Kernel vectors represent an elegant representation for the retrieval of pattern associations, where the input patterns are corrupted by both erosive and dilative noise. However, their action completely fails when a particular kind of erosive noise, even of very low percentage, corrupts the input pattern. In this paper, a theoretical justification of this fact is given and a new method is proposed for the construction of kernel vectors for binary patterns associations. The new kernels are not binary but "gray", because they contain elements with values in the interval [0, 1]. It is shown, both theoretically and experimentally that the new kernel vectors carry the good properties of conventional kernel vectors and, at the same time, they can be easily computed. Moreover, they do not suffer from the particular noise deficiency of the conventional kernel vectors. The recalling result is in general a gray pattern, which in the sequel undergoes a simple thresholding action and passes through a simple Hamming network to produce high recall rates, even in heavily corrupted patterns Retrieval of pattern associations is very significant for a variety of scientific disciplines including data analysis, signal and image understanding and intelligent control.
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