|Stochastic Systems Group|
Classification and Linear Dimensionality Reduction via Level Set Segmentation
Kush R. Varshney
A variational approach based on level set methods popular in image segmentation is presented for learning discriminative classifiers in general feature spaces. Nonlinear, nonparametric decision boundaries are obtained by minimizing an energy functional that incorporates a margin-based loss function. The class of level set contour decision boundaries is discussed in terms of the structural risk minimization principle. A variation on l1 feature subset selection is developed.
The level set approach is extended to also perform linear dimensionality reduction. Dimensionality reduction is represented by a matrix on the Stiefel manifold. Optimization is performed by coordinate descent, including gradient descent along Stiefel manifold geodesics.
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