Statistics and Computing

, Volume 25, Issue 2, pp 471–486

Regularised PCA to denoise and visualise data

Article

DOI: 10.1007/s11222-013-9444-y

Cite this article as:
Verbanck, M., Josse, J. & Husson, F. Stat Comput (2015) 25: 471. doi:10.1007/s11222-013-9444-y

Abstract

Principal component analysis (PCA) is a well-established dimensionality reduction method commonly used to denoise and visualise data. A classical PCA model is the fixed effect model in which data are generated as a fixed structure of low rank corrupted by noise. Under this model, PCA does not provide the best recovery of the underlying signal in terms of mean squared error. Following the same principle as in ridge regression, we suggest a regularised version of PCA that essentially selects a certain number of dimensions and shrinks the corresponding singular values. Each singular value is multiplied by a term which can be seen as the ratio of the signal variance over the total variance of the associated dimension. The regularised term is analytically derived using asymptotic results and can also be justified from a Bayesian treatment of the model. Regularised PCA provides promising results in terms of the recovery of the true signal and the graphical outputs in comparison with classical PCA and with a soft thresholding estimation strategy. The distinction between PCA and regularised PCA becomes especially important in the case of very noisy data.

Keywords

Principal component analysis Shrinkage Regularised PCA Fixed effect model Denoising Visualisation 

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Applied Mathematics DepartmentAgrocampus OuestRennesFrance

Personalised recommendations