  A quantitative data-driven comparison among supernovae (SNe) based on their
spectral time series combined with multi-band photometry is presented. We use
an unsupervised Random Forest algorithm as a metric on a set of 82
well-documented SNe representing all the main spectroscopic types, in order to
embed these in an abstract metric space reflecting shared correlations between
the objects. We visualize the resulting metric space in 3D, revealing strong
agreement with the current spectroscopic classification scheme. The embedding
splits Type Ib supernovae into two groups, with one subgroup exhibiting
broader, less prominent, higher-velocity lines than the other, possibly
suggesting a new SN Ib subclass is required. The method could be to classify
newly discovered SNe according to their distance from known event groups, or
ultimately to devise a new, spectral-temporal classification scheme. Such an
embedding could also depend on hidden parameters which may perhaps be
physically interpretable.
