Discovering the intrinsic dimensionality of BLOSUM substitution matrices using evolutionary MDS

Abstract

The paper shows the application of the multidimensional scaling to discover the intrinsic dimensionality of the substitution matrices. These matrices are used in Bioinformatics to compare amino acids in the alignment procedures. However, the methodology can be used in other applications to discover the intrinsic dimensionality of a wide class of symmetrical matrices. The discovery of the intrinsic dimensionality of substitutions matrices is a data processing problem with applications in chemical evolution. The problem is related with the number of relevant physical, chemical and structural characteristic involved in these matrices. Many studies have dealt with the identification of relevant characteristic sets for these matrices, but few have concerned with establishing an upper bound of their cardinality. The methodology of multidimensional scaling is used to map the substitution matrix information in a virtual low dimensional space. The relationship between the quality of this process and the dimensionality of the mapping provides clues about the number of characteristics which better represents the matrix. To avoid the local minima problem, a genetic algorithm is used to minimize the objective function of the multidimensional scaling procedure. The main conclusion is that the number of effective characteristics involved in substitution matrices is small.