Regularisation for PCA- and SVD-type matrix factorisations
This work tackles noise robustness in matrix factorisations for applications like dimension reduction and clustering, but it appears incremental as it revisits existing regularisation approaches without claiming major breakthroughs.
The paper addresses the sensitivity of SVD and PCA to noise in input data by exploring how different regularisation formulations affect the solutions, but it does not report specific numerical results or improvements.
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.