Alzheimer’s disease (AD) and mild cognitive impairment (MCI) are progressive neurocognitive disorders, for which early detection is crucial to reducing clinical, social, and economic burdens. Electroencephalography (EEG), with its non-invasive nature, low cost, and high temporal resolution, provides a valuable tool for assessing brain dynamics. However, traditional EEG analyses face challenges due to high data dimensionality and the difficulty of extracting discriminative features across multiple channels. This study proposes an efficient approach to reduce computational complexity in multichannel EEG analysis by integrating channel information and performing optimized channel selection. We analyzed EEG data from an open-access database, comprising 160 participants (40 AD, 25 MCI, and 95 healthy controls). Following preprocessing and frequency band extraction, the 19-channel data were transformed into a single signal via an amplitude-based conversion algorithm. Subsequently, channel selection was performed using two distinct strategies: selecting the channel with the most frequent dominant amplitude, and selecting the channel with the maximum phase value. Subsequently, nonlinear features—including Higuchi fractal dimension, Lyapunov exponent, and sample entropy—were extracted. These features were then classified using a support vector machine (SVM). Model performance was evaluated using K-Fold and leave-one-subject-out (LOSO) cross-validation in both one-vs-one and one-vs-all modes. Results demonstrated a gradual decrease in EEG complexity from healthy controls to MCI and AD groups. The highest classification accuracy was achieved in the gamma band for distinguishing controls from MCI (78.06%) and from AD (70.27%) using the data transformation approach. Both the alpha and gamma bands demonstrated superior performance compared to other frequency bands, particularly when using the data transformation and dominant-amplitude channel selection methods. Furthermore, K-Fold cross-validation yielded consistently higher accuracy compared to the LOSO. Overall, combining nonlinear EEG features with optimized channel selection, particularly in the alpha and gamma bands, presents a promising approach for detecting and monitoring AD and MCI.