An Improvement on the Moore-Penrose Generalized Inverse Associative Memory

Abstract

An improvement of the Moore-Penrose generalized inverse associative memory method is presented. It is known that for noisy input key vectors the associative memory is extremely sensitive (unstable) and association errors become unacceptably large, particularly as the number of vectors approaches the number of components per vector. Using singular value decomposition the association behavior of the associative memory is analyzed theoretically and its association error is shown to consist of two kinds of errors. One is due to the linear dependency of the key vectors (dependency error), and the other is due to the input additive noise (noise error). For noisy input key vectors the noise error is greatly increased when at least one small eigenvalue of the key space exists. It is found that the noise error can be changed to the dependency error by eliminating the corresponding eigenvalues. Therefore, if the eigenvalues are appropriately eliminated, stable association behavior can be realized and the association error reduced. In the proposed improvement method an elimination condition of the eigenvalues is given. The proposed method is greatly effective for noisy input key vectors.