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：本文提出了一种名为SIGTRON的新型多项式参数化S型函数，它是带有感知机的扩展非对称S型函数，并介绍了其配套凸模型——SIGTRON不平衡分类（SIC）模型。该模型采用虚拟的SIGTRON诱导凸损失函数。与传统的π加权代价敏感学习模型不同，SIC模型在损失函数上没有外部π权重，而是在虚拟SIGTRON诱导损失函数中引入内部参数。因此，当给定的训练数据集接近良好平衡条件时，我们证明所提出的SIC模型对数据集的变化（如训练集与测试集之间尺度类别不平衡比率的不一致性）具有更强的适应性。这种适应性通过构建偏斜超平面方程实现。此外，我们提出了一种基于区间二分线搜索的拟牛顿优化（L-BFGS）框架，用于虚拟凸损失的计算。实验结果表明，在测试分类准确率方面，所提方法在51个二分类数据集和67个多分类数据集上优于π加权凸焦点损失和平衡分类器LIBLINEAR（逻辑回归、SVM和L2SVM）。在训练数据集尺度类别不平衡比率不显著但存在不一致性的二分类问题中，每个数据集上测试准确率最高的SIC模型组（TOP1）优于著名的基于核的分类器LIBSVM（采用RBF核的C-SVC）。