Conventional classification assumes a balanced sample distribution among classes. However, such a premise leads to biased performance over the majority class (with the highest number of instances). The Twin Support Vector Machines (TWSVM) obtained great prominence due to their low computational burden compared to the standard SVM. Besides, traditional machine learning seeks methods whose solution depends on a convex problem or semi-positive definite similarity matrices. Yet, this kind of matrix cannot adequately represent many real-world applications. The above defines the need to use non-negative measures as an indefinite function in a Reproducing Kernel Kreĭn Space (RKKS). This paper proposes a novel approach called Kreĭn Twin Support Vector Machines (KTSVM), which appropriately incorporates indefinite kernels within a TWSVM-based gradient optimization. To code pertinent input patterns within an imbalanced data discrimination, our KTSVM employs an implicit mapping to a RKKS. Also, our approach takes advantage of the TWSVM scheme’s benefits by creating two parallel hyperplanes. This promotes the KTSVM optimization in a gradient-descent framework. Results obtained on synthetic and real-world datasets demonstrate that our solution performs better in terms of imbalanced data classification than state-of-the-art techniques.

中文翻译：

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用于不平衡数据分类的 Kreĭn 双支持向量机

传统分类假设类别之间的样本分布是平衡的。然而，这样的前提会导致大多数类（实例数量最多）的性能出现偏差。与标准 SVM 相比，双支持向量机 (TWSVM) 因其计算负担较低而获得了巨大的关注。此外，传统的机器学习寻求解决方案依赖于凸问题或半正定相似矩阵的方法。然而，这种矩阵并不能充分代表许多现实世界的应用。上面定义了在再生内核 Kreĭn 空间 (RKKS) 中使用非负度量作为不定函数的需要。本文提出了一种称为 Kreĭn 双支持向量机 (KTSVM) 的新颖方法，该方法在基于 TWSVM 的梯度优化中适当地结合了不定核。为了在不平衡的数据区分中编码相关的输入模式，我们的 KTSVM 采用了到 RKKS 的隐式映射。此外，我们的方法通过创建两个并行超平面来利用 TWSVM 方案的优点。这促进了梯度下降框架中的 KTSVM 优化。在合成数据集和真实数据集上获得的结果表明，我们的解决方案在不平衡数据分类方面比最先进的技术表现更好。