Consistency the Decision Function of K-nearest Neighbors by Using α-mixing Random Stochastic

The statistical classification is one of the advanced topics in the statistics in its many ways, including the Kernel method, the Histogram and the k-nearest neighbors used in this research, and the subject of the study of the consistency of decision functions is one of the topics that concern many researchers, in previous studies has been studied the consistency of the k-nearest neighbors in the independent case, and when the sample studied is dependent it becomes necessary to use the concept of mixing using different mixing coefficients Therefore, in this research, we aim to prove the consistency of the k-nearest neighbors in the case of weak correlation, i.e. we will prove that the follow-up of the k-nearest neighbors is consistent when the training sample is α-mixing random stochastic, or strong mixing, we came through a simulation of an experimental sample of different functions that the best k value (the number of best neighborhoods) is three neighborhoods, the study recommended subsequent research to obtain stronger convergence of the decision function as a study of the almost certain convergence of the k-nearest neighbors under other mixing conditions.