Outlier detection in non-elliptical data by kernel MRCD

Abstract

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.

Partial least median of squares regression

“…RSIMPLS assumes its data conform to multivariate Gaussian distribution. Otherwise, the performance of RSIMPLS can be less satisfactory 13 . Besides, RSIMPLS may produce nondeterministic results because of employing a random process.…”

“…Otherwise, the performance of RSIMPLS can be less satisfactory. 13 Besides, RSIMPLS may produce nondeterministic results because of employing a random process. To be sure, RSIMPLS can be made deterministic by using a deterministic MCD algorithm.…”

Commercialization of state-owned broadcast networks in China: a case study on the operation of Beijing Renmin Radio Station

“…The idea of incorporating depth (outlyingness) to construct MCD estimators has been considered in the literature. For example, the Stahel-Donoho outlyingness (Donoho, 1982), equivalent to the projection depth, is applied to determine an h-subset consisting of the h points with the lowest outlyingness, and the corresponding sample mean and covariance matrix are used as one initial value for the C-step (Hubert et al, 2005a;Schreurs et al, 2021). Debruyne and Hubert (2009) studied the influence function and asymptotic relative efficiency of the estimators obtained directly based on such a subset (without the reweighted step).…”

“…We can see that the denoised images for the proposed methods are more clear than those for the Sample, which verifies the influence of adding noise on evaluating scatter and the efficiency of the proposed methods. As in Schreurs et al (2021), we also calculate the mean absolute error MAE =…”

“…Furthermore, Boudt et al (2020) generalizes the MCD to high-dimensional cases as the minimum regularized covariance determinant (MRCD). Other variants include the orthogonalized Gnanadesikan-Kettenring (Maronna and Zamar, 2002), the minimum (regularized) weighted covariance determinant (Roelant et al, 2009;Kalina and Tichavskỳ, 2021), and kernel MRCD for non-elliptical data (Schreurs et al, 2021).…”