论文标题
对于Fisher判别分析及其分类的变体，不平等的协方差意识
Unequal Covariance Awareness for Fisher Discriminant Analysis and Its Variants in Classification
论文作者
论文摘要
Fisher判别分析（FDA）是特征提取和分类的重要工具之一。此外，它激发了基于FDA的许多改进技术的发展，以适应不同的问题或数据类型。但是，这些方法都没有使用以下事实：在实际情况下，FDA中相等协方差矩阵的假设通常不满足。因此，我们为FDA提出了一个新的分类规则，该规则解释了这一事实，从而减轻了FDA中不平等协方差矩阵的影响。此外，由于我们仅修改分类规则，因此可以将同样的应用程序应用于许多FDA变体，从而进一步改进这些算法。理论分析表明，与从FDA到二次判别分析相比，新的分类规则允许隐式使用类协方差矩阵，同时增加了少量参数的数量。我们通过实验说明了我们的想法，该实验与原始分类规则相比，基于我们的新分类规则表明了修改后的算法的出色性能。
Fisher Discriminant Analysis (FDA) is one of the essential tools for feature extraction and classification. In addition, it motivates the development of many improved techniques based on the FDA to adapt to different problems or data types. However, none of these approaches make use of the fact that the assumption of equal covariance matrices in FDA is usually not satisfied in practical situations. Therefore, we propose a novel classification rule for the FDA that accounts for this fact, mitigating the effect of unequal covariance matrices in the FDA. Furthermore, since we only modify the classification rule, the same can be applied to many FDA variants, improving these algorithms further. Theoretical analysis reveals that the new classification rule allows the implicit use of the class covariance matrices while increasing the number of parameters to be estimated by a small amount compared to going from FDA to Quadratic Discriminant Analysis. We illustrate our idea via experiments, which show the superior performance of the modified algorithms based on our new classification rule compared to the original ones.
