On Lempel-Ziv complexity for multidimensional data analysis

In this paper, a natural extension of the Lempel-Ziv complexity for several finite-time sequences, defined on finite size alphabets is proposed. Some results on the defined joint Lempel-Ziv complexity are given, as well as properties in connection with the Lempel-Ziv complexity of the individual sequences. Also, some links with Shannon entropies are exhibited and, by analogy, some derived quantities are proposed. Lastly, the potential use of the extended complexities for data analysis is illustrated on random boolean networks and on a proposed multidimensional extension of the minority game.