Alzheimer's disease (AD), a chronic neurodegener-ative brain disorder, caused by the accumulation of abnormal proteins called amyloid, is one of the prominent causes of mortality worldwide. Since there is a scarcity of experienced neurologists, manual diagnosis of AD is very time-consuming and error-prone. Hence, automatic diagnosis of AD draws significant attention nowadays. Machine learning (ML) algorithms such as deep learning are widely used to support early diagnosis of AD from magnetic resonance imaging (MRI). However, they provide better accuracy in binary classification, which is not the case with multi-class classification. On the other hand, AD consists of a number of early stages, and accurate detection of them is necessary. Hence, this research focuses on how to support the multi-stage classification of AD particularly in its early stage. After the MRI scans have been preprocessed (through median filtering and watershed segmentation), benchmark pre-trained convolutional neural network (CNN) models (AlexNet, VGG16, VGG19, ResNet18, ResNet50) carry out automatic feature ex-traction. Then, principal component analysis is used to optimize features. Conventional machine learning classifiers (Decision Tree, K-Nearest Neighbors, Support Vector Machine, Linear Program-ming Boost, and Total Boost) are deployed using the optimized features for staging AD. We have exploited the Alzheimer's disease Neuroimaging Initiative(ADNI) data set consisting of AD, MCIs (MCI), and cognitive normal (CN) classes of images. In our experiment, the SVM classifier performed better with the extracted ResNet50 features, achieving multi-class classification accuracy of 99.78% during training, 99.52% during validation, and 98.71% during testing. Our approach is distinctive because it combines the advantages of deep feature extractors, conventional classifiers, and feature optimization.