Entropy measures for biological signal analyses

Entropies are among the most popular and promising complexity measures for biological signal analyses. Various types of entropy measures exist, including Shannon entropy, Kolmogorov entropy, approximate entropy (ApEn), sample entropy (SampEn), multiscale entropy (MSE), and so on. A fundamental question is which entropy should be chosen for a specific biological application. To solve this issue, we focus on scaling laws of different entropy measures and introduce an ensemble forecasting framework to find the connections among them. One critical component of the ensemble forecasting framework is the scaledependent Lyapunov exponent (SDLE), whose scaling behavior is found to be the richest among all the entropy measures. In fact, SDLE contains all the essential information of other entropy measures, and can act J. Gao ( ) PMB Intelligence LLC, PO Box 2077, West Lafayette, IN 47996, USA e-mail: [email protected] J. Gao Mechanical and Materials Engineering, Wright State University, Dayton, OH 45435, USA J. Hu Affymetrix, Inc., 3380 Central Expressway, Santa Clara, CA 95051, USA W.-w. Tung Department of Earth & Atmospheric Sciences, Purdue University, West Lafayette, IN 47907, USA as a unifying multiscale complexity measure. Furthermore, SDLE has a unique scale separation property to aptly deal with nonstationarity and characterize highdimensional and intermittent chaos. Therefore, SDLE can often be the first choice for exploratory studies in biology. The effectiveness of SDLE and the ensemble forecasting framework is illustrated by considering epileptic seizure detection from EEG.