  High-dimensional data classification is a fundamental task in machine
learning and imaging science. In this paper, we propose a two-stage multiphase
semi-supervised classification method for classifying high-dimensional data and
unstructured point clouds. To begin with, a fuzzy classification method such as
the standard support vector machine is used to generate a warm initialization.
We then apply a two-stage approach named SaT (smoothing and thresholding) to
improve the classification. In the first stage, an unconstraint convex
variational model is implemented to purify and smooth the initialization,
followed by the second stage which is to project the smoothed partition
obtained at stage one to a binary partition. These two stages can be repeated,
with the latest result as a new initialization, to keep improving the
classification quality. We show that the convex model of the smoothing stage
has a unique solution and can be solved by a specifically designed primal-dual
algorithm whose convergence is guaranteed. We test our method and compare it
with the state-of-the-art methods on several benchmark data sets. The
experimental results demonstrate clearly that our method is superior in both
the classification accuracy and computation speed for high-dimensional data and
point clouds.
