Counterpropagation CPG Neural Networks — The Predictors

An enhanced concept of Kohonen networks is the CPG nenral network, hrst introduced by Hecht-Nielsen [64], The CPG network can be established by nsing basically a Kohonen layer and an additional ontpnt layer. The inpnt layer contains the input objects (e.g., molecular descriptors). The output layer contains the variables to be predicted, such as a one- or mnltidimensional property of the corresponding molecules. Additionally, a topological map layer [65,66] may be added that contains classes for the individnal test cases (Fignre 4.15). 

The iterative training procedure adapts the network in a way that similar input objects are also situated close together on the topological map. The network s topological layer can be seen as a two-dimensional grid, which is folded and distorted into the -dimensional input space to preserve the original structure as well as possible. Clearly, any attempt to represent an n-dimensional space in two dimensions will result in loss of detail however, the technique is useful to visualize data that might otherwise be hard to understand. 

Once the network is trained, the topological map represents a classification sheet. Some or all of the units in the topological map may be labeled with class names. If the distance is small enough, then the case is assigned to the class. A new vector presented to the Kohonen network ends up in its central neuron in the topological map layer. The central neuron points to the corresponding neuron in the output layer. A CPG neural network is able to evaluate the relationships between input and output information and to make predictions for missing output information. 

FIGURE 4.16 Different tasks solved by ANNs for the data analysis of a mnltidimensional object. Classification performs the assignment of inpnt objects X to predefined classes y. Modeling creates a functional relationship between the input objects and other multidimensional data. Mapping allows for reducing the input objects to a usually two-dimensional plane. Association allows assigning input objects to other multidimensional data on the basis of their relationships. 

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