Support vector machine classification problems are considered
in this talk. The 1-norm soft margin classifier will be analyzed
in detail. First, a counterexample is presented to show that
the misclassification error of the classifier with linear kernel
does not converge to the infimum of the errors generated
by linear functions. Then we provide positive convergence
results. It is confirmed that the support vector machine
classification algorithms with polynomial kernels are
always efficient when the degree of the kernel polynomial
is large enough. The rate of convergence is given. We
shall also discuss the p-norm soft margin classifiers and other
support vector machine algorithms.
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