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9. Association

The capacity to associate is closely related to the recognition of similarities between different objects. Neural networks can also be conceived of as memories, because they store the information they have learned from the training data in the form of weights or "synaptic strengths". Should a new object be fed into the neural network whose input data resemble those of an object used in training, some network architectures are able to recognize this and yield the stored object from the training phase as output.
This ability of neural networks to associate, to recognize similarities in given data, has been exploited very little in chemistry up to now. Even the two studies presented here are essentially only feasibility studies. The basic solution to a problem is demonstrated here on small, simply structured data sets. For a real-world application however, larger sets of more complex data would have to be investigated.

9.1. Adjustment of Base Lines

Systematic deviations from the base line may be observed in many spectra and could be caused by impurities, the influence of solvents, or problems with technical equipment. Five different types of base line (normal, ascending, descending, concave, convex) were stored in a Hopfield network as simple black pixel-patterns in a matrix consisting of 6 x 20 points [65]. Then a simple, simulated spectrum which contained a convex base line was fed into the thus trained Hopfield network. After three iterations the pattern for this baseline was output by the network (Fig. 44).

Fig. 44. Five types of base lines of a spectrum (top), a much simplified spectrum with a concave baseline (bottom left) and the concave base line recognized by the neural network after three iterations (bottom right).

Afterwards therefore, a background correction could be undertaken for this spectrum. We have already pointed out in this review that a real-world application would need a far higher resolution; thus the base lines would have to be represented by a larger pixel matrix (e.g., 20 x 250). However, because of the basic limitations on the storage capacity of Hopfield networks, and in order to make good predictions, 2 x 107 matrix elements would need to be checked. It only makes sense to carry out this task by hardware implementations of parallel neural networks.
Because of the storage and calculation problems presented by Hopfield networks, the same task was also investigated with a Hamming network [65]. A Hamming network [66], which requires far less memory capacity, was in fact also able to be solve the problem. However, in this case too, only a 7 x 20 matrix was used to represent the five types of base line; an application which uses experimental data with a high resolution has yet to appear.

9.2. Identification of Spectra

Another feasibility study was made into how slightly altered UV spectra (e.g., through the influence of solvents) might be recognized [67]. Prototypes of UV spectra were represented by a sequence of points (pixels) in two 10 x 10 fields; the first field containing the band maxima was placed at the input of an adaptive bidirectional associative memory (ABAM), and the second field, comprising the tailing portions, was placed at the output (Fig. 45a). Because of the bidirectional nature of the ABAM the terms input and output are of course purely arbitrary.

Fig. 45. Grid representation of an ultraviolet spectrum (a) and fuzzy coded forms of this spectrum (gray dotted fields) (b).

The ABAM was trained with five model UV spectra coded in this way. For testing fuzzy codings and slightly altered spectra were used (cf. Fig. 45b). The recall capability of the ABAM was heavily dependent on the choice of various network parameters; however, in the end a set of parameters was found that was able to recall all five spectra learned from the input of its distorted counterpart.

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Johann.Gasteiger@chemie.uni-erlangen.de