We propose a statistical learning model for classifying cognitive processes based on distributed patterns of neural activation in the brain, acquired via functional magnetic resonance imaging (fMRI). In the proposed learning machine, local meshes are formed around each voxel. The distance between voxels in the mesh is determined by using functional neighborhood concept. In order to define functional neighborhood, the similarities between the time series recorded for voxels are measured and functional connectivity matrices are constructed. Then, the local mesh for each voxel is formed by including the functionally closest neighboring voxels in the mesh. The relationship between the voxels within a mesh is estimated by using a linear regression model. These relationship vectors, called Functional Connectivity aware Local Relational Features (FC-LRF) are then used to train a statistical learning machine. The proposed method was 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 and Support Vector Machine, 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 Functional Mesh Learning model, which range in 62-68% is superior to the classical multi-voxel pattern analysis (MVPA) methods, which range in 40-48%, for ten semantic categories.