Two-dimensional multi-layer Factor Graphs in Reduced Normal Form

We build a multi-layer architecture using the Bayesian framework of the Factor Graphs in Reduced Normal Form (FGrn). This model allows great modularity and unique localized learning equations. The multi-layer architecture implements a hierarchical data representation that via belief propagation can be used for learning and inference in pattern completion, correction and classification. We apply the framework to images extracted from a standard data set.