  We consider the Hopfield neural network as a model of associative memory and
we define its neuronal interaction matrix $\mathbf{J}$ as a function of a set
of $K \times M$ binary vectors $\{\mathbf{\xi}^{\mu, A}
\}_{\mu=1,...,K}^{A=1,...,M}$ representing a sample of the reality that we want
to retrieve. In particular, any item $\mathbf{\xi}^{\mu, A}$ is meant as a
corrupted version of an unknown ground pattern $\mathbf{\zeta}^{\mu}$, that is
the target of our retrieval process. We consider and compare two definitions
for $\mathbf{J}$, referred to as supervised and unsupervised, according to
whether the class $\mu$, each example belongs to, is unveiled or not, also,
these definitions recover the paradigmatic Hebb's rule under suitable limits.
The spectral properties of the resulting matrices are studied and used to
inspect the retrieval capabilities of the related models as a function of their
control parameters.
