Mixing Bandt-Pompe and Lempel-Ziv approaches: another way to analyze the complexity of continuous-state sequences

STEEVE ZOZOR; DIEGO MATEOS; PEDRO W. LAMBERTI

EUROPEAN PHYSICAL JOURNAL B - CONDENSED MATTER

SPRINGER

Lugar: Berlin; Año: 2014

1434-6028

In this paper, we propose to mix the approach underlying Bandt-Pompe permutation entropy with Lempel-Ziv complexity, to design what we call Lempel-Ziv permutation complexity. The principle consists of two steps: (i) transformation of a continuous-state series that is intrinsically multivariate or arises from embedding into a sequence of permutation vectors, where the components are the positions of the components of the initial vector when re-arranged; (ii) performing the Lempel-Ziv complexity for this series of ?symbols?, as part of a discrete finite-size alphabet. On the one hand, the permutation entropy of Bandt-Pompe aims at the study of the entropy of such a sequence; i.e., the entropy of patterns in a sequence (e.g., local increases or decreases). On the other hand, the Lempel-Ziv complexity of a discretestate sequence aims at the study of the temporal organization of the symbols (i.e., the rate of compressibility of the sequence). Thus, the Lempel-Ziv permutation complexity aims to take advantage of both of these methods. The potential from such a combined approach ? of a permutation procedure and a complexity analysis ? is evaluated through the illustration of some simulated data and some real data. In both cases, we compare the individual approaches and the combined approach.