  The adaptation rule for Vector Quantization algorithms, and consequently the
convergence of the generated sequence, depends on the existence and properties
of a function called the energy function, defined on a topological manifold.
Our aim is to investigate the conditions of existence of such a function for a
class of algorithms examplified by the initial ''K-means'' and Kohonen
algorithms. The results presented here supplement previous studies and show
that the energy function is not always a potential but at least the uniform
limit of a series of potential functions which we call a pseudo-potential. Our
work also shows that a large number of existing vector quantization algorithms
developped by the Artificial Neural Networks community fall into this category.
The framework we define opens the way to study the convergence of all the
corresponding adaptation rules at once, and a theorem gives promising insights
in that direction. We also demonstrate that the ''K-means'' energy function is
a pseudo-potential but not a potential in general. Consequently, the energy
function associated to the ''Neural-Gas'' is not a potential in general.
