Granular clustering with partial supervision

The paper is concerned with the problem of the explicit granulation of data in presence of some labeled patterns. The granulation process is realized as an organic growth of multi-dimensional hyperboxes guided by a compatibility measure. The organic growth signifies that there are no prior assumptions about the number and shape of the information granules. Instead, only the relative position and size of the patterns in the pattern space determine the progression of the granulation process. The rationale for a specific form of the compatibility measure is explained using some illustrative examples. The inclusion of a small number of labeled patterns in the input data is shown to provide a very effective way of coping with complex decision hyperplanes in multi-dimensional pattern spaces. The method is illustrated using several synthetic data sets as well as the Iris data set that is widely regarded as a reference for the comparison of classification and clustering algorithms