  The support vector machine (SVM) is a widely used method for classification.
Although many efforts have been devoted to develop efficient solvers, it
remains challenging to apply SVM to large-scale problems. A nice property of
SVM is that the non-support vectors have no effect on the resulting classifier.
Motivated by this observation, we present fast and efficient screening rules to
discard non-support vectors by analyzing the dual problem of SVM via
variational inequalities (DVI). As a result, the number of data instances to be
entered into the optimization can be substantially reduced. Some appealing
features of our screening method are: (1) DVI is safe in the sense that the
vectors discarded by DVI are guaranteed to be non-support vectors; (2) the data
set needs to be scanned only once to run the screening, whose computational
cost is negligible compared to that of solving the SVM problem; (3) DVI is
independent of the solvers and can be integrated with any existing efficient
solvers. We also show that the DVI technique can be extended to detect
non-support vectors in the least absolute deviations regression (LAD). To the
best of our knowledge, there are currently no screening methods for LAD. We
have evaluated DVI on both synthetic and real data sets. Experiments indicate
that DVI significantly outperforms the existing state-of-the-art screening
rules for SVM, and is very effective in discarding non-support vectors for LAD.
The speedup gained by DVI rules can be up to two orders of magnitude.
