This data set consists of 2480 measurements from 30 sensors of an industrial pulp process. An expert has preprocessed the signal by roughly compensating for time lags of the process which originate from the finite speed of pulp flow through the process.
In order to get an idea of the dimensionality of the data, linear FA was applied to the data and compared with the nonlinear FA. It turned out that linear FA needs over twice as many sources for representing as much data as the nonlinear FA , which is a clear evidence for the nonlinearity of the data manifold.
Again several different structures and initialisations for the MLP network were tested and the cost function was found to be minimised by a model having 10 sources and 30 hidden neurons. The estimated sources are shown in Fig. 9 and the nonlinear reconstruction from sources to observations together with the original time series are shown in Fig. 10. Many of the reconstructions are strikingly accurate and in some cases it seems that the reconstructions have even less noise than the original signals. This is somewhat surprising since the time dependencies in the signal were not included in the model. The observation vectors could be arbitrarily shuffled and the model would still produce the same results.