  Solving different types of optimization models (including parameters fitting)
for support vector machines on large-scale training data is often an expensive
computational task. This paper proposes a multilevel algorithmic framework that
scales efficiently to very large data sets. Instead of solving the whole
training set in one optimization process, the support vectors are obtained and
gradually refined at multiple levels of coarseness of the data. The proposed
framework includes: (a) construction of hierarchy of large-scale data coarse
representations, and (b) a local processing of updating the hyperplane
throughout this hierarchy. Our multilevel framework substantially improves the
computational time without loosing the quality of classifiers. The algorithms
are demonstrated for both regular and weighted support vector machines.
Experimental results are presented for balanced and imbalanced classification
problems. Quality improvement on several imbalanced data sets has been
observed.
