An Algebraic Approach to Ensemble Clustering

In clustering, consensus clustering aims at providing a single partition fitting a consensus from a set of independently generated. Common procedures, which are mainly statistical and graph-based, are recognized for their robustness and ability to scale-up. In this paper, we provide a complementary and original viewpoint over consensus clustering, by means of algebraic definitions which allow to ascertain the nature of available inferences in a systematic approach (e.g. a knowledge base). We found our approach on the lattice of partitions, for which we shall disclose how some operators can be added with the aim to express a formula representing the consensus. We show that adopting an incremental approach may assist to retain significant amount of aggregate data which fits well with the set of input clustering´s. Beyond that ability to model formulae, we also note that its potential cannot be easily captured through such a logical system. It is due to the volatile nature of handling partitions which finally impacts on ability to draw some valuable conclusions.