Multivariate Data Retrieval Modified by Random Noise using Lattice Autoassociative Memories with Eroded or Dilated Input Residuals

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.