On coMADs and Principal Component Analysis

Principal Component Analysis (PCA) is a popular method for linear dimensionality reduction. It is often used to discover hidden correlations or to facilitate the interpretation and visualization of data. However, it is liable to suffer from outliers. Strong outliers can skew the principal components and as a consequence lead to a higher reconstruction loss. While there exist several sophisticated approaches to make the PCA more robust, we present an approach which is intriguingly simple: we replace the covariance matrix by a so-called coMAD matrix. The first experiments show that PCA based on the coMAD matrix is more robust towards outliers.