Despite growing evidence of aberrant neuronal complexity in Alzheimer's disease (AD), it remains unclear how this variation arises. Neural oscillations reportedly comprise different functions depending on their own properties. Therefore, in this study, we investigated details of the complexity of neural oscillations by decomposing the oscillations into frequency, amplitude, and phase for AD patients. We applied resting-state magnetoencephalography (MEG) to 17 AD patients and 21 healthy control subjects. We first decomposed the source time series of the MEG signal into five intrinsic mode functions using ensemble empirical mode decomposition. We then analyzed the temporal complexities of these time series using multiscale entropy. Results demonstrated that AD patients had lower complexity on short time scales and higher complexity on long time scales in the alpha band in temporal regions of the brain. We evaluated the alpha band complexity further by decomposing it into amplitude and phase using Hilbert spectral analysis. Consequently, we found lower amplitude complexity and higher phase complexity in AD patients. Correlation analyses between spectral complexity and decomposed complexities revealed scale-dependency. Specifically, amplitude complexity was positively correlated with spectral complexity on short time scales, whereas phase complexity was positively correlated with spectral complexity on long time scales. Regarding the relevance of cognitive function to the complexity measures, the phase complexity on the long time scale was found to be correlated significantly with the Mini-Mental State Examination score. Additionally, we examined the diagnostic utility of the complexity characteristics using machine learning (ML) methods. We prepared a feature pool using multiple sparse autoencoders (SAEs), chose some discriminating features, and applied them to a support vector machine (SVM). Compared to the simple SVM and the SVM after feature selection (FS + SVM), the SVM with multiple SAEs (SAE + FS + SVM) had improved diagnostic accuracy. Through this study, we 1) advanced the understanding of neuronal complexity in AD patients using decomposed temporal complexity analysis and 2) demonstrated the effectiveness of combining ML methods with information about signal complexity for the diagnosis of AD.