  We present a graph-based variational algorithm for multiclass classification
of high-dimensional data, motivated by total variation techniques. The energy
functional is based on a diffuse interface model with a periodic potential. We
augment the model by introducing an alternative measure of smoothness that
preserves symmetry among the class labels. Through this modification of the
standard Laplacian, we construct an efficient multiclass method that allows for
sharp transitions between classes. The experimental results demonstrate that
our approach is competitive with the state of the art among other graph-based
algorithms.
