  Cross-validation (CV) is a popular method for model-selection. Unfortunately,
it is not immediately obvious how to apply CV to unsupervised or exploratory
contexts. This thesis discusses some extensions of cross-validation to
unsupervised learning, specifically focusing on the problem of choosing how
many principal components to keep. We introduce the latent factor model, define
an objective criterion, and show how CV can be used to estimate the intrinsic
dimensionality of a data set. Through both simulation and theory, we
demonstrate that cross-validation is a valuable tool for unsupervised learning.
