Identifying Relevant Formal Concepts through the Collapse Index

In this paper we introduce the Collapse Index, a new measure of the relevance of individual formal concepts in a concept lattice, the application of which improves the performance of concept pruning and reduces the bias against "outlier" concepts. The measure determines the relevance of a formal concept in the lattice by calculating the minimum number of objects which need to be removed from the domain before the formal concept collapses. We demonstrate the effectiveness of the Collapse Index as a measure of pattern selection by comparing the collapse indices found in two datasets. We cover the case where the two datasets are disjoint and the case where one dataset is a subset of the other. Results are contrasted to those of the Stability Index measure.