Parameter Selection for Using Permutation Entropy in Cetacean Whistle Detection

This study investigates the optimal parameter selection for permutation entropy (PE) in cetacean whistle detection, focusing on the Indo-Pacific humpback dolphin (Sousa chinensis). PE, a statistical measure quantifying time series complexity, has shown promise in signal detection within noisy environments. However, its effectiveness heavily depends on two key parameters: embedding dimension <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(d)$</tex> and embedding delay <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(\tau)$</tex>. Through systematic analysis of simulated tonal and broadband signals, we explore how different combinations of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$d$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\tau$</tex> affect detection performance, quantified by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\Delta H$</tex> - the difference in PE between signal-plus-noise and noise-only sections. Our findings demon-strate that <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$d=6$</tex> offers an optimal balance between detection accuracy and computational efficiency. For <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\tau$</tex>, we establish a relationship with sampling frequency <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(f_{s})$</tex> and signal frequency <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(f_{0})$</tex>, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\tau=f_{s}/(2f_{0})$</tex> maximizes <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\Delta H$</tex>. This relationship allows for adaptive parameter selection across various cetacean species and recording conditions. We further validate our approach using simulated broadband signals that mimic the down-sweep characteristics of Indo-Pacific humpback dolphin whistles. This study provides a comprehensive framework for optimizing PE-based cetacean whistle detection, enhancing the sensitivity and reliability of acoustic monitoring techniques in marine mammal research and conservation efforts.