Abstract
Lattice associative memories were proposed as an alternative approach to work with a set of associated vector pairs for which the storage and retrieval stages are based in the theory of algebraic lattices. Several techniques have been established to deal with the problem of binary or real valued vector recall from corrupted inputs. This paper presents a thresholding technique coupled with statistical correlation pattern index search to enhance the recall performance of lattice auto-associative memories for multivariate data inputs degraded by random noise. By thresholding a given noisy input, a lower bound is generated to produce an eroded noisy version used to boost the min-lattice auto-associative memory inherent retrieval capability. Similarly, an upper bound is generated to obtain a dilated noisy version used to enhance the max-lattice auto-associave memory response. A self contained theoretical foundation is provided including a visual example of a multivariate data set composed of grayscale images that show the increased retrieval capability of this type of associative memories.
Highlights
Morphological associative memories (MAMs) were introduced more than two decades ago as a new paradigm for the storage and recall of pattern associations [3]
In most correlation type associative memory models, the storage and recall stages use conventional algebra whereas computation in MAMs are based on the mathematical theory of minimax algebra [4,5,6]; since the standard minimax matrix algebra is a specific instance of a lattice algebraic structure, MAMs are named lattice associative memories (LAMs)
It was shown that the canonical auto-associative morphological memories (AMMs) have unlimited storage capacity, give perfect recall for all exemplar patterns, and are robust for exclusively erosive or dilative noise; based on stronger assumptions, similar results were corroborated for hetero-associative morphological memories (HMMs)
Summary
Morphological associative memories (MAMs) were introduced more than two decades ago as a new paradigm for the storage and recall of pattern associations [3]. It was shown that the canonical auto-associative morphological memories (AMMs) have unlimited storage capacity, give perfect recall for all exemplar patterns, and are robust for exclusively erosive or dilative noise; based on stronger assumptions, similar results were corroborated for hetero-associative morphological memories (HMMs). To regain the LAAMs inherent computational functionality to cope with different amounts of impulsive random noise, in this paper, we introduce a novel technique using thresholded noisy inputs followed by statistical correlation pattern indexing, to generate an erosive or dilative noisy version of the input pattern and show the LAAMs enhanced recall performance by means of an illustrative example.
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