Abstract:
Dimensionality reduction (DR) is an efficient approach to reduce the size of
data by capturing the informative intrinsic features and discarding the noise. DR
methods can be grouped through a variety of categories, e.g. supervised/ unsupervised,
linear/non-linear or parametric/non-parametric. Objective function based
methods can be grouped into convex and non convex. Non convex methods have
the tendency to converge to local optimal solutions which may differ from the desired
global solution. To overcome this problem, one can frame a non convex problem
as a convex problem. A direct transformation of a non convex formulation into a
convex formulation is non trivial.
In this project, we chose a non convex, linear, supervised, multi-class, non
parametric DR method’s objective, which can be framed using convex formulation.
We present the process of convex formulation, different methods of implementation,
approaches to increase efficiency and numerical analysis results.
