Feature selection through composition of rough–fuzzy sets

The well known principle of curse of dimensionality links both dimensions of a dataset stating that as dimensionality increases samples become too sparse to effectively extract knowledge. Hence dimensionality reduction is essential when there are many features and not sufficient samples.We describe an algorithm for unsupervised dimensionality reduction that exploits a model of the hybridization of rough and fuzzy sets. Rough set theory and fuzzy logic are mathematical frameworks for granular computing forming a theoretical basis for the treatment of uncertainty in many real–world problems. The hybrid notion of rough fuzzy sets comes from the combination of these two models of uncertainty and helps to exploit, at the same time, properties like coarseness and vagueness. Experimental results demonstrated that the proposed approach can effectively reduce dataset dimensionality whilst retaining useful features when class labels are unknown or missing.