Pattern Recognition, 4th Edition

4.19.1. Expansion in Kernel Functions and Model Sparsification

In this subsection, we will briefly discuss classifiers that resemble to (or, even are inspired by) the SVMs, in an effort to establish bridges among different methodologies. We have already done so in Section 4.18 for the SVM, RBF, and multilayer neural networks. After all, it is a small world! Using the Gaussian kernel in Eq. (4.72), we obtain(4.77)where we have used αⁱ = λⁱyⁱ. Equation (4.77) is very similar to the Parzen expansion of a pdf, discussed in Chapter 2. There are a few differences, however. In contrast to the Parzen expansion, g(x) in (4.77) is not a pdf function; that ...