Binary autoassociative morphological memories derived from the kernel method and the dual kernel method

Morphological associative memories (MAMs) belong to the class of morphological neural networks. The recording scheme used in the original MAM models is similar to the correlation recording recipe. Recording is achieved by means of a maximum (M-XY model) or minimum (W-XY model) of outer products. Notable features of autoassociative morphological memories (AMMs) include optimal absolute storage capacity and one-step convergence. The fixed points of AMMs can be characterized exactly in terms of the original patterns. Unfortunately, AMM fixed points include a large number of spurious memories. A combination of the M-XX model and the kernel method yields another binary AMM model. In this paper, we also introduce a dual kernel method. A new, dual model is given by a combination of the W-XX model and the dual kernel method. The new AMM models exhibit better error correction capabilities than M-XX and W-XX and a reduced number of spurious memories which can be easily described in terms of the fundamental memories. Finally, we present yet another pair of AMMs with very similar properties. Although these models are also derived from the kernel or dual kernel methods, their construction depends on less restrictive conditions.