In this thesis, we propose novel representations to extract discriminative information in functional Magnetic Resonance Imaging (fMRI) data for cognitive state and gender classification. First, we model the local relationship among a set of fMRI time series within a neighborhood by considering temporal information obtained from all measurements in time series. The estimated relationships, called Mesh Arc Descriptors (MADs) are employed to represent information in fMRI data. Second, we adapt encoding methods frequently used in computer vision domain, namely Fisher Vectors (FV), Vector of Locally Aggregated Descriptors (VLAD) and Bag-of-Words (BoW) to encode local MADs. In this thesis we show that employing MADs outperform state-of-the-art fMRI representations and their further encoding with FV gives superior performance over MADs. Then, we propose a hierarchical framework, in which the fMRI signal is decomposed into multiple subbands, mesh networks are constructed for each subband separately and the decisions of classifiers trained with multi-resolution mesh-networks are fused. It is shown that, hierarchical multi-resolution mesh networks outperform mesh-networks constructed for original fMRI signal. Finally, we adapt multi-resolution approach for gender classification using fMRI data. Decisions of classifiers trained with multi-resolution multi-task mesh networks are fused in a 2-level hierarchical architecture to discriminate gender. The proposed framework performs better compared to single-layer architectures fusing only multi-task or only multi-resolution mesh networks.