Categorization is a fundamental information processing phenomenon in the brain. It is critical for animals to compress an abundance of stimulations into groups to react quickly and efficiently. In addition to labels, categories possess an internal structure: the goodness measures how well any element belongs to a category. Interestingly, this categorization leads to an altered perception referred to as categorical perception: for a given physical distance, items within a category are perceived closer than items in two different categories. A subtler effect is the perceptual magnet: discriminability is reduced close to the prototypes of a category and increased near its boundaries. Here, starting from predefined abstract categories, we naturally derive the internal structure of categories and the phenomenon of categorical perception, using an information theoretical framework that involves both probabilities and pairwise similarities between items. Essentially, we suggest that pairwise similarities between items are to be tuned to render some predefined categories as well as possible. However, constraints on these pairwise similarities only produce an approximate matching, which explains concurrently the notion of goodness and the warping of perception. Overall, we demonstrate that similarity-based information theory may offer a global and unified principled understanding of categorization and categorical perception simultaneously.
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