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, 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 achieved by creating a skewed hyperplane equation. 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 $\pi$-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.

翻译：本文提出一种新的多项式参数化Sigmoid函数，命名为SIGTRON，它是带有感知器的扩展非对称Sigmoid函数；同时提出其伴随凸模型——SIGTRON非平衡分类模型（SIC），该模型采用虚拟SIGTRON诱导的凸损失函数。与传统的$\pi$加权代价敏感学习模型不同，SIC模型不在损失函数上施加外部$\pi$权重，而是将内部参数嵌入虚拟SIGTRON诱导的损失函数中。因此，当给定训练数据集接近良好平衡条件时，我们证明所提出的SIC模型对数据集变化（例如训练集与测试集之间尺度-类别-不平衡比率的不一致性）具有更强的自适应性。这种自适应性通过生成倾斜超平面方程实现。此外，我们提出一种基于区间二分线搜索的拟牛顿优化（L-BFGS）框架，用于求解虚拟凸损失。实验表明，在$51$个二分类数据集和$67$个多分类数据集上，所提方法在测试分类精度上优于$\pi$加权凸焦点损失和平衡分类器LIBLINEAR（逻辑回归、SVM和L2SVM）。在二分类问题中，当训练数据集的尺度-类别-不平衡比率不显著但存在不一致性时，针对每个数据集取得最佳测试精度的SIC模型组（TOP$1$）优于著名的基于核的分类器LIBSVM（采用RBF核的C-SVC）。