A new topological entropy-based approach for measuring similarities among piecewise linear functions

In this paper we present a novel methodology based on a topological entropy, the so-called persistent entropy, for addressing the comparison between discrete piecewise linear functions. The comparison is certified by the stability theorem for persistent entropy that is presented here. The theorem is used in the implementation of a new algorithm. The algorithm transforms a discrete piecewise linear function into a filtered simplicial complex that is analyzed via persistent homology and persistent entropy. Persistent entropy is used as a discriminant feature for solving the supervised classification problem of real long-length noisy signals of DC electrical motors. The quality of classification is stated in terms of the area under receiver operating characteristic curve (AUC=93.87%).