The Application of Lempel-Ziv Complexity in Medicine Science, Nature Science, Social Science, and Engineering: A Review and Prospect

Lempel-Ziv complexity (LZC) is an algorithm used to quantify the complexity of a data sequence by calculating the number of independent substrings contained in the sequence. LZC succeeds in detecting abnormal patterns in signals and is widely employed for identifying anomalies and recognizing patterns in several fields, such as medical science, natural science, social science, and engineering. The objective of this study is to investigate the theory, improvement, and application of LZC in different fields. Firstly, a brief overview of the areas where LZC is utilized is provided. Next, the principle and process of signal complexity characterization are examined, along with a comparison of its advantages to entropy. Following this, we will present a detailed review of the improvement techniques and uses of LZC, focusing on three key areas: encoding methods, multiscale methods, and noise reduction methods. Lastly, this paper presents the unresolved matters and potential areas for further investigation LZC.