Learning optimization of neural networks used for MIMO applications based on multivariate functions decomposition

Abstract

An approach based on multivariate function decomposition is presented with the aim of performing the learning optimization of multi-input-multi-output (MIMO) feed-forward neural networks (NNs). The proposed approach is mainly dedicated to all those cases in which the training set used for the learning process of MIMO NNs is sizeable and consequently the learning time and the computational cost are too large for an effective use of NNs. The basic idea of the presented approach comes from the fact that it is possible to approximate a multivariate function by means of a series containing only univariate functions. On the other hand, in many practical cases, the conversion of a MIMO NN into several multi-input-single-output (MISO) NNs is frequently adopted and investigated into state-of-the-art NNs. The proposed method introduces a further transformation, i.e. the decomposition of a MISO NN into a collection of single-input-single-output (SISO) NNs. This MISO–SISOs decomposition is performed using the previously cited series coming from the technique of the multivariate decomposition of functions. In this way, each SISO NN can be trained on each one-dimensional function returned from the cited decomposition, i.e. using limited data. Moreover, the present approach is easy to be implemented on a parallel architecture. In conclusion, the presented approach allows us to treat a MIMO NN as a collection of SISO NNs. Experimental results will be shown with the aim of proving that the proposed method is effective for a strong reduction of learning time by preserving anyway the accuracy.