Constructing lattice based on irreducible concepts

摘要

The construction of concept lattices is one of the key issues of formal concept analysis. Many methods and algorithms are proposed to build a lattice, among which, incremental algorithms are more appropriate in real-life applications that work with dynamic datasets. But they cost much time to locate generators before generating a real concept. The batch algorithms generate concepts quickly. However, they ignore the procedure of building lattice relationship. In this paper, we build the lattice from meet-irreducible attribute concepts by using generators directly, and make optimizations in key steps. We yield the relationship among concepts during the generating process that saves much time in contrast to other batch algorithms. In addition to proving the correctness of our algorithm, we evaluate its performance on some real datasets and compare it with an incremental algorithm called FastAddIntent. The results show that our algorithm mainly depends on the numbers of concepts and the numbers of attributes, which achieves good performance, especially to large formal contexts.