Optimal Initial Conditions for Nonlinear Mapping of Multidimensional Signals

Abstract

Complicated signals used in telecommunication are described by many parameters, hence they are presented in multidimensional space. Sammon’s method of simultaneous nonlinear mapping onto the plane is used for clustering of the signals. The essence of the method is to preserve the inner structure of distances among the vectors of parameters of signals in multidimensional space after mapping them onto the plane. The quality of mapping is characterized by mapping error which very depends on initial conditions. The initial conditions are chosen on the plane randomly or along diagonal. There is no way to choose optimal initial conditions, therefore mapping algorithm often finds the local maximum of a functional that characterizes the mapping quality which is not global. In the paper operation of mapping has been revealed and sequential mapping has been proposed for choosing of optimal initial conditions. The sequential mapping gives slightly bigger mapping error then that of simultaneous one but it gives optimal initial conditions for simultaneous method, which maps the signal later with less mapping error. Numerous experiments confirm that. Ill. 6, bibl. 6 (in English; summarries in Lithuanian, English and Russian).