We employ random geometric digraphs to construct semi-parametric classifiers. These data-random digraphs belong to parameterized random digraph families called proximity catch digraphs (PCDs). A related geometric digraph family, class cover catch digraph (CCCD), has been used to solve the class cover problem by using its approximate minimum dominating set and showed relatively good performance in the classification of imbalanced data sets. Although CCCDs have a convenient construction in $${\mathbb {R}}^d$$ R d , finding their minimum dominating sets is NP-hard and their probabilistic behaviour is not mathematically tractable except for $$d=1$$ d = 1 . On the other hand, a particular family of PCDs, called proportional-edge PCDs (PE-PCDs), has mathematically tractable minimum dominating sets in $${\mathbb {R}}^d$$ R d ; however their construction in higher dimensions may be computationally demanding. More specifically, we show that the classifiers based on PE-PCDs are prototype-based classifiers such that the exact minimum number of prototypes (equivalent to minimum dominating sets) is found in polynomial time on the number of observations. We construct two types of classifiers based on PE-PCDs. One is a family of hybrid classifiers that depends on the location of the points of the training data set, and another type is a family of classifiers solely based on class covers. We assess the classification performance of our PE-PCD based classifiers by extensive Monte Carlo simulations, and compare them with that of other commonly used classifiers. We also show that, similar to CCCD classifiers, our classifiers tend to be robust to the class imbalance in classification as well.

中文翻译：

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使用接近捕捉有向图进行分类

我们采用随机几何有向图来构建半参数分类器。这些数据随机有向图属于称为接近捕捉有向图 (PCD) 的参数化随机有向图族。相关的几何有向图族类覆盖捕获有向图（CCCD）已被用于通过使用其近似最小支配集来解决类覆盖问题，并在不平衡数据集的分类中表现出较好的性能。尽管 CCCD 在 $${\mathbb {R}}^d$$ R d 中有一个方便的构造，但找到它们的最小支配集是 NP 难的，并且除了 $$d=1$$ d 之外，它们的概率行为在数学上难以处理= 1。另一方面，一个特定的 PCD 家族，称为比例边 PCD（PE-PCD），在 $${\mathbb {R}}^d$$ R d 中具有数学上易于处理的最小支配集；然而，它们在更高维度上的构造可能在计算上要求很高。更具体地说，我们表明基于 PE-PCD 的分类器是基于原型的分类器，因此在多项式时间内可以找到精确的最小原型数量（相当于最小支配集）。我们基于 PE-PCD 构建了两种类型的分类器。一种是依赖于训练数据集点位置的混合分类器族，另一种是仅基于类覆盖的分类器族。我们通过广泛的蒙特卡罗模拟评估基于 PE-PCD 的分类器的分类性能，并将它们与其他常用分类器的分类性能进行比较。我们还表明，类似于 CCCD 分类器，