Shannon Entropy Over Approximate Entropy: An Adaptive Regularity Measure

• Activity Number: 432
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: International Chinese Statistical Association
• Author(s): Wei Han*+ and Abraham J Wyner
• Companies: University of Pennsylvania and The Wharton School, University of Pennsylvania
• Keywords: Approximate Entropy ; Shannon Entropy ; Regularity Measure ; Lempel-Ziv sliding window ; Electroencephalography

Abstract

Approximate Entropy, as an approximation of Kolmogrov-Sinai entropy, is the widely accepted method to quantify the regularity in data, especially medical data. However, it quantifies the regularity only up to the second order, while real data may carry much more. In this paper, we demonstrate the connection between Approximate entropy and Shannon entropy. Based on that, we propose the adaptive Shannon entropy approximation methods (e.g., Lempel-Ziv sliding window method) as an alternative approach to quantify the regularity of data. The new approach has the advantage of adaptively choosing the order of regularity to analyze based on the data. Later, we compare the results of Lempel-Ziv sliding window method with Approximation Entropy on the electroencephalography (EEG) data to measure the depth of anesthesia. The Lempel-Ziv sliding window method yields more accurate results, especially for low entropy data.