Statistical Technique in Clustering Problems

Abstract: The problem of evaluating and improving the quality of clustering multispectral data is considered. A method for calculating the distance between clusters is developed. Vectors of each cluster are considered as implementations of some random vector. Sampling distribution functions (SDF) are found and the errors of the approximation of unknown exact distribution functions by SDFs are obtained. The distance between two clusters is defined as the distance between two SDFs. The criteria for indiscernible, overlapping, and disjoint clusters are defined. A technique to improve clustering is proposed in which indiscernible (or indiscernible and overlapping) clusters are merged. The results of numerical experiments on simulated data are given. It is shown that the technique can decompose the data into the initial groups of vectors. The results of numerical experiments with real data are given. The real data are multispectral images of the HYPERION sensor, obtained above the ocean under a clear sky and broken clouds. It is shown that the presented technique can distinguish clouds and their shadows in the images. © 2023, Pleiades Publishing, Ltd.