On the application of orthogonal transformation for the design and analysis of feedforward networks

Orthogonal transformation, which can lead to compaction of information, has been used in two ways to optimize on the size of feedforward networks: 1) through the selection of optimum set of time-domain inputs, and the optimum set of links and nodes within a neural network (NN); and 2) through the orthogonalization of the data to be used in NN's, in case of processes with periodicity. The proposed methods are efficient and are also extremely robust numerically. The singular value decomposition (SVD) and QR with column pivoting factorization (QRcp) are the transformations used. SVD mainly serves as the null space detector; QRcp coupled with SVD is used for subset selection, which is one of the main operations on which the design of the optimal network is based. SVD has also been used to devise a new approach for the assessment of the convergence of the NN's, which is an alternative to the conventional output error analysis.<
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