Title: Indefinite Kernel Logistic Regression,
Abstract: Traditionally, kernel learning methods requires positive definitiveness on
the kernel, which is too strict and excludes many sophisticated similarities,
that are indefinite, in multimedia area. To utilize those indefinite kernels,
indefinite learning methods are of great interests. This paper aims at the
extension of the logistic regression from positive semi-definite kernels to
indefinite kernels. The model, called indefinite kernel logistic regression
(IKLR), keeps consistency to the regular KLR in formulation but it essentially
becomes non-convex. Thanks to the positive decomposition of an indefinite
matrix, IKLR can be transformed into a difference of two convex models, which
follows the use of concave-convex procedure. Moreover, we employ an inexact
solving scheme to speed up the sub-problem and develop a concave-inexact-convex
procedure (CCICP) algorithm with theoretical convergence analysis. Systematical
experiments on multi-modal datasets demonstrate the superiority of the proposed
IKLR method over kernel logistic regression with positive definite kernels and
other state-of-the-art indefinite learning based algorithms.