1 research outputs found
Total Variation and Euler's Elastica for Supervised Learning
In recent years, total variation (TV) and Euler's elastica (EE) have been
successfully applied to image processing tasks such as denoising and
inpainting. This paper investigates how to extend TV and EE to the supervised
learning settings on high dimensional data. The supervised learning problem can
be formulated as an energy functional minimization under Tikhonov
regularization scheme, where the energy is composed of a squared loss and a
total variation smoothing (or Euler's elastica smoothing). Its solution via
variational principles leads to an Euler-Lagrange PDE. However, the PDE is
always high-dimensional and cannot be directly solved by common methods.
Instead, radial basis functions are utilized to approximate the target
function, reducing the problem to finding the linear coefficients of basis
functions. We apply the proposed methods to supervised learning tasks
(including binary classification, multi-class classification, and regression)
on benchmark data sets. Extensive experiments have demonstrated promising
results of the proposed methods.Comment: ICML201