  We present a method for performing Principal Component Analysis (PCA) on
noisy datasets with missing values. Estimates of the measurement error are used
to weight the input data such that compared to classic PCA, the resulting
eigenvectors are more sensitive to the true underlying signal variations rather
than being pulled by heteroskedastic measurement noise. Missing data is simply
the limiting case of weight=0. The underlying algorithm is a noise weighted
Expectation Maximization (EM) PCA, which has additional benefits of
implementation speed and flexibility for smoothing eigenvectors to reduce the
noise contribution. We present applications of this method on simulated data
and QSO spectra from the Sloan Digital Sky Survey.
