Efficiently Finding Conceptual Clustering Models with Integer Linear Programming

Conceptual clustering combines two long-standing machine learning tasks: the unsupervised grouping of similar instances and their description by symbolic concepts. In this paper, we decouple the problems of finding descriptions and forming clusters by first mining formal concepts (i.e. closed itemsets), and searching for the best k clusters that can be described with those itemsets. Most existing approaches performing the two steps separately are of a heuristic nature and produce results of varying quality. Instead, we address the problem of finding an optimal constrained conceptual clustering by using integer linear programming techniques. Most other generic approaches for this problem tend to have problems scaling. Our approach takes advantageous of both techniques, the general framework of integer linear programming, and high-speed specialized approaches of data mining. Experiments performed on UCI datasets show that our approach efficiently finds clusterings of consistently high quality.