  This article presents a new polynomial parameterized sigmoid called SIGTRON,
which is an extended asymmetric sigmoid with Perceptron, and its companion
convex model called SIGTRON-imbalanced classification (SIC) model that employs
a virtual SIGTRON-induced convex loss function. In contrast to the conventional
$\pi$-weighted cost-sensitive learning model, the SIC model does not have an
external $\pi$-weight on the loss function but has internal parameters in the
virtual SIGTRON-induced loss function. As a consequence, when the given
training dataset is close to the well-balanced condition considering the
(scale-)class-imbalance ratio, we show that the proposed SIC model is more
adaptive to variations of the dataset, such as the inconsistency of the
(scale-)class-imbalance ratio between the training and test datasets. This
adaptation is justified by a skewed hyperplane equation, created via
linearization of the gradient satisfying $\epsilon$-optimal condition.
  Additionally, we present a quasi-Newton optimization(L-BFGS) framework for
the virtual convex loss by developing an interval-based bisection line search.
Empirically, we have observed that the proposed approach outperforms (or is
comparable to) $\pi$-weighted convex focal loss and balanced classifier
LIBLINEAR(logistic regression, SVM, and L2SVM) in terms of test classification
accuracy with $51$ two-class and $67$ multi-class datasets. In binary
classification problems, where the scale-class-imbalance ratio of the training
dataset is not significant but the inconsistency exists, a group of SIC models
with the best test accuracy for each dataset (TOP$1$) outperforms LIBSVM(C-SVC
with RBF kernel), a well-known kernel-based classifier.
