Abstract
In this study, we introduce a concept of feature space reduction, in which the reduction process is guided by a criterion of structure retention. In other words, the features forming the reduced space are selected in such a way that the original structure present in the highly dimensional space is retained in the reduced space to the highest possible extent. The quality of structure retention is quantified by means of the reconstruction criterion, which dwells on an idea of granulation and degranulation and quantifies an extent to which the information granules are capable of representing original patterns while being expressed by them. Fuzzy clustering (and Fuzzy C-Means, FCM, in particular) is used as an algorithmic vehicle of information granulation. The quality of information granules (and the granular structure, in general) is expressed by the reconstruction error. Given the combinatorial character of the selection process, the underlying optimization process is realized through the use of evolutionary optimization (Genetic Algorithms) and Particle Swarm Optimization (PSO). Experiments are provided. We show that, depending upon the specific data set, their structural content can be preserved even for a relatively significant reduction of the dimensionality of the feature space.