Investigation of Sequential Mapping of Multidimensional Data

Abstract

In the paper the results of investigations of the sequential nonlinear mapping [5] of multidimensional data for data structure analysis and visualization are presented. This method differs from Sammon’s method of simultaneous nonlinear mapping of multidimensional data onto the plane [1] that after simultaneous mapping of several data vectors at the very beginning, later one can work sequentially in a real time. This way one can watch the states of technological processes or dynamic systems, which are described by vectors consisting of many parameters, watch state’s changes and see instant system’s failures [7]. The method has been investigated according ability to differ the data groups (clustering) when at the beginning the number of data groups is taken to be less than really exists, according mapping errors dependence on a value of factor for correction co-ordinates on the plane and according mapping errors dependence on initial conditions. It was showed that the sequential nonlinear mapping differs the groups of data when the number of initial vectors, mapped simultaneously, is taken to be less by one than really exists. The factor for correction co-ordinates on the plane for the sequential nonlinear mapping can be taken in the range from 0.25 to 0.75. Mapping errors depend on both the sort of initial conditions and the nature of data. Ill. 10, bibl. 11 (in Lithuanian; summary in Lithuanian, English and Russian).,/p>