In human non-verbal communication, the change from one facial expression to another is as important as each individual facial expression; thus, it would be desirable to have a system which can evolve animated sequences of facial expressions.
Since a facial expression in a N-parameter model can be represented as a
point in a N-dimensional space, one could represent animation by adding
an extra dimension, that of time, and represent linear transformations
between expressions as lines between points in N+1-dimensional space-time.
It is, however, my considered belief that linear transformations would be
inadequate for serious use, yielding only mechanical, stiff movements.
There may be several ways around this; one would be to, when interpolating a
parameter between two values 
and 
, map its position onto a
cosine curve with range 
; another may be to make the
animation paths splines rather than lines.