3 research outputs found
Cauchy robust principal component analysis with applications to high-deimensional data sets
Principal component analysis (PCA) is a standard dimensionality reduction
technique used in various research and applied fields. From an algorithmic
point of view, classical PCA can be formulated in terms of operations on a
multivariate Gaussian likelihood. As a consequence of the implied Gaussian
formulation, the principal components are not robust to outliers. In this
paper, we propose a modified formulation, based on the use of a multivariate
Cauchy likelihood instead of the Gaussian likelihood, which has the effect of
robustifying the principal components. We present an algorithm to compute these
robustified principal components. We additionally derive the relevant influence
function of the first component and examine its theoretical properties.
Simulation experiments on high-dimensional datasets demonstrate that the
estimated principal components based on the Cauchy likelihood outperform or are
on par with existing robust PCA techniques