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Regularized fisher linear discriminant through two threshold variation strategies for imbalanced problems

机译：通过两种阈值变化策略对不平衡问题进行正则化Fisher线性判别

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摘要

Fisher Linear Discriminant (FLD) has been widely applied to classification tasks due to its simple structure, analytical optimization, and useful criterion. However, when dealing with imbalanced datasets, even though the weight vector of FLD could be trained correctly to preserve the global distribution information of samples, the threshold of FLD might be seriously misled by the extreme proportion of classes. In order to modify the threshold and preserve the weight vector at the same time so as to improve FLD in imbalanced cases, this paper first regularizes the original FLD in a way inspired by the locality preserving projection, and then utilizes two strategies to optimize the threshold: the multi-thresholds selection strategy trains several FLDs with different empirically-defined thresholds, and then selects the optimal threshold out; the threshold-eliminated strategy generates two hyperplanes parallel to the original one built by FLD, and then utilizes a heuristic similarity metric for prediction. It is seen that the former seeks new threshold instead of the old one, while the latter ignores the original threshold. After introducing both strategies into the regularized FLD, two new classifiers are proposed in this paper and abbreviated as RFLD-S1 and RFLD-S2, respectively. Subsequently, the comprehensive comparison experiments on forty-one datasets among nine typical classifiers validate the effectiveness of the proposed methods. Especially, RFLD-S1 performs better than RFLD-S2 and achieves the best on most datasets. (C) 2018 Elsevier B.V. All rights reserved.
机译：Fisher线性判别（FLD）由于其结构简单，分析优化和有用的准则而被广泛应用于分类任务。但是，当处理不平衡的数据集时，即使可以正确地训练FLD的权重向量以保留样本的全局分布信息，FLD的阈值也可能会因类别的极端比例而严重误导。为了在不平衡的情况下修改阈值并同时保留权重向量以改善FLD，本文首先通过保留局部投影的方法对原始FLD进行正则化，然后利用两种策略来优化阈值：多阈值选择策略训练多个具有不同经验定义阈值的FLD，然后从中选择最佳阈值；消除阈值的策略会生成两个与FLD构建的原始超平面平行的超平面，然后利用启发式相似性度量进行预测。可以看出，前者寻求新的阈值而不是旧的阈值，而后者则忽略了原始的阈值。在将两种策略引入正则化FLD之后，本文提出了两个新的分类器，分别简称为RFLD-S1和RFLD-S2。随后，在9个典型分类器上对41个数据集进行的全面比较实验验证了所提方法的有效性。特别是，RFLD-S1的性能优于RFLD-S2，并且在大多数数据集上均达到最佳。 （C）2018 Elsevier B.V.保留所有权利。

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