  Type Ia supernova cosmology depends on the ability to fit and standardize
observations of supernova magnitudes with an empirical model. We present here a
series of new models of Type Ia Supernova spectral time series that capture a
greater amount of supernova diversity than possible with the models that are
currently customary. These are entitled SuperNova Empirical MOdels
(\textsc{SNEMO}\footnote{https://snfactory.lbl.gov/snemo}). The models are
constructed using spectrophotometric time series from $172$ individual
supernovae from the Nearby Supernova Factory, comprising more than $2000$
spectra. Using the available observations, Gaussian Processes are used to
predict a full spectral time series for each supernova. A matrix is constructed
from the spectral time series of all the supernovae, and Expectation
Maximization Factor Analysis is used to calculate the principal components of
the data. K-fold cross-validation then determines the selection of model
parameters and accounts for color variation in the data. Based on this process,
the final models are trained on supernovae that have been dereddened using the
Fitzpatrick and Massa extinction relation. Three final models are presented
here: \textsc{SNEMO2}, a two-component model for comparison with current
Type~Ia models; \textsc{SNEMO7}, a seven component model chosen for
standardizing supernova magnitudes which results in a total dispersion of
$0.100$~mag for a validation set of supernovae, of which $0.087$~mag is
unexplained (a total dispersion of $0.113$~mag with unexplained dispersion of
$0.097$~mag is found for the total set of training and validation supernovae);
and \textsc{SNEMO15}, a comprehensive $15$ component model that maximizes the
amount of spectral time series behavior captured.
