A new graphical model called Cognitive Process Graph (CPG) is proposed, for classifying cognitive processes based on neural activation patterns which are acquired via functional Magnetic Resonance Imaging (fMRI) in brain. In the CPG, first local meshes are formed around each voxel. Second, the relationships between a voxel and its neighbors in a local mesh, which are estimated by using a linear regression model, are used to form the edges among the voxels (graph nodes) in the CPG. Then, a minimum spanning tree (MST) of the CPG which spans all the voxels in the region of interest is computed. The arc weights of the MST are used to represent the underlying cognitive processes. The proposed method reduces the curse of dimensionality problem that is caused by very large dimension of the feature space of the fMRI measurements, compared to number of instances. Finally, the arc weights computed over the path of the MST called MST-Features (MST-F) are used to train a statistical learning machine. The proposed method is tested on a recognition memory experiment, including data pertaining to encoding and retrieval of words belonging to ten different semantic categories. Two popular classifiers, namely k-Nearest Neighbor (k-NN) and Support Vector Machine (SVM), are trained in order to predict the semantic category of the item being retrieved, based on activation patterns during encoding. The classification performance of the proposed learning modelis superior to the classical multi-voxel pattern analysis (MVPA) methods for the underlying cognitive process.