A novel quantum inspired algorithm for sparse fuzzy cognitive maps learning

Fuzzy cognitive maps (FCMs) represent a graphical modeling technique based on the decision-making and reasoning rules and algorithms similar to those used by humans. The graph-like structure and the execution model of FCMs respectively allow static and dynamic analyses to be carried out. The learning algorithms of FCMs that are based on expert opinion are weak in dynamic analysis, and fully automatic algorithms are weak in static analysis. In this paper, for providing the facility for simultaneous static and dynamic analyses, a new training algorithm called the quantum FCM (QFCM) is presented. In our proposed algorithm, the quantum inspired evolutionary algorithm (QEA) and the particle swarm optimization algorithm are employed for generating static and dynamic analyses properties respectively. In the QFCM, instead of coding the presence and absence of links between concepts with 1 and 0, respectively, the probability of their existence or inexistence is modeled with a Q-bit (the smallest information unit in the QEA) and, depending on the outcome of dynamic analysis, the quantum state of this Q-bit is updated. Using a probabilistic representation instead of 0 and 1, in addition to creating diversity in the solution space, can lead to escapes from many local optima; which is an issue of concern in the optimization of FCM structure. Experiments on synthetic, real-life, and gene regulatory network reconstruction problems demonstrated that not only does QFCM find potentially good structures, providing static analysis, but also it brings about low data error, showing good dynamic property. Furthermore, QFCM successfully outshined most of the state-of-the-art FCM’s learning algorithms, without any need to human knowledge, illustrating its power in this regard.