Shadow-Cuts Minimization/Maximization and Complex Hopfield Neural Networks

In this article, we continue our very recent work by extending it to the complex case. Having been inspired real Hopfield neural network (HNN) results, investigations here yield various novel some of which are as follows. First, “biased pseudo-cut” concept HNN (CHNN) case, introduce a “shadow-cut” that is defined sum intercluster phased edges. Second, while discrete-time strictly minimizes in each neuron state change, CHNN “tends” minimize shadow-cut (as energy function minimized). Third, these definitions pose L-phased graph clustering (partitioning) problem shadow-cuts minimized (or maximized) for Hermitian and directed graphs whose edges (possibly arbitrary positive/negative) numbers. Finally, combining pioneering algorithm GADIA Babadi Tarokh their modified versions, propose simple indirect algorithms solve minimization/maximization problem. The proposed naturally include well its special cases. computer simulations confirm findings.