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Many vs. Few Similarities

[GR91], [Mar89], [MO89], and [Ros73a] have all argued that common nouns label objects similar across many inter-related and correlated properties. In contrast, dimensional adjectives label objects that are alike on only one property. This difference between nouns and adjectives has important conceptual consequences (see especially Markman, 1989). For example, knowing that an object is a bird allows predictions about many different properties of the object but knowing that an object is a member of the category WHITE-THINGS supports only predictions about the object's color.

This difference also has important implications for similarity-based learning, as illustrated in Figure gif. This figure represents the extensions of idealized nouns and adjectives as regions in a multidimensional space of all possible objects. The relevant spaces are hyperspaces of many dimensions, all of those along which noun and adjective meanings vary, but for ease of illustration we confine ourselves to three dimensions. For example, the dimensions shown could represent SIZE, SMOOTHNESS, and SHININESS. Each of the outlined regions within the large cube represents a hypothetical category associated with a single word, and instances of the category would be points within the region. As can be seen in the figure, categories organized by many dimensional similarities (cubes with thick outlines) are small and compactly shaped relative to those that are organized by similarity on just one property. Thus, the idealized noun is uniformly and closely bounded in all directions. It is a hypercube or hypersphere. In contrast, members of an adjective category are tightly constrained in only one direction (the relevant dimension) but extend indefinitely in all others. The idealized dimensional-adjective category thus may be thought of as a ``hyperslab.'' Further, the volume of idealized noun categories, compact in all dimensional directions, is relatively small whereas the volume of adjective categories, extending indefinitely in all directions but one, is great.

 

 


: Typical Noun and Adjective Categories. Only three dimensions from the set of dimensions distinguishing the categories are shown. Noun categories appear in thick outline, adjective categories in thin outline.

Given ordinary ideas about similarity and generalization, these differences clearly favor nouns. The within-category similarity is greater for the nouns than the adjectives in Figure gif. Further for nouns, generalization can be non-selective in all directions but for adjectives generalization must be selectively inhibited in one direction. Learning about adjectives but not nouns thus requires discovering and selectively attending to one relevant direction in the multi-dimensional space.



next up previous
Next: Category Overlap Up: Differences in Similarity Previous: Differences in Similarity



Michael Gasser
Fri Dec 6 13:15:34 EST 1996