Pattern Retrieval by Quaternionic Associative Memory with Dual Connections

An associative memory based on Hopfield-type neural network, called Quaternionic Hopfield Associative Memory with Dual Connection (QHAMDC), is presented and analyzed in this paper. The state of a neuron, input, output, and connection weights are encoded by quaternion, a class of hypercomplex number systems with non-commutativity for its multiplications. In QHAMDC, calculation for an internal state of a neuron is conducted by two types of multiplications for neuron’s output and connection weight. This makes robustness of the proposed associative memory for retrieval of patterns. The experimental results show that the performances of retrieving patterns by QHAMDC are superior to those by the previous QHAM.

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