Overcoming the Empirical Challenges of Geometric Similarities: A Model-Based Review

Similarity is fundamental to cognition, shaping both foundational and higher-order processes. Cognitive theories often adopt a geometric approach, where similarity is defined by the distance or angle between objects in a psychological space, successfully explaining many perceived similarity relations. However, the validity of such geometric similarity models has been questioned by diverse empirical challenges, such as violations of the metric axioms (minimality, symmetry, and triangle inequality), the common features effect (common features increasing similarity), contextual effects (similarity relations shifting with the presence of other objects), and nearest neighbor effects (single objects considered as most similar to many others). The present work reviews evidence showing that geometric similarity models can address many of these challenges through psychologically plausible extensions of the model formalizations. Some extensions add parameters within the standard framework, such as feature-specific attention or object-specific biases (e.g., salience or frequency). Others generalize the geometric framework itself, through similarity functions that go beyond distances or angles, or psychological spaces that represent objects as something other than points on a multidimensional map. Each extension addresses specific empirical challenges while maintaining cognitive plausibility. These findings suggest that geometric models, when appropriately extended, provide a robust foundation for understanding human similarity relations and offer a path toward comprehensive theories of higher-order cognition.