Representation is representation of similarities

Behavioral and Brain Sciences 21 (4):449-467 (1998)
Abstract
Intelligent systems are faced with the problem of securing a principled (ideally, veridical) relationship between the world and its internal representation. I propose a unified approach to visual representation, addressing both the needs of superordinate and basic-level categorization and of identification of specific instances of familiar categories. According to the proposed theory, a shape is represented by its similarity to a number of reference shapes, measured in a high-dimensional space of elementary features. This amounts to embedding the stimulus in a low-dimensional proximal shape space. That space turns out to support representation of distal shape similarities which is veridical in the sense of Shepard's (1968) notion of second-order isomorphism (i.e., correspondence between distal and proximal similarities among shapes, rather than between distal shapes and their proximal representations). Furthermore, a general expression for similarity between two stimuli, based on comparisons to reference shapes, can be used to derive models of perceived similarity ranging from continuous, symmetric, and hierarchical, as in the multidimensional scaling models (Shepard, 1980), to discrete and non-hierarchical, as in the general contrast models (Tversky, 1977; Shepard and Arabie, 1979)
Keywords affordance   categorization   constancy   distal/proximal stimulus   features   invariance   isomorphism   mental models   perception   representation   similarity   visual shape recognition
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O. Shagrir (2012). Structural Representations and the Brain. British Journal for the Philosophy of Science 63 (3):519-545.
Tomer Fekete (2010). Representational Systems. Minds and Machines 20 (1):69-101.

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