# persim.persistent_entropy¶

The persistent entropy has been defined in [1]. A precursor of this definition was given in [2] to measure how different bars of the barcode are in length.

[1] M. Rucco, F. Castiglione, E. Merelli, M. Pettini, Characterisation of the idiotypic immune network through persistent entropy, in: Proc. Complex, 2015. [2] H. Chintakunta, T. Gentimis, R. Gonzalez-Diaz, M.-J. Jimenez, H. Krim, An entropy-based persistence barcode, Pattern Recognition 48 (2) (2015) 391–401.

Implementation of persistent entropy

Author: Eduardo Paluzo Hidalgo (cimagroup, University of Seville) contact: epaluzo@us.es

Functions

 persistent_entropy(dgms[, keep_inf, …]) Perform the persistent entropy values of a family of persistence barcodes (or persistence diagrams).
persim.persistent_entropy.persistent_entropy(dgms, keep_inf=False, val_inf=None, normalize=False)[source]

Perform the persistent entropy values of a family of persistence barcodes (or persistence diagrams). Assumes that the input diagrams are from a determined dimension. If the infinity bars have any meaning in your experiment and you want to keep them, remember to give the value you desire to val_Inf.

Parameters
• dgms (ndarray (n_pairs, 2) or list of diagrams) – array or list of arrays of birth/death pairs of a persistence barcode of a determined dimension.

• keep_inf (bool, default False) – if False, the infinity bars are removed. if True, the infinity bars remain.

• val_inf (float, default None) – substitution value to infinity.

• normalize (bool, default False) – if False, the persistent entropy values are not normalized. if True, the persistent entropy values are normalized.

Returns

ps (ndarray (n_pairs,)) – array of persistent entropy values corresponding to each persistence barcode.