Associative Operations Based on Difference-Slice Data Processing

Abstract

Associative operations are effectively used to solve such application problems as sorting, searching for certain features, and identifying extreme (maximum/minimum) elements in data sets. Thus, determining the maximum number as a result of sorting a numerical array is an acceptable operation in implementing the competition mechanism in neural networks. In addition, determining the average number in a numerical series by sorting significantly speeds up the process of median filtering of images and signals. In this case, the implementation of median filtering requires the use of sorting with the ranking of the elements of the number array. This paper analyses the possibilities of associative operations implementing the elements of a vector (one-dimensional) array of numbers based on processing by difference slices (DS). A simplified description of DS processing with a selection of the common part of the elements of the vector and the difference slice formed from its elements is given. In addition, elements of the binary mask matrix are used as an example of a topological feature matrix. The proposed approach allows for the formation of the ranks of the elements of the initial vector, as a result of sorting in ascending order of their numerical values. The paper shows a schematic representation of the process of DS processing, as well as an example of DS processing of a number vector in the form of a table, which shows the formation sequence of numbers of the sorted array and the ranks of numbers of the initial array. Therefore, the proposed use of topological features allows to determine the comparative relations between the elements of the numerical array in the process of spatially distributed DS processing, as well as to confirm the versatility of this approach.