Reverse Clustering: A New Perspective in Data Analysis

“Reverse clustering” is an approach, conceptualized and developed by S. Zadrożny, J. Kacprzyk and J. W. Owsiński, with collaboration of J. Stańczak and K. Opara, having the aim of shedding light on some data structuring problems, which can be ultimately framed in terms of cluster analysis, although not necessarily from the very start. The essence of reverse clustering is as follows: for some data set X, describing a definite set I of entities, and some given partition PA of the set I, find a clustering procedure, which, when applied to X, yields a partition PB, which is possibly similar to PA. Thus, trivially, if PA were obtained on the basis of X with the use of some of the classical clustering algorithms, then one should obtain PB identical to it, and the algorithm found should be the same as that used to obtain PA. Yet, there is a wide multiplicity of situations, in which (i) PA may have been obtained on the basis of data different from X, at least to an extent; and (ii) our trust in PA (or the knowledge regarding its origin and character) may vary quite significantly, from being absolutely sure to regarding PA as a sort of (initial) proposal to be discussed. The paper outlines both the fundamental message of the approach and the significant cases of its application, especially when PA is treated as a kind of hypothesis, with conclusions of pragmatic as well as more general character.