The functions fit and minfit are S4
  genetics that extract the best model object and the best
  fit object respectively, from a collection of models or
  from a wrapper object.
fit<- sets the fitted model in a fit object. It is
  meant to be called only when developing new NMF
  algorithms, e.g. to update the value of the model stored
  in the starting point.
fit(object, ...) fit(object) <- value minfit(object, ...)
nmf.A fit object differs from a model object in that it contains data about the fit, such as the initial RNG settings, the CPU time used, etc..., while a model object only contains the actual modelling data such as regression coefficients, loadings, etc...
That best model is generally defined as the one that achieves the maximum/minimum some quantitative measure, amongst all models in a collection.
In the case of NMF models, the best model is the one that achieves the best approximation error, according to the objective function associated with the algorithm that performed the fit(s).
signature(object = "NMFfit"): Returns
  the NMF model object stored in slot 'fit'.
  
      signature(object = "NMFfitX"): Returns
  the model object that achieves the lowest residual
  approximation error across all the runs.
  
      It is a pure virtual method defined to ensure fit
  is defined for sub-classes of NMFfitX, which
  throws an error if called.
signature(object = "NMFfitX1"): Returns
  the model object associated with the best fit, amongst
  all the runs performed when fitting object.
  
      Since NMFfitX1 objects only hold the best fit,
  this method simply returns the NMF model fitted by
  object -- that is stored in slot fit.
signature(object = "NMFfitXn"): Returns
  the best NMF fit object amongst all the fits stored in
  object, i.e. the fit that achieves the lowest
  estimation residuals.
  
      signature(object = "NMFfit", value =
  "NMF"): Updates the NMF model object stored in slot
  'fit' with a new value.
  
      signature(object = "NMFfit"):
  Returns the object its self, since there it is the result
  of a single NMF run.
  
      signature(object = "NMFfitX"):
  Returns the fit object that achieves the lowest residual
  approximation error across all the runs.
  
      It is a pure virtual method defined to ensure
  minfit is defined for sub-classes of
  NMFfitX, which throws an error if called.
signature(object = "NMFfitX1"):
  Returns the fit object associated with the best fit,
  amongst all the runs performed when fitting
  object.
  
      Since NMFfitX1 objects only hold the best fit,
  this method simply returns object coerced into an
  NMFfit object.
signature(object = "NMFfitXn"):
  Returns the best NMF model in the list, i.e. the run that
  achieved the lower estimation residuals.
  
      The model is selected based on its deviance value.