Bi-directional optimal reduction of dimensionality in multi-channel seismic signal processing using neural networks

Abstract

Most previous approaches to dimensionality-reduction of multi-channel seismic data assume a linear constraint surface, such as principal-component analysis. Such methods buy simplicity at a sacrifice of generality, which will not work with a non-linear constraint surface. Even with such a disadvantage, the traditional methods can, in the linear cases, eventually map the multi-dimensional data to an eigenspace of a lower dimension with no loss of useful information. One previous nonlinear dimensionality-reduction method based on neural networks can simply map the multi-dimensional data to a constraint surface whose proper dimension can be determined only by experiments when prior information about the constraint surface inherent in the multi-dimensional data is sparse. When the selected dimension is not proper, there will be much loss of useful information. Based on the self-organizing properties of neural networks and the multi-layered perceptrons' ability of internal representation of the input patterns in the hidden units, a more general method is proposed to achieve optimal dimensionality-reduction which can discover the optimal dimension and type of constraint inherent in the multi-dimensional data with the least loss of information, and map the data from a n-dimensional feature space onto a m-dimensional 'generalized-eigenspace' (m < n) embedded in the n-dimensional feature space. This new dimensionality-reducer consists of two parallel neural nets which, respectively from opposite directions, search for the optimal dimension and type of the 'generalized-eigenspace'. The improved error back-propagation algorithm is used to update weights between the units of the different layers. A modified simulated annealing procedure is used to change the sizes of the two middle hidden layers of the two parallel neural nets so as to achieve finally an optimal dimensionality-reduction. Real multi-channel seismic data are used to test this new approach. The results demonstrate its usefulness and advantages over the previous neural dimensionality-reducer.