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Ultimate Order Statistics-Based Prototype Reduction Schemes

机译：基于最终订单统计的原型缩减方案

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The objective of Prototype Reduction Schemes (PRSs) and Border Identification (BI) algorithms is to reduce the number of training vectors, while simultaneously attempting to guarantee that the classifier built on the reduced design set performs as well, or nearly as well, as the classifier built on the original design set. In this paper, we shall push the limit on the field of PRSs to see if we can obtain a classification accuracy comparable to the optimal, by condensing the information in the data set into a single training point. We, indeed, demonstrate that such PRSs exist and are attainable, and show that the design and implementation of such schemes work with the recently-introduced paradigm of Order Statistics (OS)-based classifiers. These classifiers, referred to as Classification by Moments of Order Statistics (CMOS) is essentially anti-Bayesian in its modus operandus. In this paper, we demonstrate the power and potential of CMOS to yield single-element PRSs which are either "selective" or "creative", where in each case we resort to a non-parametric or a parametric paradigm respectively. We also report a single-feature single-element creative PRS. All of these solutions have been used to achieve classification for real-life data sets from the UCI Machine Learning Repository, where we have followed an approach that is similar to the Naieve-Bayes' (NB) strategy although it is essentially of an anti-Naieve-Bayes' paradigm. The amazing facet of this approach is that the training set can be reduced to a single pattern from each of the classes which is, in turn, determined by the CMOS features. It is even more fascinating to see that the scheme can be rendered operational by using the information in a single feature of such a single data point. In each of these cases, the accuracy of the proposed PRS-based approach is very close to the optimal Bayes' bound and is almost comparable to that of the SVM.
机译：原型缩减方案（PRS）和边界识别（BI）算法的目标是减少训练向量的数量，同时尝试保证基于简化设计集构建的分类器的性能与分类器相同或几乎相同。基于原始设计集的分类器。在本文中，我们将限制PRS的范围，以查看是否可以通过将数据集中的信息浓缩到单个训练点中来获得与最佳可比的分类精度。我们确实证明了这样的PRS存在并且是可以实现的，并且表明这种方案的设计和实现与最近引入的基于订单统计（OS）的分类器范式一起工作。这些分类器称为按阶矩统计量分类（CMOS），其本质上是反贝叶斯方法。在本文中，我们演示了CMOS产生单元素PRS的能力和潜力，这些元素要么是“选择性的”，要么是“创意的”，在每种情况下，我们分别诉诸于非参数或参数范式。我们还报告了单功能单元素创意PRS。所有这些解决方案均已用于从UCI机器学习存储库中对现实生活中的数据集进行分类，在该分类中，我们遵循了与Naieve-Bayes（NB）策略相似的方法，尽管该方法本质上是一种反奈夫·贝叶斯的范式。这种方法令人惊奇的方面是，可以将训练集从每个类别简化为单个模式，而这又由CMOS功能决定。更加令人着迷的是，可以通过在这样的单个数据点的单个功能中使用信息来使该方案变得可操作。在每种情况下，所提出的基于PRS的方法的准确性都非常接近最佳贝叶斯界限，并且几乎可以与SVM的准确性相提并论。

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