Improved empirical models for Type Ia SNe

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: SNEMO2, a two-component model for comparison with current Type Ia models; SNEMO7, a seven-component model chosen for standardizing supernova magnitudes, which results in a total dispersion of 0.100mag for a validation set of supernovae, of which 0.087mag is unexplained (a total dispersion of 0.113mag with an unexplained dispersion of 0.097mag is found for the total set of training and validation supernovae); and SNEMO15, a comprehensive 15-component model that maximizes the amount of spectral time-series behavior captured.