Rough-Fuzzy C-Medoids Algorithm and Selection of Bio-Basis for Amino Acid Sequence Analysis

In most pattern recognition algorithms, amino acids cannot be used directly as inputs since they are nonnumerical variables. They, therefore, need encoding prior to input. In this regard, bio-basis function maps a nonnumerical sequence space to a numerical feature space. It is designed using an amino acid mutation matrix. One of the important issues for the bio-basis function is how to select the minimum set of bio-bases with maximum information. In this paper, we describe an algorithm, termed as rough-fuzzy c{hbox{-}}{rm{medoids}} (RFCMdd) algorithm, to select the most informative bio-bases. It is comprised of a judicious integration of the principles of rough sets, fuzzy sets, the c{hbox{-}}{rm{medoids}} algorithm, and the amino acid mutation matrix. While the membership function of fuzzy sets enables efficient handling of overlapping partitions, the concept of lower and upper bounds of rough sets deals with uncertainty, vagueness, and incompleteness in class definition. The concept of crisp lower bound and fuzzy boundary of a class, introduced in RFCMdd, enables efficient selection of the minimum set of the most informative bio-bases. Some new indices are introduced for evaluating quantitatively the quality of selected bio-bases. The effectiveness of the proposed algorithm, along with a comparison with other algorithms, has been demonstrated on different types of protein data sets.