  Functional data analysis involves data described by regular functions rather
than by a finite number of real valued variables. While some robust data
analysis methods can be applied directly to the very high dimensional vectors
obtained from a fine grid sampling of functional data, all methods benefit from
a prior simplification of the functions that reduces the redundancy induced by
the regularity. In this paper we propose to use a clustering approach that
targets variables rather than individual to design a piecewise constant
representation of a set of functions. The contiguity constraint induced by the
functional nature of the variables allows a polynomial complexity algorithm to
give the optimal solution.
