Concept Lattice Reduction Using Integer Programming

抄録

Concept lattice reduction is an important task related to formal concept analysis (FCA), a technique for knowledge extraction from binary relational data. Concept lattice reduction aims to approximate the input of FCA, called formal contexts, into simpler ones so that the volume and complexity of the output of FCA, called formal concepts, will also be reduced. A widely-preferred strategy for the task is object reduction, which approximates the input context by merging similar objects in it. While many methods were developed based on this strategy, we found that they may have two problems. First, the “approximate” context generated by such methods may introduce too many unnecessary modifications to the original one, making it hard to be considered a proper approximation. Second, these methods may unexpectedly insert or eliminate some concepts after reduction, which may cause significant changes to the knowledge extracted by FCA. To solve these problems, we introduce a new method using integer linear programming, which translates concept lattice reduction into an integer linear optimization problem and can suppress the changes caused to the input contexts and extracted concepts by adding corresponding linear constraints. We conduct experiments on several data sets to prove that our method works.