An Exemplar Model of Classification in Single and Combined Categories

This paper describes an exemplar-based model of people’s classification and typicality judgements in both single and combined categories. This model, called the diagnostic evidence model, explains the observed family resemblance structure of single categories; the productive nature of category combination; the observed overextension of typicality judgments in some combined categories; and the situations in which that overextension occurs. The model also gives a close fit to quantitative results from a representative single-category classification data-set. Models of categorisation need to explain two basic aspects of human cognition: our ability to classify items as members of single categories such as fish or cat, and our ability to classify items as members of combinations of categories such as wild cat or pet fish. A successful model should account for the graded structure of classification in single categories: the fact that people’s judgements of membership typicality for items in categories are proportional to the items’ family resemblance to members of those categories (Rosch, 1978; Rosch & Mervis, 1975). A successful model should also account for the productivity of category combination: the fact that people are able to understand and judge membership in new combinations of categories, even if no already-existing examples of those combinations are known. This combinatorial productivity is important because it underlies our ability to think new thoughts and understand new expressions. In many currently popular models of categorisation (e.g. the context theory; Medin & Schaffer, 1978), an item’s membership in a category is proportional to its similarity to the stored exemplars of that category. While this approach gives a good account for the graded structure of single categories, it has difficulty explaining the productivity of category combination, which involves classification in combinations for which no stored exemplars are available (Rips, 1995). This paper describes an exemplar-based model of classification in single and combined categories which explains the family resemblance structure of single categories, the productivity of category combination, and other specific results in both domains. The model, called the diagnostic evidence model, extends a successful earlier theory (Costello & Keane, 1997, in-pressA, in-pressB). The first part of the paper presents the diagnostic evidence model of categorisation in single and combined categories, and gives its account for family resemblance and productivity in combination. The second part demonstrates the model by showing how it explains the observed overextension of typicality in some combined categories. Overextension occurs when people rate an item as a poor member of both constituents of a combination, but as a good member of the combination as a whole; for example, when goldfish are rated as untypical members of the categories pet and fish, but as typical members of the combination pet fish (Hampton, 1988). Overextension has posed problems for a number of theories of category combination. The diagnostic evidence model accounts for results on overextension, and explains why overextension occurs in some combinations but not in others. The third part of the paper demonstrates this model further by showing how it gives a good fit to quantitative results from a representative classification data-set (Nosofsky, Palmeri, & McKinley, 1994); a fit as close as that given by exemplar-similarity models such as the context theory. The diagnostic evidence model The diagnostic evidence model extends an earlier theory of the interpretation of noun-noun combined phrases, called the constraint theory (Costello & Keane, 1997, in-press-A). That theory set out to explain the diversity of interpretations which people produce for noun-noun combinations: the fact that people sometimes interpret combinations by forming conjunctions between the combining categories (as in the interpretation "pet bird: a parrot or some other bird which is also a pet"), sometimes by asserting relations between the categories (as in “jungle bird: a bird that lives in jungles ”), and sometimes by transferring properties from one concept to the other (as in “skunk bird: a bird that smells bad”). Constraint theory explains this diversity by describing a combination process that forms mental representations satisfying three constraints of diagnosticity, plausibility and informativeness. Each interpretation type represents a different way of satisfying these constraints. The theory has been tested in a computer program which simulates the interpretation of noun-noun combinations, producing each interpretation type and generating results that agreed with people’s interpretations of those combinations (Costello & Keane, in-press-A). Further, Costello & Keane (in-press-B) have provided direct experimental evidence for diagnosticity's role in the formation of combined categories. The diagnostic evidence model extends constraint theory to give a quantitative account of classification typicality in single and combined categories. The model focuses on the diagnosticity constraint. The model assumes that people represent categories by storing sets of category exemplars in memory. From these sets, diagnostic attributes for categories are computed: these attributes serve to identify category members. An item’s membership typicality in a single or combined category is a function of the diagnosticity of its attributes for that category or for the constituent categories of that combination. An item has a high degree of membership typicality in a category if it has attributes that are highly diagnostic for that category. An item has a high degree of typicality in a combination if it has some attributes highly diagnostic for one constituent of the combination, and other attributes highly diagnostic for the other. Two novelties in this model are its method for computing attribute diagnosticity, and its logic for combining attribute diagnosticity and evidence for membership in combinations. I describe these below. Attribute Diagnosticity Diagnostic attributes are attributes which occur frequently in instances of a category, but rarely in instances in that category’s contrast set (set of non-members of the category). These attributes serve to identify members of a category: an new item possessing an attribute which is highly diagnostic for a given category is likely to be a member of that category. The diagnosticity of attribute x for category C is defined in Equation 1. Let K be the contrast set for category C. Let jx be 1 if an instance j possesses attribute x, and 0 otherwise. D(x|C|K), the diagnosticity of x for C relative to contrast set K, is equal to the number of instances in C which possess x, divided by the total number of instances in C (|C|) plus the number of instances in K which possess x: