论文标题
在异质数据中使用灵活的判别分析进行稳健分类
Robust classification with flexible discriminant analysis in heterogeneous data
论文作者
论文摘要
线性和二次判别分析是众所周知的经典方法，但可能会严重遭受非高斯分布和/或污染数据集的影响，这主要是因为基本的高斯假设并不强大。为了填补这一空白，本文提出了一个新的鲁棒判别分析，其中每个数据点都由其自身的椭圆形对称（ES）分布及其自身的任意量表参数绘制。这样的模型允许可能非常异构，独立但非相同分布的样品。在得出新的决策规则之后，与最先进的方法相比，最大可能的参数估计和分类非常简单，快速和健壮。
Linear and Quadratic Discriminant Analysis are well-known classical methods but can heavily suffer from non-Gaussian distributions and/or contaminated datasets, mainly because of the underlying Gaussian assumption that is not robust. To fill this gap, this paper presents a new robust discriminant analysis where each data point is drawn by its own arbitrary Elliptically Symmetrical (ES) distribution and its own arbitrary scale parameter. Such a model allows for possibly very heterogeneous, independent but non-identically distributed samples. After deriving a new decision rule, it is shown that maximum-likelihood parameter estimation and classification are very simple, fast and robust compared to state-of-the-art methods.
