Characterization of Type Ia Supernova Light Curves Using Principal
  Component Analysis of Sparse Functional Data
  With growing data from ongoing and future supernova surveys it is possible to
empirically quantify the shapes of SNIa light curves in more detail, and to
quantitatively relate the shape parameters with the intrinsic properties of
SNIa. Building such relationship is critical in controlling systematic errors
associated with supernova cosmology. Based on a collection of well-observed
SNIa samples accumulated in the past years, we construct an empirical SNIa
light curve model using a statistical method called the functional principal
component analysis (FPCA) for sparse and irregularly sampled functional data.
Using this method, the entire light curve of an SNIa is represented by a linear
combination of principal component functions, and the SNIa is represented by a
few numbers called principal component scores. These scores are used to
establish relations between light curve shapes and physical quantities such as
intrinsic color, interstellar dust reddening, spectral line strength, and
spectral classes. These relations allow for descriptions of some critical
physical quantities based purely on light curve shape parameters. Our study
shows that some important spectral feature information is being encoded in the
broad band light curves, for instance, we find that the light curve shapes are
correlated with the velocity and velocity gradient of the Si II $\lambda$6355
line. This is important for supernova surveys, e.g., LSST and WFIRST. Moreover,
the FPCA light curve model is used to construct the entire light curve shape,
which in turn is used in a functional linear form to adjust intrinsic
luminosity when fitting distance models.
