High-dimensional outlier detection using random projections

TL;DR

This paper introduces a new high-dimensional outlier detection method using random projections and univariate detection techniques, avoiding covariance matrix estimation in high dimensions.

Contribution

It proposes a novel random projections-based procedure for outlier detection in high-dimensional Gaussian data, eliminating the need for covariance matrix estimation.

Findings

Effective in high-dimensional settings

Performs well on simulated datasets

Validated on real datasets

Abstract

There exist multiple methods to detect outliers in multivariate data in the literature, but most of them require to estimate the covariance matrix. The higher the dimension, the more complex the estimation of the matrix becoming impossible in high dimensions. In order to avoid estimating this matrix, we propose a novel random projections-based procedure to detect outliers in Gaussian multivariate data. It consists in projecting the data in several one-dimensional subspaces where an appropriate univariate outlier detection method, similar to Tukey's method but with a threshold depending on the initial dimension and the sample size, is applied. The required number of projections is determined using sequential analysis. Simulated and real datasets illustrate the performance of the proposed method.