Extracting optimal association rules over numeric attributes

Data Mining is the process of finding novel, useful and understandable patterns in massive data. Association rules are a commonly used method to discover these patterns. Until recently, the known techniques for generating association rules required that the data fields (called attributes) be binary. In a series of papers, F’ukuda, Yoda, and collaborators have developed an approach to obtain association rules on numeric attributes. They have found optimal association rules for 2-dimensional numeric antecedents, where the shape of the region obtained is a convex region; their algorithm has time complexity O(n’.‘) on a grid of n pixels. We obtain efficient algorithms to find optimal association rules for 2-dimensional numeric antecedents, where the shape of the region obtained is what we call an anchored convex region or an anchored triagular region. These algorithms have time complexity O(n). However, unless P = NP, no polynomial time algorithm finds. an anchored convex region or anchored triangular region which is optimal with regard to support or confidence. These two classes of region can find application in situations where it is known from the outset that the data of greatest interest lies close to one edge of the grid, and where the improvement in execution speed from O(n’.‘) to O(n) is critical.