Regularisation for PCA- and SVD-type matrix factorisations (2106.12955v1)

Abstract: Singular Value Decomposition (SVD) and its close relative, Principal Component Analysis (PCA), are well-known linear matrix decomposition techniques that are widely used in applications such as dimension reduction and clustering. However, an important limitation of SVD/PCA is its sensitivity to noise in the input data. In this paper, we take another look at the problem of regularisation and show that different formulations of the minimisation problem lead to qualitatively different solutions.