Alzheimer's disease (AD) is the most common type of dementia in the elderly. Approximately, 26 million people worldwide are affected by AD. Among the various diagnostic methods for Alzheimer's disease, MRI brain imaging can display sharp changes in brain tissues. It can be used as a method for early diagnosis of Alzheimer's disease. Considering the high volume of features related to brain tissue thickness, requires the using feature reduction methods. For this purpose, statistical tests pair sample test and Independent sample test was used. After careful selection of key features, for reducing the number of features, SAS which is a kernel-based feature selection algorithm is used in linear and nonlinear mode. At the end, neural network classification, decision trees, nearest neighbor and Naïve Bayes algorithms are used for modeling. Results show that the classification accuracy of obtained feature subsets have better results compare to the original data set.