  Principal component analysis (PCA) is by far the most widespread tool for
unsupervised learning with high-dimensional data sets. Its application is
popularly studied for the purpose of exploratory data analysis and online
process monitoring. Unfortunately, fine-tuning PCA models and particularly the
number of components remains a challenging task. Today, this selection is often
based on a combination of guiding principles, experience, and process
understanding. Unlike the case of regression, where cross-validation of the
prediction error is a widespread and trusted approach for model selection,
there are no tools for PCA model selection which reach this level of
acceptance. In this work, we address this challenge and evaluate the utility of
the cross-validated ignorance score with both simulated and experimental data
sets. Application of this method is based on the interpretation of PCA as a
density model, as in probabilistic principal component analysis, and is shown
to be a valuable tool to identify an optimal number of principal components.
