An extended asymmetric sigmoid with Perceptron (SIGTRON) for imbalanced linear classification

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 π-weighted costsensitive learning model, the SIC model does not have an external π-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 π-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 (TOP1) outperforms LIBSVM(C-SVC with RBF kernel), a well-known kernel-based classifier. The main hindrance of the process is that the dataset is imbalanced [1], [2], [3] and inconsistent [4]. It is worth noting that we can improve the scale imbalance through various normalization methods [6], [7]. In our experiments, we use the well-organized datasets in [8].