Extending Fuzzy Cognitive Maps with Tensor-Based Distance Metrics

Abstract

Cognitive maps are high level representations of the key topological attributes of real or abstract spatial environments progressively built by a sequence of noisy observations. Currently such maps play a crucial role in cognitive sciences as it is believed this is how clusters of dedicated neurons at hippocampus construct internal representations. The latter include physical space and, perhaps more interestingly, abstract fields comprising of interconnected notions such as natural languages. In deep learning cognitive graphs are effective tools for simultaneous dimensionality reduction and visualization with applications among others to edge prediction, ontology alignment, and transfer learning. Fuzzy cognitive graphs have been proposed for representing maps with incomplete knowledge or errors caused by noisy or insufficient observations. The primary contribution of this article is the construction of cognitive map for the sixteen Myers-Briggs personality types with a tensor distance metric. The latter combines two categories of natural language attributes extracted from the namesake Kaggle dataset. To the best of our knowledge linguistic attributes are separated in categories. Moreover, a fuzzy variant of this map is also proposed where a certain personality may be assigned to up to two types with equal probability. The two maps were evaluated based on their topological properties, on their clustering quality, and on how well they fared against the dataset ground truth. The results indicate a superior performance of both maps with the fuzzy variant being better. Based on the findings recommendations are given for engineers and practitioners.

Keywords

• cognitive graphs
• self organizing maps
• tensor distance metrics
• higher order data
• topological error
• Myers-Briggs Type Indicator