Affiliations: Department Matemática Aplicada, Universidad de
Málaga, Campus de Teatinos, 29071 Málaga, Spain. E-mail:
merida@ctima.uma.es | Department Lenguaje y Ciencias de la Computación,
Universidad de Málaga, Campus de Teatinos, 29071 Málaga, Spain. E-mail:
munozp@lcc.uma.es
Note: [] Corresponding author
Abstract: This paper shows a new type Hopfield multivalued recurrent neural
model (MREM) and some of its learning capabilities. So, the network can be used
as an associative memory (multivalued counterpart of Hopfield network).
Moreover, when only two states ({-1, 1} or {0, 1}) are allowed, the network
coincides with the bipolar or binary Hopfield discrete models. Although there exist some other multivalued type Hopfield models,
this model uses, in a more proper way, the multivalued information contained in
a multivalued neuron. It is possible because we have considered that the
interaction between neurons is expressed by a general real function between
their outputs, whereas most of others models use the product function that
produces only two possible values with a drastic lost of the multivalued
information. The introduction of this function of the outputs of neurons (that we
are naming function of similarity as it measures the similarity between
the outputs of neurons) allows to represent more properly the interaction
between two similar, but different, neuron outputs (for example: waves, colors,
etc.) than a binary (or previous multivalued models) do. In this paper, a method to load a set of patterns into the network
has been studied. That method generalizes the Hopfield's one when multivalued
neurons are been considered. Finally, it is shown that by using an augmented network and loading
augmented patterns we can avoid the storage of spurious patterns into the
network, as the well-known effect of loading the opposite pattern into the
Hopfield's network. For this new storage technics has been obtained an
expression that allows to set bounds to the capacity of the network. It must be considered that multivalued patterns contains much more
information than bipolar ones. So, for similar capacity value a multivalued
network must be preferred to another one whose neuron outputs can take only two
values.
