On the performance of Quaternionic Bidirectional Auto-Associative Memory

This paper presents Quaternionic Bidirectional Auto-Associative Memory (QBAAM) that is an associative memory network storing patterns with multiple levels. A part of neurons in the network are quaternionic neurons, where their states are encoded by quaternion, which is a four-dimensional hypercomplex number system. These neurons can represent three kinds of discretized phases, i.e., three-dimensional multilevel values. The rest of neurons are conventional (real-valued) neurons. QBAAM is expected to have a rich representation ability by employing quaternionic neurons, as well as to have fewer spurious patterns in the network by a combination of real-valued and quaternionic neurons. The experimental results show that high robustness of noisy inputs is achieved by QBAAM, as compared with Quaternionic Hopfield Associative Memory where all neurons in the network are quaternionic neurons.