Similarity and categorization are fundamental processes in human cognition that help complex organisms make sense of the cacophony of information in their environment. These processes are critical for tasks such as recognizing objects, making decisions, and forming memories. In this review, we provide an overview of the current state of knowledge on similarity and psychological spaces, discussing the theories, methods, and empirical findings that have been generated over the years. Although the concept of similarity has important limitations, it plays a key role in cognitive modeling. The review surfaces three key themes. First, similarity and mental representations are merely two sides of the same coin, existing as a similarity-representation duality that defines a psychological space. Second, both the brain's mental representations and the study of mental representations are made possible by exploiting second-order isomorphism. Third, similarity analysis has near-universal applicability across all levels of cognition, providing a common research language.
Keywords: category learning; embedding; psychological space; representation; similarity.