Although linear and quadratic discriminant analysis are widely recognized classical methods, they can encounter significant challenges when dealing with non-Gaussian distributions or contaminated datasets. This is primarily due to their reliance on the Gaussian assumption, which lacks robustness. We first explain and review the classical methods to address this limitation and then present a novel approach that overcomes these issues. In this new approach, the model considered is an arbitrary Elliptically Symmetrical (ES) distribution per cluster with its own arbitrary scale parameter. This flexible model allows for potentially diverse and independent samples that may not follow identical distributions. By deriving a new decision rule, we demonstrate that maximum-likelihood parameter estimation and classification are simple, efficient, and robust compared to state-of-the-art methods.

翻译：尽管线性判别分析和二次判别分析是广泛认可的经典方法，但在处理非高斯分布或受污染数据集时可能面临显著挑战，这主要源于其对高斯假设的依赖而导致鲁棒性不足。我们首先阐述并回顾了经典方法应对该局限性的策略，继而提出一种解决上述问题的新方法。该方法假设每个聚类服从任意椭圆对称分布且具有各自的尺度参数，此灵活模型允许样本存在潜在多样性与独立性，无需服从同一分布。通过推导新决策规则，我们证明与现有先进方法相比，基于该模型的最大似然参数估计与分类任务兼具简洁性、高效性与鲁棒性。