Autonomous Learning Parameters of the Local Submodels
In the previous chapter the methods for structure design (if we use prior knowledge or regular data partitioning) and learning (if using clustering or data clouds) were described. It was mentioned that when using data clouds there are no parameters of the structure as such. In clustering, which are additional parameters (the position of the cluster centers which in some methods are means of the data samples, while in some other methods, such as AutoCluster, these are selected data samples as in the data clouds). These additional parameters concern the cluster radii.
Parameters that define the structure of the system are equal to the number of focal points that need to be selected (and possibly also cluster radii, if we use clustering instead of data clouds). It was described how to find them in the previous chapter. In this chapter the focus will be on the parameters of the local submodels (consequents). In general, local submodels can take various forms, for example singletons – zero order, linear – first order, Gaussian, triangular, trapezoid, polynomial, and so on.
Without loss of generality, we can assume linear submodels, because they include the simpler type of zero-order singletons as a special case and they are the most widely used type. For a set of locally valid linear submodels (see Figure 4.2) the task is to find the optimal values of parameters A in terms of minimising the error of prediction/classification/control/estimation/filtering. ...