A complexity measure for symbolic sequences and applications to DNA

TL;DR

This paper introduces a new complexity measure for symbolic sequences based on entropy of domain lengths, demonstrating its desirable properties and applying it to analyze genetic sequences' complexity profiles.

Contribution

A novel complexity measure for symbolic sequences based on segmentation and entropy, with proven properties and applications to DNA analysis.

Findings

The measure satisfies properties of a good complexity metric.

It is dependent on the analysis level of the sequence.

Applied to genetic sequences, revealing their complexity profiles.

Abstract

We introduce a complexity measure for symbolic sequences. Starting from a segmentation procedure of the sequence, we define its complexity as the entropy of the distribution of lengths of the domains of relatively uniform composition in which the sequence is decomposed. We show that this quantity verifies the properties usually required for a ``good'' complexity measure. In particular it satisfies the one hump property, is super-additive and has the important property of being dependent of the level of detail in which the sequence is analyzed. Finally we apply it to the evaluation of the complexity profile of some genetic sequences.