Kernel discriminant analysis Using Fuzzy Spatial Autocorrelation
(with an application)

A thesis
Submitted to the council of the college of Administration &Economics\ University of Karbala as partial fulfillment of the requirements for the degree of Philosophy of Statistics Sciences

By
Sackineh Shamel Jasem

Supervision
Prof. Dr . Shorouk Abdul Reda Saeed Al-Sabbah

Abstract
Most statistical methods, including machine learning methods, 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.) This assumption is adopted by most traditional models of data analysis, but in some cases in the natural world, this assumption is inappropriate for such data because it will fail to determine autocorrelation. Spatial Autoregressive: Therefore, spatial discriminant analysis seeks to achieve an accurate classification of spatial elements in the context of blurring and uncertainty related to spatial data using the principle of fuzzy sets.
The thesis came with the aim of proposing a Spatial Kernel Fuzzy Discriminant Analysis (SKFDA) method and comparing the proposed method with Linear Discriminant Analyzes(LDA) – Kernel Discriminant Analyzes(KDA) – Kernel Fuzzy Discriminant Analysis (KFDA), Spatial Kernel Fuzzy Discriminant Analysis (SKFDA). using two measures of overall accuracy (Overall Accuracy OA) and average classification accuracy (Average Accuracy AA) by choosing six variable sizes within each class (20, 50, 100, 200,500, 1000) and determining the number of classes, as Two categories were identified for the purpose of applying discriminant analysis methods by choosing three ratios for the training samples (0.30, 0.50, 0.80), the bandwidth of the observations was chosen (hv=700), and six values for the spatial bandwidth were randomly selected (hs=1, 1.5, 2, 3, 6, 10) and choosing a Gaussian function in all methods, and it was reached that when the sample size (n=20, 50) the linear discriminant analysis method achieved an advantage over the rest of the discriminant analysis methods. As the sample size increased and became (n = 100, 200, 500, 1000), the advantage of the proposed method increased, but at the positional smoothing parameter hs = 1, 1.5, 2, 3, while if the value of hs increased from (3), the advantage of the proposed method decreased and the advantage increased. The method of core discriminant analysis and core fuzzy discriminant analysis. The proposed method was the best when the sample size was n = 1000 and hs = 3. The higher the smoothing parameter hs, the greater the preference for the RLA method and the linear discriminant analysis method, then followed by the spatial core discriminant analysis method, then the spatial core fuzzy discriminant analysis method, and finally the linear discriminant analysis method. On the practical side, a group of slides amounting to (980) slides were used, taken with a magnetic resonance imaging (MRI) machine of the human brain for people with different types of brain tumors: meningioma (glioma) with a number of slides amounting to (185) and glioma (meningioma) with a number of slides amounting to (210). A pituitary tumor with a number of slices of (150), an acoustic nerve tumor with a number of slices of (270), and a tumor and metastatic tumors of (165) were taken from the magnetic resonance unit at the Warith International Foundation for Oncology. International Cancer Institute in the Holy Governorate of Karbala, and the (SKFDA) method was applied to real data. It was concluded that the proposed method implemented the tumor classification process with a high accuracy of (98.68) and with a high classification accuracy for each type of tumor, and that the classifications classified by the proposed method were close to the classifications that were achieved. Obtained from the oncology center.