  This work proposes the Bregman-Tweedie classification model and analyzes the
domain structure of the extended exponential function, an extension of the
classic generalized exponential function with additional scaling parameter, and
related high-level mathematical structures, such as the Bregman-Tweedie loss
function and the Bregman-Tweedie divergence. The base function of this
divergence is the convex function of Legendre type induced from the extended
exponential function. The Bregman-Tweedie loss function of the proposed
classification model is the regular Legendre transformation of the
Bregman-Tweedie divergence. This loss function is a polynomial parameterized
function between unhinge loss and the logistic loss function. Actually, we have
two sub-models of the Bregman-Tweedie classification model; H-Bregman with
hinge-like loss function and L-Bregman with logistic-like loss function.
Although the proposed classification model is nonconvex and unbounded,
empirically, we have observed that the H-Bregman and L-Bregman outperform, in
terms of the Friedman ranking, logistic regression and SVM and show reasonable
performance in terms of the classification accuracy in the category of the
binary linear classification problem.
