On generalized bidimensional ensemble permutation entropy

Entropy measurements have become an invaluable resource when analyzing data. Features that can be mathematically calculated in an image or a time series of data can be useful discrimination elements that allow the design of learning algorithms. Permutation entropy in its different versions has been used in time series from real data in the field of economics or medicine as well as in image analysis. Recently, ensemble versions of the measures have been proposed. The underlying idea is to consider the average of the bidimensional entropy when different square shape patterns are selected. These measures are proposed for bidimensional data, mainly images. Nevertheless, in the case of ensemble permutation entropy, some restrictions appeared since the size of the image should be greater than 9!=362880 pixels, which greatly restricts the possibilities of application. In this paper, we highlight this fact and propose modified versions of bidimensional ensemble permutation entropy that generalize the original one allowing us to extend the type of data to which it is applicable. We will show some practical examples. For this purpose, we have applied these measures to different databases with the aim of improving the information (in terms of discrimination) of the data content.