To the question of restoring symbol sequences encoding noisy periodic functions

Abstract

In business informatics, one of the research subjects is the analysis of data on processes in applied subject areas; here problems of qualitative analysis arise. Such problems arise, for example, in the qualitative study of log files of business processes, in the analysis and prediction of time series and other processes of a different nature. Quite often, to represent information about the processes under study, the methods of qualitative analysis use symbolic coding, which makes it possible to remove unnecessary detailing of numerical descriptions. The relevance of this study is due to the fact that when working with the raw data, researchers often face the presence of noise and distortions of the data, which significantly complicates the solution of the problems of qualitative analysis. When working with symbolic representations of the processes under study, which quite often have a periodic nature, we observe noise of deletion, insertion and replacement of symbols, which complicate the solution of the problem of revealing and analyzing the periodicity. This article deals with the problem of recovering periodic symbolic sequences obtained by coding from samples of continuous periodic functions and distorted by noise of insertion, replacement and deletion of symbols. Trigonometric functions are considered as a specific example of synthetic time series data. To encode trigonometric functions, alphabets of various cardinalities are used. The article presents an experimental study of the dependence of the quality characteristics of the method of period and a periodically repeating fragment recovery, previously proposed by the authors and improved in this study. For alphabets of different cardinalities at fixed sampling intervals, the fraction of sequences with a satisfactorily reconstructed period and the relative error in determining the period are given. The quality of reconstruction of a periodically repeating fragment is estimated by the edit distance from the reconstructed periodic sequence to the original sequence distorted by noise.