  Principal component analysis (PCA) is a well-established method commonly used
to explore and visualise data. A classical PCA model is the fixed effect model
where 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 propose a regularised version of PCA that boils down to
threshold the 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 gap between PCA and
regularised PCA is all the more important that data are noisy.
