Simple Proof of Convergence of the SMO Algorithm for Different SVM Variants


In this transient, we offer a new proof of the asymptotic convergence of the sequential minimum optimization (SMO) algorithm for both the foremost violating combine and second order rules to pick out the combine of coefficients to be updated. The proof is additional self-contained, shorter, and easier than previous ones and features a different flavor, partially building upon Gilbert's original convergence proof of its algorithm to unravel the minimum norm problem for convex hulls. It is valid for each support vector classification (SVC) and support vector regression, which are formulated beneath a general drawback that encompasses them. Moreover, this general downside will be additional extended to conjointly cowl other support vector machines (SVM)-related issues like $nu$-SVC or one-class SVMs, while the convergence proof of the slight variant of SMO needed for them remains essentially unchanged.

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