Sorting concepts by priority using the theory of monotone systems

Abstract

Formal concept analysis is a powerful tool for conceptual modeling and knowledge discovery. As size of a concept lattice can easily get very large, there is a need for presenting information in the lattice in a more compressed form. We propose a novel method MONOCLE for this task that is based on the theory of monotone systems. The result of our method is a sequence of concepts, sorted by "goodness" thus enabling us to select a subset and a corresponding sub-lattice of desired size. That is achieved by defining a weight function that is monotone, correlated with area of data table covered and inversely correlated to overlaps of concepts. We can also use monotone systems theory of "kernels" to detect good cut-off points in the concept sequence. We apply our method to social and economic data of two Estonian islands and show that results are compact and useful. © 2008 Springer-Verlag.