Early diagnosis of mild cognitive impairment is an effective way to intervene Alzheimer's disease. At present, rest-state functional magnetic resonance imaging and machine learning methods are often used in the auxiliary diagnosis of mild cognitive impairment. The key is to use blood oxygen level dependent (BOLD) signals to construct the functional connection of the brain. Aiming at the problem of various external noise interference in brain resting BOLD signals, a reconstruction method combined with multiple empirical mode decomposition and Pearson correlation and a polar positive negative reconstruction criterion are proposed. The posterior cingulate cortex, the central node of the brain default mode network, is used as a template to reconstruct BOLD signals to reduce external noise interference. The experimental results show that the functional connection based on pole positive negative reconstruction criterion can improve the difference of data in classification performance compared with the data before noise reduction, and further improve the classification performance while reducing the dimension of the data set in feature selection performance. In addition, the above performance is better than the traditional reconstruction criterion. Finally, the optimal feature subset after noise reduction is statistically analyzed. It is found that the insula may be the relevant brain area of the default mode network, and the cerebellar vermis and posterior cingulate cortex may constitute a cognitive function compensation network, which is a rare conclusion in previous studies.