Complex-valued bidirectional auto-associative memory

Complex-valued Hopfield Associative Memory (CHAM) can store multi-valued patterns. But CHAM stores not only given training patterns but also many spurious patterns, such as their rotated patterns, at the same time. These rotated patterns and spurious patterns reduce the noise robustness of the CHAM. In the present work, we propose Complex-valued Bidirectional Auto-Associative Memory (CBAAM) as a model of auto-associative memory which improves the noise robustness. CBAAM consists of two layers. Although the structure of CBAAM is a Bidirectional Associative Memory (BAM), CBAAM works as an auto-associative memory, because the one layer is a visible layer and the other one is an invisible layer. The visible layer consists of complex-valued neurons and can process multi-valued patterns. The invisible layer consists of real-valued neurons and can reduce pseudo-memory such as rotated patterns. Thus, CBAAM has strong noise robustness. In the computer simulations, we show that the noise robustness of CBAAM highly exceeds that of CHAM. Especially, we find that CBAAM maintains high noise robustness independent of the resolution factor.