Informatica

In the paper the sequential nonlinear mapping has been investigated in order to reveal its features. The method was investigated by a plenty of experiments using various sorts of data. For illustrations there are presented results using “marginal” data: the first data gives the smallest mapping error, and the other data gives the largest one. The sequential nonlinear mapping has been investigated according ability to differ the data groups (clustering) when at the beginning the number of groups is taken to be less than really exists. It was showed that the sequential nonlinear mapping differs the groups of data well even though the number of them is taken to be less by one than really exists. The experiments show that 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.

In the paper two methods for data structure analysis and visualisation are presented: the simultaneous nonlinear mapping (Sammon, 1969) and the sequential one (Montvilas, 1995). These two methods were compared according ability to map the data on the plane, mapping accuracy and a mapping time. It was showed that the sequential nonlinear mapping has some bigger total mapping error but needs considerable less calculation time than that of the simultaneous one. Examples are given.

A new method for a creation of the information system for sequential identification of states of technological processes or other dynamic systems for their supervision and control is considered. The states of dynamic system can be unknown and can change themselves abruptly or slowly. The method is based on a sequential nonlinear mapping of many-dimensional vectors of parameters (collection of which describes the present state of dynamic systems) into two-dimensional vectors in order to reflect the states and their changes on the PC screen and to observe the situation by means of computer. The mapping error function is chosen and expressions for sequential nonlinear mapping are obtained. The mapping preserves the inner structure of distances among the vectors. Examples are given.

A method for processing sequential information of states of technological processes or other complicated dynamic systems and for sequential detection of many abrupt or slow changes in several unknown states is considered. The method is based on a sequential nonlinear mapping of many-dimensional vectors of parameters (collection of which describes the present state of dynamic systems) into two-dimensional vectors in order to reflect the states and their changes on the PC screen. The mapping error function is chosen and expressions for sequential nonlinear mapping are obtained. The mapping preserves the inner structure of distances among the vectors. An example is given. A theoretical minimum amount of parameter vectors mapped simultaneously at the very beginning is obtained.

An algorithm for the sequential analysis of multivariate data structure is presented. The algorithm is based on the sequential nonlinear mapping of L-dimensional vectors from the L-hyperspace into a lower-dimensional (two-dimensional) vectors such that the inner structure of distances among the vectors is preserved. Expressions for the sequential nonlinear mapping are obtained. The mapping error function is chosen. Theoretical minimum amount of the very beginning simultaneously mapped vectors is obtained.

An essentially new method for discrete sequential detection of abrupt or slow multiple changes in several unknown properties of random processes is considered. The method is based on a sequential nonlinear mapping into two-dimensional vectors of many-dimensional vectors of parameters which describe the properties of random process. The mapping error function is chosen and the expressions for sequential nonlinear mapping are presented along with some experimental results. Theoretical minimum amount of at the very beginning simultaneously mapped vectors is obtained.

An algorithm for the sequential analysis of multivariate data is, presented along with some experimental results. The algorithm is based upon the sequential nonlinear mapping of L-dimensional vectors from the L-hiperspace into a lower-dimensional (two-dimensional) vectors such that the inner structure of distances between the vectors is preserved. Expressions for the sequential nonlinear mapping are obtained. The sequential nonlinear mapping is applied to sequential c1usterization of random processes and creation of an essentially new method for sequential detection of many abrupt or slow changes in several unknown states of dynamic systems.

An essentially new method for sequential detection of many abrupt or slow changes in several unknown states of dynamic systems is presented. This method is based on the sequential nonlinear mapping into two-dimensional vectors of many-dimensional vectors which describe the present system states. The expressions for sequential nonlinear mapping are obtained. The mapping preserves the inner structure of distances between the vectors. Examples are given.