Cost-sensitive Feature Selection for Support Vector Machines
Sandra Benítez-Peña Rafael Blanquero Emilio Carrizosa Pepa Ramírez-Cobo
Feature Selection is a crucial procedure in Data Science tasks such as
Classification, since it identifies the relevant variables, making thus the
classification procedures more interpretable, cheaper in terms of measurement
and more effective by reducing noise and data overfit. The relevance of
features in a classification procedure is linked to the fact that
misclassifications costs are frequently asymmetric, since false positive and
false negative cases may have very different consequences. However,
off-the-shelf Feature Selection procedures seldom take into account such
cost-sensitivity of errors.
  In this paper we propose a mathematical-optimization-based Feature Selection
procedure embedded in one of the most popular classification procedures,
namely, Support Vector Machines, accommodating asymmetric misclassification
costs. The key idea is to replace the traditional margin maximization by
minimizing the number of features selected, but imposing upper bounds on the
false positive and negative rates. The problem is written as an integer linear
problem plus a quadratic convex problem for Support Vector Machines with both
linear and radial kernels.
  The reported numerical experience demonstrates the usefulness of the proposed
Feature Selection procedure. Indeed, our results on benchmark data sets show
that a substantial decrease of the number of features is obtained, whilst the
desired trade-off between false positive and false negative rates is achieved.