Mining pure patterns in texts

We herein investigate finding unusual patterns from a given string as a text. In the present paper, the pattern is expressed as a substring of the string. The natural assumption with respect to the frequency of a pattern is that the shorter the length of the pattern, the larger the frequency of the pattern. We define a pattern to be pure if the frequencies of all of the substrings of the pattern are the same as the frequency of the pattern. This means that the substrings appear only within the pattern in the string. This condition is in contrast to the natural assumption. The present paper proposes three statistics for quantifying the purity of a pattern, i.e., probability, entropy, and difference, which are calculated based on the frequency of the pattern and its substrings. Experiments using DNA sequences reveal that patterns with large probability correspond to the features of the sequences.