A model with an intrinsic property of learning higher order correlations

A neural network model that can learn higher order correlations within the input data without suffering from the combinatorial explosion problem is introduced. The number of parameters scales as M x N, where M is the number such that no higher order network with less than M higher order terms can implement the same input data set and N is the dimensionality of the input vectors. In order to have better generalization, the model was designed to realize a supervised learning such that after learning, output for any input vector is the same as the output of a higher order network that implements the same input data set using M number of higher order terms. Unlike the case in product units, the local minima problem does not pose itself as a severe problem in the model. Simulation results for some problems are presented and the results are compared with the results of a multilayer feedforward network. It is observed that the model can generalize better than the multilayer feedforward network.