基于核MRCD的非椭圆数据离群点检测
Outlier detection in non-elliptical data by kernel MRCD
AI总结：
本文提出核最小正则化协方差行列式（KMRCD）估计器，通过在核特征空间中计算MRCD并利用核技巧加速，实现对非椭圆高维数据的快速稳健离群点检测。
摘要：
最小正则化协方差行列式方法（MRCD）是一种用于多元位置和散度的稳健估计器，它通过拟合稳健协方差矩阵来检测离群点。其正则化保证了协方差矩阵在任意维度下都是良态的。MRCD假设非离群观测值大致服从椭圆分布，但许多数据集并不具有这种形式。此外，当变量数量增加时，MRCD的计算时间会大幅增加，而如今具有许多变量的数据集十分常见。所提出的核最小正则化协方差行列式（KMRCD）估计器解决了这两个问题。它不限于椭圆数据，因为它隐式地在核诱导的特征空间中计算MRCD估计。本文构造了一种快速算法，该算法从基于核的初始估计出发，并利用核技巧加速后续计算。基于KMRCD估计，提出了一种标记离群点的规则。KMRCD算法在模拟中表现良好，并在真实数据上进行了说明。
英文摘要：
The minimum regularized covariance determinant method (MRCD) is a robust estimator for multivariate location and scatter, which detects outliers by fitting a robust covariance matrix to the data. Its regularization ensures that the covariance matrix is well-conditioned in any dimension. The MRCD assumes that the non-outlying observations are roughly elliptically distributed, but many datasets are not of that form. Moreover, the computation time of MRCD increases substantially when the number of variables goes up, and nowadays datasets with many variables are common. The proposed Kernel Minimum Regularized Covariance Determinant (KMRCD) estimator addresses both issues. It is not restricted to elliptical data because it implicitly computes the MRCD estimates in a kernel induced feature space. A fast algorithm is constructed that starts from kernel-based initial estimates and exploits the kernel trick to speed up the subsequent computations. Based on the KMRCD estimates, a rule is proposed to flag outliers. The KMRCD algorithm performs well in simulations, and is illustrated on real-life data.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
