Can triconcepts become triclusters?

Abstract

Two novel approaches to triclustering of three-way binary data are proposed. Tricluster is defined as a dense subset of a ternary relation Y defined on sets of objects, attributes, and conditions, or, equivalently, as a dense submatrix of the adjacency matrix of the ternary relation Y. This definition is a scalable relaxation of the notion of triconcept in Triadic Concept Analysis, whereas each triconcept of the initial data-set is contained in a certain tricluster. This approach generalizes the one previously introduced for concept-based biclustering. We also propose a hierarchical spectral triclustering algorithm for mining dense submatrices of the adjacency matrix of the initial ternary relation Y. Finally, we describe some applications of the proposed techniques, compare proposed approaches and study their performance in a series of experiments with real data-sets.