Comparing the method of spatial kernel fuzzy discriminant analysis with spatial kernel discriminant analysis using simulation

Abstract

Most statistical methods, including machine learning method, rely on the assumption that the data samples used in the analysis are independent and uniformly distributed, which is called the term (Identically Independent Distributed (iid)). However, this assumption about the independence of observations is not consistent with spatial data. Cases occur in many scientific fields such as ecology, image analysis, epidemiology, medical studies, etc. because they will fail to determine spatial autoregressive correlation. The Spatial Kernel Fuzzy Discriminant Analysis (SKFDA) method It takes into account the spatial reliability of the data by determining the inaccuracy in assigning the diffusion matrix between classes and within classes using the principle of fuzzy sets and comparing this method with the method of spatial core discriminant analysis through two measures of overall accuracy (Overall Accuracy OA) and average classification accuracy (Average Accuracy AA). By choosing three sample sizes within each category, which are (50, 200, 1000), and determining the number of categories, as two categories were identified for the purpose of applying discriminant analysis methods, by choosing two ratios for the training samples, which are (0.30, 0.8), and a bandwidth was chosen for the observations (h_v=700). ) and randomly select four spatial bandwidth values (h_s=1, 3, 6, 10) and choose a Gaussian core function in these two methods.