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Applying machine learning methods to various modality medical images and clinical data for early diagnosis of Alzheimer's disease (AD) and its prodromal stage has many significant results. So far, the image data input to classifier mainly focus on 2D or 3D images. Although some functional imaging technologies, such as functional magnetic resonance imaging (fMRI), generate 4D data which contain both spatial and time-varying information of the brain, for the lack of suitable 4D image processing algorithm, these 4D data were always used by transforming them into functional connectivity or slicing them into 2D/3D pictures which causing apparent information loss. In this paper, we present a 4D deep learning model (C3d-LSTM) for AD discrimination, which is able to utilize the spatial and time-varying information simultaneously by dealing with 4D fMRI data directly. The proposed C3d-LSTM combines a series of 3D convolutional neural networks (CNNs) to extract spatial features from each volume of 3D static image in fMRI image sequence. Then the feature maps obtained were put into the long short-term memory (LSTM) network to capture the time-varying information contained in the data. Because of the design of structure, C3d-LSTM became an end-to-end data-driven model, which was more convenient for processing 4D fMRI data. The model proposed conducted on the AD Neuroimaging Initiative dataset for algorithm evaluation compared with controlled experiments. Results showed that using 4D fMRI data directly with the proposed method did make a far better result for AD detection than the methods using functional connectivity, 2D, or 3D fMRI data. It demonstrated our assumption that making the most of the natural spatial and temporal information preserved in 4D fMRI data is significant for AD detection and can increase the performance of the classifier. Meanwhile the result implied that the C3d-LSTM model proposed is a suitable model for processing 4D fMRI data and extracting the spatio-temporal property of fMRI data fully for diagnosis of AD. [ABSTRACT FROM AUTHOR]