基于几何有向图族的不平衡数据分类
Classification of Imbalanced Data with a Geometric Digraph Family
摘要：
我们使用一个称为类覆盖捕获有向图（CCCD）的几何有向图族来解决统计分类中的类不平衡问题。CCCD为类覆盖问题提供了图论解决方案，并已用于分类。我们评估CCCD分类器的分类性能，通过广泛的蒙特卡罗模拟，比较它们与文献中常用的其他分类器。特别是，我们表明，CCCD分类器执行相对较好时，一类是更频繁的比其他两类设置，类不平衡问题的一个例子。我们还指出了类不平衡和类重叠问题之间的关系，以及它们对CCCD分类器和其他分类方法以及一些通过构造对类不平衡具有鲁棒性的最新算法的性能的影响。在模拟数据集和真实数据集上的实验表明，CCCD分类器对类不平衡问题具有较好的鲁棒性。CCCD从多数类中大幅欠采样，同时保留欠采样过程中丢弃点的信息。然而，许多最先进的方法通过集成分类器来保持这些信息，但是CCCD只产生具有相同属性的单个分类器，这使得它既吸引人又快速。
英文摘要：
We use a geometric digraph family called class cover catch digraphs (CCCDs) to tackle the class imbalance problem in statistical classification. CCCDs provide graph theoretic solutions to the class cover problem and have been employed in classification. We assess the classification performance of CCCD classifiers by extensive Monte Carlo simulations, comparing them with other classifiers commonly used in the literature. In particular, we show that CCCD classifiers perform relatively well when one class is more frequent than the other in a two-class setting, an example of the class imbalance problem. We also point out the relationship between class imbalance and class overlapping problems, and their influence on the performance of CCCD classifiers and other classification methods as well as some state-of-the-art algorithms which are robust to class imbalance by construction. Experiments on both simulated and real data sets indicate that CCCD classifiers are robust to the class imbalance problem. CCCDs substantially undersample from the majority class while preserving the information on the discarded points during the undersampling process. Many state-of-the-art methods, however, keep this information by means of ensemble classifiers, but CCCDs yield only a single classifier with the same property, making it both appealing and fast.
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