A Stochastic Model of Noises for Periodic Symbol Sequences
Abstract
The construction of almost periodic sequences is needed for the analysis of the cycles’ detection methods, identification of symbolic sequences’ features and sensitivity analysis. Two probabilistic models of noise are proposed for constructing almost periodic symbolic sequences. Models provide various types of noise in a periodic sequence, such as changing, adding and deleting characters. Thus, on the basis of a periodic symbolic sequence, an almost periodic sequence is constructed.
It is necessary to ensure a given level of noise in the constructed almost periodic sequence. The required level of simulated noise is guaranteed by a two-level model, in which the positions for simulated noise are determined at the first level, based on the discrete random variable, chosen by the researcher. At the second level, the necessary changes are made at the corresponding positions using a random variable that simulates the noise itself. The second model is based on simulated noise with probability (depending on the noise level) in each element of the sequence.
The observed noise level is calculated based on the Levenshtein distance between the original periodic sequence and the almost periodic sequence that we constructed. The observed noise level is always somewhat less than the level of the noise simulated, since when calculating the Levenshtein distance, a shorter way of obtaining a noisy sequence from a periodic one can be found than the one that is used in constructing an almost periodic sequence.
A comparison of the proposed models for the proximity of the noise level they provide to a given noise level is made. The computational experiment showed that the observed noise level is closer to that provided by the two-level model. The software implementation of these models will be used in future to study the algorithms for finding cycles in noisy periodic symbolic sequences.
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