In recent years, interest has grown in using computer-aided diagnosis (CAD) for Alzheimer's disease (AD) and its prodromal stage, mild cognitive impairment (MCI). However, existing CAD technologies often overfit data and have poor generalizability. In this study, we proposed a sparse-response deep belief network (SR-DBN) model based on rate distortion (RD) theory and an extreme learning machine (ELM) model to distinguish AD, MCI, and normal controls (NC). We used [18F]-AV45 positron emission computed tomography (PET) and magnetic resonance imaging (MRI) images from 340 subjects enrolled in the ADNI database, including 116 AD, 82 MCI, and 142 NC subjects. The model was evaluated using five-fold cross-validation. In the whole model, fast principal component analysis (PCA) served as a dimension reduction algorithm. An SR-DBN extracted features from the images, and an ELM obtained the classification. Furthermore, to evaluate the effectiveness of our method, we performed comparative trials. In contrast experiment 1, the ELM was replaced by a support vector machine (SVM). Contrast experiment 2 adopted DBN without sparsity. Contrast experiment 3 consisted of fast PCA and an ELM. Contrast experiment 4 used a classic convolutional neural network (CNN) to classify AD. Accuracy, sensitivity, specificity, and area under the curve (AUC) were examined to validate the results. Our model achieved 91.68% accuracy, 95.47% sensitivity, 86.68% specificity, and an AUC of 0.87 separating between AD and NC groups; 87.25% accuracy, 79.74% sensitivity, 91.58% specificity, and an AUC of 0.79 separating MCI and NC groups; and 80.35% accuracy, 85.65% sensitivity, 72.98% specificity, and an AUC of 0.71 separating AD and MCI groups, which gave better classification than other models assessed.
