Numerical Representation of Symbolic Data

Abstract

A method of direct numerical representation of symbolic data is proposed. The method starts with parsing a sequence into an ordered set (spectrum) of distinct, non-overlapping short strings of symbols (words). Next, the words spectrum is mapped onto a vector of binary components in a high dimensional, linear space. The numerical representation allows for some arithmetical operations on symbolic data. Among them is a meaningful average spectrum of two sequences. As a test, the new numerical representation is used to build centroid vectors for the k-means clustering algorithm. It significantly enhanced the clustering quality. The advantage over the conventional approach is a high score of correct clustering several real character sequences like novel, DNA and protein.