Redundant dictionary spaces as a general concept for the analysis of non-vectorial data

Abstract

Many types of data we are facing today are non-vectorial. But most of the analysis techniques are based on vector spaces and heavily depend on the underlying vector space properties. In order to apply such vector space techniques to non-vectorial data, so far only highly specialized methods have been suggested. We present a uniform and general approach to construct vector spaces from non-vectorial data. For this we develop a procedure to map each data element in a special kind of coordinate space which we call redundant dictionary space (RDS). The mapped vector space elements can be added, scaled and analyzed like vectors and thus allows any vector space analysis techniques to be used with any kind of data. The only requirement is the existence of a suitable inner product kernel. © 2012 Springer-Verlag.