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In practice, this property is quite useful, especially when considering the utility of a multiple of Gaussian kernels, as used in the family of RBF-NNs. 3). 11) K(x) = unit via the link weight(s) 0 ; otherwise where θs is a certain constant. This view then allows us to subsume the concept of symbolic connectionist models such as Minsky’s knowledge-line (K-Line) (Minsky, 1985). e. represented by a single kernel unit) can have a generalisation capability which could, to a greater extent, mitigate the “curse-of-dimensionality”, in which, practically speaking, the exponentially growing number of data points soon exhausts the entire memory space.
Therefore, it is generally considered that, not to mention the accommodation of new classes, to achieve a flexible network configuration by an MLP-NN similar to that by a PNN/GRNN (that is, the quick network growing and shrinking) is very hard. , 2001). For the network reconfiguration of MLP-NNs, it is thus normally necessary for the iterative training to start from scratch. From another point of view, by MLP-NNs, the separation of the pattern space is represented in terms of the hyperplanes so formed, whilst that performed by PNNs and GRNNs is based upon the location and spread of the RBFs in the pattern space.
No ) . e. 16) and can be eventually reduce to a simple kernel memory representation as shown in Fig. 4. 3 Topological Variations in Terms of Kernel Memory In the previous section, it was described that both the neural network GRNN and PNN can be subsumed into the kernel memory concept, where only a layer of Gaussian kernels and a set of the kernels, each with a linear operator, are used, as shown in Fig. 4. However, within the kernel context, there essentially exist no such structural restrictions, and any topological form of the kernel memory representation is possible.