Alzheimer's disease (AD) is the most common cause of dementia and a progressive neurodegenerative condition, characterized by a decline in cognitive function. Symptoms usually appear gradually and worsen over time, becoming severe enough to interfere with individual daily tasks. Thus, the accurate diagnosis of both AD and the prodromal stage (i.e., mild cognitive impairment (MCI)) is crucial for timely treatment. As AD is inherently dynamic, the relationship between AD indicators is unclear and varies over time. To address this issue, we first aimed at investigating differences in atrophic patterns between individuals with AD and MCI and healthy controls (HCs). Then we utilized multiple biomarkers, along with filter- and wrapper-based feature selection and an extreme learning machine- (ELM-) based approach, with 10-fold cross-validation for classification. Increasing efforts are focusing on the use of multiple biomarkers, which can be useful for the diagnosis of AD and MCI. However, optimum combinations have yet to be identified and most multimodal analyses use only volumetric measures obtained from magnetic resonance imaging (MRI). Anatomical structural MRI (sMRI) measures have also so far mostly been used separately. The full possibilities of using anatomical MRI for AD detection have thus yet to be explored. In this study, three measures (cortical thickness, surface area, and gray matter volume), obtained from sMRI through preprocessing for brain atrophy measurements; cerebrospinal fluid (CSF), for quantification of specific proteins; cognitive score, as a measure of cognitive performance; and APOE ε4 allele status were utilized. Our results show that a combination of specific biomarkers performs well, with accuracies of 97.31% for classifying AD vs. HC, 91.72% for MCI vs. HC, 87.91% for MCI vs. AD, and 83.38% for MCIs vs. MCIc, respectively, when evaluated using the proposed algorithm. Meanwhile, the areas under the curve (AUC) from the receiver operating characteristic (ROC) curves combining multiple biomarkers provided better classification performance. The proposed features combination and selection algorithm effectively classified AD and MCI, and MCIs vs. MCIc, the most challenging classification task, and therefore could increase the accuracy of AD classification in clinical practice. Furthermore, we compared the performance of the proposed method with SVM classifiers, using a cross-validation method with Alzheimer's Disease Neuroimaging Initiative (ADNI) datasets.