Low-Entropy Set Selection

Hannes Heikinheimo, Jilles Vreeken, Arno Siebes, Heikki Mannila

Abstract: Most pattern discovery algorithms easily generate very large numbers of patterns, making the results impossible to understand and hard to use. Recently, the problem of instead selecting a small subset of informative patterns from a large collection of patterns has attracted a lot of interest. In this paper we present a succinct way of representing data on the basis of itemsets that identify strong interactions. This new approach, LESS, provides a more powerful and more general technique to data description than existing approaches. Low-entropy sets consider the data symmetrically and as such identify strong interactions between attributes, not just between items that are present. Selection of these patterns is executed through the MDL-criterion. This results in only a handful of sets that together form a compact lossless description of the data. By using entropy-based elements for the data description, we can successfully apply the maximum likelihood principle to locally cover the data optimally. Further, it allows for a fast, natural and well performing heuristic. Based on these approaches we present two algorithms that provide high-quality descriptions of the data in terms of strongly interacting variables. Experiments on these methods show that high-quality results are mined: very small pattern sets are returned that are easily interpretable and understandable descriptions of the data, and can be straightforwardly visualized. Swap randomization experiments and high compression ratios show that they capture the structure of the data well.