Singular Value Decomposition Entropy for Complex Data Analysis

Entropy-based methods have gained increasing prominence in analyzing and detecting patterns in complex systems data. Key aspects such as fractality, time reversibility, and nonlinearity are commonly characterized using these methods, often in conjunction with techniques like wavelets and empirical modeling. The goal is to extract complexity indices and identify patterns that traditional methods struggle to capture. Shannon entropy obtains information from data by, e.g., extracting hidden information by removing noisy components. However, its applicability can be limited for data of short length. Approximate, sample and permutation entropies offer more flexible approaches, but their parameter dependence can complicate the interpretation of results. Singular value decomposition (SVD) entropy provides a framework for assessing pattern diversity in terms of an entropy index, reflecting an approximate dimensionality of a given dataset. This review focuses on recent SVD entropy applications across various fields and explores its potential in nonlinearity detection and transfer entropy analysis for time series, illustrated through select cases.