  In many modern data sets, High dimension low sample size (HDLSS) data is
prevalent in many fields of studies. There has been an increased focus recently
on using machine learning and statistical methods to mine valuable information
out of these data sets. Thus, there has been an increased interest in efficient
learning in high dimensions. Naturally, as the dimension of the input data
increases, the learning task will become more difficult, due to increasing
computational and statistical complexities. This makes it crucial to overcome
the curse of dimensionality in a given dataset, within a reasonable time frame,
in a bid to obtain the insights required to keep a competitive edge. To solve
HDLSS problems, classical methods such as support vector machines can be
utilised to alleviate data piling at the margin. However, when we question
geometric domains and their assumptions on input data, we are naturally lead to
convex optimisation problems and this gives rise to the development of
solutions like distance weighted discrimination (DWD), which can be modelled as
a second-order cone programming problem and solved by interior-point methods
when sample size and feature dimensions of the data is moderate. In this paper,
our focus is on designing an even more scalable and robust algorithm for
solving large-scale generalized DWD problems.
