## Dray S. (2008).
*On the number of principal components: A test of
dimensionality based on measurements of similarity between matrices*.
Computational Statistics and Data Analysis, 52:2228--2237.

An important problem in principal component analysis (PCA)
is the estimation of the correct number of components to
retain. PCA is most often used to reduce a set of observed
variables to a new set of variables of lower
dimensionality. The choice of this dimensionality is a
crucial step for the interpretation of results or
subsequent analyses, because it could lead to a loss of
information (underestimation) or the introduction of random
noise (overestimation). New techniques are proposed to
evaluate the dimensionality in PCA. They are based on
similarity measurements, singular value decomposition and
permutation procedures. A simulation study is conducted to
evaluate the relative merits of the proposed approaches.
Results showed that one method based on the RV coefficient
is very accurate and seems to be more efficient than other
existing approaches.

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