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There are two methods for counting the number of occurrences of a string inanother large string. One is to count the number of places where the string isfound. The other is to determine how many pieces of string can be extractedwithout overlapping. The difference between the two becomes apparent when thestring is part of a periodic pattern. This research reports that the differenceis significant in estimating the occurrence probability of a pattern.  In this study, the strings used in the experiments are approximated fromtime-series data. The task involves classifying strings by estimating theprobability or computing the information quantity. First, the frequencies ofall substrings of a string are computed. Each counting method may sometimesproduce different frequencies for an identical string. Second, the probabilityof the most probable segmentation is selected. The probability of the string isthe product of all probabilities of substrings in the selected segmentation.The classification results demonstrate that the difference in counting methodsis statistically significant, and that the method without overlapping isbetter.

Comparing Two Counting Methods for Estimating the Probabilities of Strings