In our era, while the life span is expanding, neurodegenerative diseases, such as Alzheimer's disease (AD), pose a great threat upon the quality of life. Currently, one of the urgent goals of neuroscientists is to detect AD in its early stages. Since recent treatments and prevention techniques aim at early and presymptomatic stages, studies carried out to present possible biomarkers are of importance. Therefore, in this study, the objective is to check the suitability of the method to the find a distinctive agent for distinguishing AD and mild cognitive impairment (MCI) patients from controls via fMRI data analysis. In order to achieve that, functional connectivity networks are obtained from an optimized auditory oddball task fMRI data via a group ICA approach using temporal concatenation of the subject data. In this analysis, the initial component number is chosen as thirty and eight different network groups are determined from the spatial classification of the components. Spectral and functional network connectivity analyses are carried out on these networks. In group comparisons, significant differences are found for small number of voxels in spatial maps. Functional connectivity network maps in MCI cases displayed a higher connectivity in precuneus region when compared to AD patients.