A Semilattice Approach towards Sparsely Connected Associative Memories

Mathematical morphology (MM) on complete lattices provides the theoretical basis for certain lattice computing models called morphological neural networks (MNNs). Morphological associative memories (MAMs) that are among the most widely known MNN models usually perform operations in the extended integer or real numbers or in the class of fuzzy sets (in which case we speak of fuzzy morphological associative memories) but can also be defined in more general complete lattice structures. Moreover, the relatively recent theory of MM on complete semilattices can be employed as a mathematical framework for novel (morphological) associative memory models. In this paper we introduce a sparsely connected associative memory model based on complete semilattices capable of dealing with the computational requirements for storing multi-valued and large-scale patterns. We finish with some experimental results concerning the problem of storing and reconstructing gray-scale as well as color images.