MaxMSE: A Novel Approach to Multiscale Entropy Analysis Using Max-Pooling to Preserve Maximal Information

This paper proposes a new approach to multiscale entropy (MSE) analysis using max-pooling for coarse-graining, inspired by convolutional neural networks, to efficiently capture important features while reducing data dimensionality. The proposed method, maxMSE, is compared with traditional multiscale entropy techniques using synthetic white and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1/f$</tex> noise, as well as resting-state EEG data for healthy young versus elderly individuals. The results demonstrate that maxMSE shows improved stability for short time series, as evidenced by a lower mean and standard deviation compared to the traditional MSE algorithm when tested on white and pink noise. maxMSE also offers competitive computational efficiency. The method's application to EEG data yields statistically significant results in distinguishing age groups, with maxMSE achieving a lower p-value <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(p=0.0217)$</tex> and a higher effect size (0.3270) compared to the traditional MSE measure with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$p= 0.1113$</tex> and undefined effect size. maxMSE complements conventional multiscale entropy by using max-pooling for coarse-graining, which retains the maximum values of data segments, whereas traditional MSE relies on moving averages.