila and Toivonen [26], we are interested in the discovery of the positive border of interesting patterns, also called the most specific interesting patterns. Many approaches have been proposed among which we quote the levelwise algorithm and the Dualize and Advance algorithm. In this paper, we propose an adaptive strategy – complementary to these two algorithms – based on four steps: 1) In order to initialize the discovery, eliciting some elements of the negative border, for instance using a levelwise strategy until a certain level k. 2) From the negative border found so far, inferring the optimistic positive border by dualization, i.e. the set of patterns whose all specializations are known to be not interesting patterns. 3) Estimating the distance between the positive border to be discovered and the optimistic positive border. 4) Based on these estimates, carrying out an adaptive search either bottom-up (the jump was too optimistic) or top-down (the solution should be very close).

We have instantiated this proposition to the problem of inclusion dependency (IND) discovery. IND is a generalization of the well known concept of foreign keys in databases and is very important in practice. We will first point out how the problem of IND discovery fits into the theoretical framework of [26]. Then, we will describe an instantiation of our adaptive strategy for IND discovery, called Zigzag, from which some experiments were conducted on synthetic databases. The underlying application of this work takes place in a project called DBA Companion devoted to the understanding of existing databases at the logical level using data mining techniques.