Permutation Entropy and Multi-scale Permutation Entropy Computation

Permutation Entropy and Multi-scale Permutation Entropy are methods for measuring time series complexity, originally developed within the MATLAB Exchange community. These techniques can analyze various types of data including biological signals, financial data, and meteorological data. Permutation Entropy is calculated by converting time series into symbolic sequences where identical values receive identical symbols, followed by computing the probability distribution of different symbol patterns appearing in the sequence. The implementation typically involves phase space reconstruction using time-delay embedding, sorting pattern recognition, and entropy calculation based on pattern frequency distribution. Multi-scale Permutation Entropy extends this concept by computing permutation entropy across different time scales through coarse-graining procedures, providing more comprehensive complexity information. These methods help researchers gain deeper insights into time series complexity and find valuable applications across multiple domains such as medical diagnosis and financial forecasting, with MATLAB implementations often utilizing functions for signal preprocessing, pattern enumeration, and multi-scale analysis.