Retrieving Sparser Fuzzy Cognitive Maps Directly from Categorical Ordinal Dataset using the Graphical Lasso Models and the MAX-threshold Algorithm

Abstract

Learning FCM models from data without any a priori knowledge and expert intervention remains a considerable problem. This research study utilizes a fully data-based learning method (the glassoFCM) for automatic design of Fuzzy Cognitive Maps (FCM) using large ordinal dataset based on the efficient capabilities of graphical lasso (glasso) models. Therefore, glasso represents its structure as a sparser graph, while maintaining a high likelihood, by producing an adjacent weighted matrix, where relationships are expressed by conditional independences. By minimizing the negative log-likelihood indicates that the model fits better to the data under the assumption that the observed data are the most likely data. The principle questioning is which of the observed concepts is the appropriate to trigger the remaining concepts in the map in order to create the glassoFCMs and obtain reasonable results. The answer derives from the FCM structure analysis based on the strength centrality indices. Moreover, the MAX-threshold algorithm based on the FCM scenario analysis is proposed in order to prune edges and retrieve sparser graphs. This algorithm shrinks the meaningless weights of the FCM, without affecting significantly the outcomes in scenario analysis. The whole approach was implemented in a business intelligence problem of evaluating the attractiveness of Belgian companies.