Censoring outliers in elliptically symmetric multivariate distribution

Abstract

In this paper, we discuss the problem of censoring outliers in a dataset with a class of complex elliptically symmetric (CES) distribution, which has various engineering applications. To this end, the regularized cost function is formulated by the maximum likelihood (ML) setting. Since the ML estimation of the free outlier subset requires solving a combinatorial problem, an efficient and low complexity algorithm is proposed that guarantees the convergence to a stationary point. Two independent and dependent penalty terms to the selected subset are considered. The conventional generalized inner product (GIP) and the submodular minimization approaches are employed in the derivation of the proposed algorithm in the independent and dependent cases, respectively. The dependent case improves performance by slightly increasing complexity. As a special case for Gaussian assumption and using a non-regularized cost function, the proposed algorithm reduces to the fast minimum covariance determinant (FMCD) algorithm, which has impressive efficiency and received considerable attention in statistics and computer science. Hence, the proposed algorithm extends/generalizes the FMCD to be applicable to the non-Gaussian distributions. The simulation results highlight that the proposed algorithms exhibit satisfactory performance in CES environments.