Using a single imaging modality to diagnose Alzheimer's disease (AD) or mild cognitive impairment (MCI) is a challenging task. FluoroDeoxyGlucose Positron Emission Tomography (FDG-PET) is an important and effective modality used for that purpose. In this paper, we develop a novel method by using single modality (FDG-PET) but multilevel feature, which considers both region properties and connectivities between regions to classify AD or MCI from normal control. First, three levels of features are extracted: statistical, connectivity, and graph-based features. Then, the connectivity features are decomposed into three different sets of features according to a proposed similarity-driven ranking method, which can not only reduce the feature dimension but also increase the classifier's diversity. Last, after feeding the three levels of features to different classifiers, a new classifier selection strategy, maximum Mean squared Error (mMsE), is developed to select a pair of classifiers with high diversity. In order to do the majority voting, a decision-making scheme, a nested cross validation technique is applied to choose another classifier according to the accuracy. Experiments on Alzheimer's Disease Neuroimaging Initiative database show that the proposed method outperforms most FDG-PET-based classification algorithms, especially for classifying progressive MCI (pMCI) from stable MCI (sMCI).