Entropy Approximation by Machine Learning Regression: Application for Irregularity Evaluation of Images in Remote Sensing

Approximation of entropies of various types using machine learning (ML) regression methods are shown for the first time. The ML models presented in this study define the complexity of the short time series by approximating dissimilar entropy techniques such as Singular value decomposition entropy (SvdEn), Permutation entropy (PermEn), Sample entropy (SampEn) and Neural Network entropy (NNetEn) and their 2D analogies. A new method for calculating SvdEn2D, PermEn2D and SampEn2D for 2D images was tested using the technique of circular kernels. Training and testing datasets on the basis of Sentinel-2 images are presented (two training images and one hundred and ninety-eight testing images). The results of entropy approximation are demonstrated using the example of calculating the 2D entropy of Sentinel-2 images and R^2 metric evaluation. The applicability of the method for the short time series with a length from N = 5 to N = 113 elements is shown. A tendency for the R^2 metric to decrease with an increase in the length of the time series was found. For SvdEn entropy, the regression accuracy is R^2 > 0.99 for N = 5 and R^2 > 0.82 for N = 113. The best metrics were observed for the ML_SvdEn2D and ML_NNetEn2D models. The results of the study can be used for fundamental research of entropy approximations of various types using ML regression, as well as for accelerating entropy calculations in remote sensing. The versatility of the model is shown on a synthetic chaotic time series using Planck map and logistic map.