Computational Intelligence Based on Lattice Theory by Vassilis G. Kaburlasos, Gerhard X. Ritter

By Vassilis G. Kaburlasos, Gerhard X. Ritter

This eighteen-chapter ebook offers the newest functions of lattice thought in Computational Intelligence (CI). The publication makes a speciality of neural computation, mathematical morphology, laptop studying, and (fuzzy) inference/logic. The booklet comes out of a different consultation held in the course of the international Council for Curriculum and guide global convention (WCCI 2006). The articles offered right here reveal how lattice idea could recommend potential choices in sensible clustering, type, trend research, and regression purposes.

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5 and explains the presence of the inhibitory dendrite whose region is depicted with dashed line. 4 Multiple Class Learning in SLLPs For better clarity of the description, the training algorithms described so far were limited to a single non-zero class, which corresponds to a single output neuron of the SLLP with dendritic structures. Below we present a straightforward generalization to multiple classes, which will invoke either one of the two procedures (elimination or merging) discussed in Sect.

The hyperboxes generated by the Orthonormal basis LNN have bigger volume (area in the 2D domain) than those generated by the standard basis LNN. In the case of OB-LNN each hyperbox is rotated appropriately because of the fact that it is working on a different orthonormal basis than the other dendrites. As it was discussed earlier in Sect. 3, each hyperbox contains information about the local orientation of the classes. This property is illustrated in Fig. 6. In this figure the decision boundaries between the two spirals generated by a SB-LNN (left) and an OB-LNN (right) are presented.

These hyperboxes were formed by the training process using 130 training samples. By observing this figure we can see the differences between the decision boundaries formed by the OB-LNN and those formed by the SB-LNN. The hyperboxes generated by the Orthonormal basis LNN have bigger volume (area in the 2D domain) than those generated by the standard basis LNN. In the case of OB-LNN each hyperbox is rotated appropriately because of the fact that it is working on a different orthonormal basis than the other dendrites.

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