The autoassociative neural network in signal analysis: I. The data dimensionality reduction and its geometric interpretation

In complex and risky plants, such as the nuclear reactors, the analysis of the signals released by the many sensors which monitor the plant represents a difficult task due to the high-dimensionality of the data. This paper is the first of two in which we tackle the problem of the dimensionality reduction by the nonlinear principal components analysis as performed by an autoassociative neural network (AANN). This network filters the many input data and releases at the bottleneck output a relatively small number of signals which capture the significant properties of the original data, thus realizing the data reduction. In the present paper, we show that the network ability in correctly reproducing as output the given input after a passage through the bottleneck layer (which by definition should have fewer nodes than either input or output layers) could be conceived as a topological mapping between abstract spaces. Apart from the less critical choice of the number of nodes in the mapping and demapping layers, the topological mapping will be successful – and the AANN will be able to perform the required data reconstruction – provided that the number of nodes of the bottleneck layer is related to the dimensionality d of the abstract projection space. We show how to obtain a numerical estimate d* for the real dimension d. This numerical estimate will firmly base the choice of the number of nodes f of the bottleneck layer, thus avoiding the usual troubling trial-and-error procedure. The power of the proposed approach is demonstrated firstly on a few geometrical cases and then on the analysis of nuclear transients simulated by the classic Chernick’s model.