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WIREs Cogn Sci
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Similarity

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Similarity is a fundamental concept within Cognitive Science. It is routinely invoked in the explanation of cognitive processes as diverse as memory retrieval, categorization, visual search, problem solving, learning, language processing, reasoning, and social behavior. At the same time, it is of fundamental practical concern to computer scientists concerned with clustering and machine learning, and it figures in many philosophical contexts. Crucially, ‘similar’ is not a relationship that simply reflects objective properties of the objects under consideration but rather is dependent on how those objects are represented by an observer. This ties theories of similarity closely to theories of representation. This article is categorized under: Philosophy > Foundations of Cognitive Science
Asymmetric similarity: From a transformational perspective moving from left to right is a simpler transformation than from right to left, because repeating the fill color of the circle can re‐use code specifying that color, whereas moving from right to left, the color of the triangle must be specified from scratch.
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Simple geometric objects illustrating the importance of relation information and hence structured representations. The stimulus in (a) differs from that of the first item in (b) not in individual features, but in the way those features are arranged. To adequately capture the similarity, spatial location thus also needs to be factored in. On a featural account, the only option is to add in more and more feature conjunctions. This runs into trouble for two reasons, for one, something like ‘on the left’ (as in, e.g., ‘black + triangle + left’), is an odd feature, given that it is not absolute spatial location that is at issue here. Secondly, it leads to a proliferation of ‘features’. All the basic elements (and all their possible combinations) must also be retained to avoid the hyperspecificity combinations would otherwise bring (if one were to only consider ‘black + triangle + left’ as a single compound feature, then (a) and the first item of (b) no longer share any features). These proliferations then make it the case, for example, that (a) and the top item of (b) share fewer features than (a) and the second item in (b).
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(a) The flexibility of mental representation: the object may variously be described as ‘a shape’, ‘a geometric object’, ‘a circle’, ‘a white circle’, and so on, depending on the context. (b) Spatial models of similarity. Items occupy points in space according to their coordinate values along the underlying dimensions. Items with similar coordinate values will be nearby, and items that are dissimilar will be far apart.
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