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6. Conclusion

A fast and extremely simple algorithm, LSVM, considerably easier to
code than SVM [11], SMO [24], SOR
[17] and ASVM [18], capable of classifying datasets
with millions of points has been proposed and implemented in a few
lines of MATLAB code. For a linear kernel, LSVM is an iterative method
which requires nothing more complex than the inversion of a single
matrix of the order of the input space plus one, and thus has the
ability to handle massive problems. For a positive semidefinite
nonlinear kernel, a single matrix inversion is required in the space of
dimension equal to the number of points classified. Hence, for such
nonlinear classifiers LSVM can handle only intermediate size
problems.
There is room for future work in reducing the number of support
vectors in the solutions yielded by LSVM. One method would be to
augment the quadratic term in in the objective function of
(7) by a 1-norm in . This should decrease the number of
support vectors as in work by [2]
where the 1-norm was used to effectively suppress features.
Additionally, the iterative algorithm itself could be modified so that
dual variables with values smaller than a tolerance would be
automatically set to zero.

Further future work includes extensions to parallel processing of
the data and handling very large datasets directly from disk as well
as extending nonlinear kernel classification to very large datasets.

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