A clustering approach using an analogy-related logical proportion

The analogical proportion “a is to b as c is to d” is one of the four homogeneous logical proportions that express different types of links between pairs of elements (a, b) and (c, d) (a, b, c, d are 4 vectors of Boolean, nominal or numerical attribute values). One of them, named inverse paralogy, expresses orthogonality between these pairs. The graded extension of the core of this logical proportion, which measures orthogonality between pairs, is the basis of the approach proposed for clustering. It operates by assigning pairs to clusters without presupposing the number of clusters in advance. It proceeds by building mini-clusters that are progressively fused when the centroids (which are pairs) of two clusters are not sufficiently orthogonal. Experiments compare the results of the proposed algorithm with the well-known k-means algorithm on benchmarks. The preliminary  results are promising.