استخدام طريقة Kernel في تحليل الارتباط القويم مع تطبيق
Author name:
عماد عادل عبد السلام عناب
Supervisor name:
ظافر حسين رشيد النجار | زكي جواد الصراف
General topic:
Administration and Economics
Specific topic:
Statistics
Degree:
Doctorate
University:
University of Baghdad - Faculty Of Administration And Economics - Department Of Statistics
Language:
Arabic
University location:
Baghdad
First pages:
07T3906 - p.pdf
Abstract:
في هذا البحث تم استعراض طريقة تحليل الارتباط القويم الخطية (Linear Canonical Correlation Analysis) والمقترحة من قبل Hotteling (1936) وتطور خوارزميات الاحتساب فيها، اذ تتلخص فكرتها بقياس معاملات الارتباط بين مجموعتين من البيانات في كل منها عدد من المتغيرات | This research studied the Linear Canonical Correlation Analysis (LCCA) proposed by Hotteling(1936) , and the development approach of it is algorithms. LCCA is a method to find the correlation coefficients between two groups of data involved different variables by calculating Eigenvalues of the block Variance - Covariance ( or correlations) matrix of the two groups, and their associated Eigenvectors as weighted to each set group data to find a series of canonical varieties to each group set. The correlation coefficient between the first canonical of each set which corresponding to the maximum eigenvalue called first canonical correlation. LCCA have some properties that should be exists to work with it , the importance one is the multivariate normal distribution of each set of data , and the linearity relationship between these variables. The research studied also the Kernel methods with some Kernel functions to establish the symmetric Gram matrix by inner Product of the original data set of each group, and then using the same approach as LCCA but in this case with a semi positive matrices instead of positive defined matrices in LCCA , this mean with combine between classic CCA and Kernel methods which is called Kernel Canonical Correlation Analysis (KCCA). The advantage of this knew method to discover more relationships between sets of variables. The goal of this research to show how to obtain the optimal weighted that when multiplicities by the original sets of data will maximize the canonical correlation coefficients. Some simulation experiments were applying here in order to find that KCCA methods exceed the assumptions of LCCA, the canonicalcorrelations that come from this new method is greater than from classic method, with consideration propose two mixed kernel functions.In application side, we suggested a true parameter ? in kernel function instead that used in simulation.
