JOURNAL zyxwvutsr OF CHEMOMETRICS, VOL. 9,423430 zyxwvu (1995) zyxwvu SHORT COMMUNICATION ALGORITHM FOR FINDING AN INTERPRETABLE SIMPLE NEURAL NETWORK SOLUTION USING PLS RASMUS BRO zyxwvu Food Technology, Department zyxwvuts of Dairy and Food Science, Royal Veterinary and Agricultural University, Thorvaldsensvej 40.6, ii, DK-1871 Frederiksberg zyxwv C, Denmark SUMMARY This communication describes the combination of a feedforward neural network (NN) with one hidden neuron and partial least squares (PLS) regression. Through training of the neural network with an algorithm that is a combination of a modified simplex, PLS and certain numerical restrictions, one gains an NN solution that has several feasible properties: (i) as in PLS the solution is qualitatively interpretable; (ii) it works faster than or comparably with ordinary training algorithms for neural networks; (iii) it contains the linear solution as a limiting case. Another very important aspect of this training algorithm is the fact that outlier detection as in ordinary PLS is possible through loadings, scores and residuals. The algorithm is used on a simple non-linear problem concerning fluorescence spectra of white sugar solutions. KEY WORDS PLS; neural network; training; interpretable BACKGROUND Feedforward neural networks (NNs) with one hidden layer and methods based on latent variables, such as principal component regression (PCR) and partial least squares (PLS) regression, are increasingly often being used as multivariate calibration methods in chemistry. Though apparently very different, there are in fact many similarities between these methods and it is possible to understand them in the light of the same methodology. Most often linear calibration methods are indeed sufficient tools for handling chemical problems, but there are occasions where the linear methods fail to give optimal results. Two examples relevant to our research group can be mentioned. In process monitoring and optimization there are many kinds of variables (physical/chemical, etc.) and often there will not be a preknown mathematical law indicating the relationship between these very different variables. We are specifically concerned with fast screening methods based on fluorescence. Often the fluorescence in an on-line application will quench, partly because dilution of the samples is impossible. Linear models are not always adequate in these situations and models such as PLS with e.g. quadratic inner relations (i.e. still linear in their parameters) do not guarantee a proper solution. A feedforward NN with one hidden layer is an interesting alternative for non-linear calibration. ' There are, however, two problems with the learning algorithms most often used for NNs, CCC 0886-9383/95/050423-08 zyxwvu 0 1995 by John Wiley & Sons, Ltd. Received 15 November 1994 Accepted 1 May 1995