  We give a classification of components of the Hodge locus in any parameter
space of smooth projective varieties. This is done using determinantal
varieties constructed from the infinitesimal variation of Hodge structures
(IVHS) of the underlying family. As a corollary we prove that the minimum
codimension for the components of the Hodge locus in the parameter space of
$m$-dimensional hypersurfaces of degree $d$ with $d\geq 2+\frac{4}{m}$ and in a
Zariski neighborhood of the point representing the Fermat variety, is obtained
by the locus of hypersurfaces passing through an $\frac{m}{2}$-dimensional
linear projective space. In the particular case of surfaces in the projective
space of dimension three, this is a theorem of Green and Voisin. In this case
our classification under a computational hypothesis on IVHS implies a weaker
version of the Harris-Voisin conjecture which says that the set of special
components of the Noether-Lefschetz locus is not Zariski dense in the parameter
space.
