论文标题
评估不可分性性关系对模糊的邻居算法的影响
Evaluation of the impact of the indiscernibility relation on the fuzzy-rough nearest neighbours algorithm
论文作者
论文摘要
模糊的粗糙集非常适合与模糊，不精确或不确定的信息一起工作，并且已成功地应用于现实世界的分类问题中。该理论的重要代表之一是模糊的rough最近的邻居（FRNN），这是一种基于经典的K-Nearebors算法的分类算法。 FRNN的症结是不可分性的关系，它衡量了感兴趣的数据集中的两个要素。在本文中，我们研究了这种不可分割性关系对FRNN分类表现的影响。除了基于距离功能和内核的关系外，我们还首次探讨了距离度量学习对FRNN的影响。此外，我们还基于使用每个类别内的相关性的Mahalanobis距离引入了不对称的，特定的关系，并且对常规的Mahalanobis距离显示出显着改善，但仍被曼哈顿距离击败。总体而言，邻里组件分析算法被认为是表现最好的，准确性的交易速度。
Fuzzy rough sets are well-suited for working with vague, imprecise or uncertain information and have been succesfully applied in real-world classification problems. One of the prominent representatives of this theory is fuzzy-rough nearest neighbours (FRNN), a classification algorithm based on the classical k-nearest neighbours algorithm. The crux of FRNN is the indiscernibility relation, which measures how similar two elements in the data set of interest are. In this paper, we investigate the impact of this indiscernibility relation on the performance of FRNN classification. In addition to relations based on distance functions and kernels, we also explore the effect of distance metric learning on FRNN for the first time. Furthermore, we also introduce an asymmetric, class-specific relation based on the Mahalanobis distance which uses the correlation within each class, and which shows a significant improvement over the regular Mahalanobis distance, but is still beaten by the Manhattan distance. Overall, the Neighbourhood Components Analysis algorithm is found to be the best performer, trading speed for accuracy.
