Caricatures and Prototypes
1
Conceptual Interrelatedness and Caricatures
Robert L. Goldstone
IndianaUniversity
Mark Steyvers
University of California, Irvine
Brian J. Rogosky
IndianaUniversity
Running head: CARICATURES AND PROTOTYPES
Word count: 6,244
Abstract
Concepts are interrelated to the extent that the characterization of one concept is influenced by another concept, and isolated to the extent that the characterization of one concept is independent of other concepts. The relative categorization accuracy of the prototype and caricature of a concept can be used as a measure of concept interrelatedness. The prototype is the central tendency of a concept, whereas a caricature deviates from the concept’s central tendency in the direction opposite to the central tendency of other acquired concepts. The prototype is predicted to be relatively well categorized when a concept is relatively independent of other concepts, but the caricature is predicted to be relatively well categorized when a concept is highly related to other concepts. Support for these predictions comes from manipulations of the labels given to simultaneously acquired concepts (Experiment 1) and the order of categories during learning (Experiment 2).
Conceptual Interrelatedness and Caricatures
Concepts seem to be simultaneously connected to each other and to the external world. On the one hand, concepts seem to gain their meaning by the role that they play within a network of concepts (Collins & Quillian, 1969; Field, 1977). The notion of a “conceptual web” by which concepts all mutually define one another has been highly influential in all of the major fields that comprise cognitive science, including linguistics (Saussure, 1915/1959), computer science (Lenat & Feigenbaum, 1991), psychology (Landauer & Dumais, 1997), and philosophy (Block, 1999). However, there is also dissatisfaction in some quarters with the circularity of this conceptual web account. Researchers have argued that concepts must be grounded in the external world rather than merely related to each other (Harnad, 1990). The British empiricists argued that our conceptual ideas originate in recombinations of sensory impressions (Hume, 1740/1973). More recently, Barsalou (1999; Goldstone & Barsalou, 1998; Solomon & Barsalou, 2001) has argued that concepts are not amodal, completely abstracted symbols, but rather are intrinsically perceptually based.
In an attempt to reconcile arguments for a conceptual web and externally grounded concepts, Goldstone (1996) described a continuum between purely isolated and purely interrelated concepts, arguing that a concept is interrelated to the extent that its characterization is influenced by other concepts. Goldstone’s empirical basis for the continuum was the convergence of a set of experimental manipulations and measures of conceptual interrelatedness. A set of manipulations was designed to influence the degree of interrelatedness between simultaneously acquired concepts, and the influence of these manipulations was gauged by a set of measures of interrelatedness. These experiments gave support to the hypothesis that fairly minimal experimental manipulations were capable of changing how influential one concept was on another concept’s representation and processing. The goal of the current experiments is to further test the claim for a continuum between isolated and interrelated concepts, using rich and naturalistic stimuli, and new manipulations and measures of interrelatedness.
Isolated and Interrelated Concepts
In evaluating the claim for a continuum between isolated and interrelated concepts, it is helpful to consider theories at the two poles of the continuum. We will consider representative models of isolated and interrelated concepts, leaving a fuller description to Goldstone (1996).
Conceptual interrelatedness is a component of many linguistic treatments of concepts. Ferdinand de Saussure (1915/1959) argued that all concepts are completely “negatively defined,” that is, defined solely in terms of other concepts. He contended that “language is a system of interdependent terms in which the value of each term results solely from the simultaneous presence of the others” (p. 114) and that “concepts are purely differential and defined not in terms of their positive content but negatively by their relations with other terms in the system” (p. 117). This notion has evolved into the modern treatment of semantic networks (Collins & Quillian, 1969; Quillian, 1967). In these networks, concepts are represented by nodes in a network, and gain their functionality by their links to other concept nodes. Often times, these links are labeled, in which case different links refer to different kinds of relations between nodes. Dog would be connected to Animal by an Is-a link, to Bone by an Eats link, and to Paw by a Has-a link. Lenat and Feigenbaum have argued (1991) that interconceptual linkages are sufficient for establishing conceptual meanings even without any external grounding of the concepts. A computational approach to word meaning that has received considerable recent attention has been to base word meanings solely on the patterns of co-occurrence between a large number of words in an extremely large text corpus (Burgess, Livesay, & Lund, 1998; Burgess & Lund, 2000; Landauer & Dumais, 1997). Mathematical techniques are used to create vector encodings of words that efficiently capture their co-occurrences. If two words, such as “cocoon” and “butterfly” frequently co-occur in an encyclopedia or enter into similar patterns of co-occurrence with other words, then their vector representations will be highly similar. The meaning of a word, its vector in a high dimensional space, is completely based on the contextual similarity of the word to other words. Finally, researchers have argued that concepts are frequently characterized by their associative relations to other concepts. Barr and Caplan (1987) provide evidence, by having subjects list features associated with words, that many concepts are characterized by what they call “extrinsic features,” features that are “represented as the relationship between two or more entities” (p. 398).
From the theories above, one might conclude that concepts cannot stand alone, and there could not be such a thing as a system with only one concept (Stich, 1983). However, if one looks at the field of pattern recognition rather than theories inspired by linguistics, then examples of isolated concepts become apparent. One way to conceive of an isolated concept is as a feature detector. A feature detector can become active when an input with a particular perceptual feature is present. Ascending in complexity, a concept can also be represented as a template in a physical or more abstract space (Edelman, 1999). If patterns are categorized by comparing them with stored templates for categories, the representation of the categories do not depend on the other categories. A category’s representation is simply the image that best matches the members of the category. It is possible to have a feature detector or template for a concept without having any other concepts in the system. Categorizing an object may require comparing the relative degrees of match of the object to the representations for the candidate categories (Nosofsky, 1986), but if the categories themselves are represented by templates or feature detectors, then each can exist independently of the other categories.
A comparison of these representative examples of interrelated and isolated concepts suggests a useful heuristic for assessing degree of interrelatedness. A Concept X is dependent on Concept Y to the extent that Concept X cannot exist without Concept Y. If the concept Vermicelli is represented as “thinner pasta than spaghetti” then no system could possess Vermicelli without also possessing Spaghetti. However, if the concept Vermicelli is represented by “a long pasta with a typical diameter of 6 mm” then possession of the concept does not depend upon possession of Spaghetti. Partial degrees of dependency owe to the multi-faceted nature of conceptual representations. A person’s concept of Vermicelli may incorporate both characterizations given above, and the relative importance of these characterizations determines how much Vermicelli’s representation is affected by the presence or absence of a Spaghetti concept.
Prototypes and Caricatures
Consider the example of two categories shown in Figure 1. Categories A and B each have 6 members, and each member has a unique combination of values on Dimensions 1 and 2. We will define the prototype of a category as the central tendency of the category along each of dimensions (Posner & Keele, 1968; Reed, 1972). The prototype of Category A has a Dimension 1 value of 2, while Category B’s prototype has a value of 4. In the experiments that follow, we use uniform distributions of dimension values in constructing categories, and consequently our description of a category prototype remains the same if we define central tendency as the average or median.
------INSERT FIGURE 1 ABOUT HERE ------
We will define a caricature of a category as an object that assumes dimension values that depart from the central tendency of the category in the opposite direction of the central tendency of other simultaneously acquired concepts. In Figure 1, “X” represents the prototype of Category B, and “Y” represents a caricature of Category B. Y has a value of 5 on Dimension 1, and this value is a distortion of Category B’s central tendency in the direction opposite of Category A. This definition of caricature captures the intuitive notion of a caricature as an exaggeration. If Category B has a large value on Dimension 1 (relative to Category A), then the caricature of Category B exaggerates this large value, in the same way that a newspaper caricature exaggerates distinctive facial features of a politician.
The current experiments investigate the conditions under which the prototype or caricature of a category is more easily categorized. On the one hand, one might predict better categorization for the prototype because it is, by definition, the item that is most similar to the members of its category (Posner & Keele, 1968; Rosch, 1975). On the other hand, one might predict better categorization accuracy for the caricature because it emphasizes a distinctive value for a category. In fact, there have been several experiments that have found a categorization advantage for caricatures relative to prototypes (Goldstone, 1996; Nosofsky, 1991; Palmeri & Nosofsky, 2001; Rhodes, Brennan, & Carey, 1987).
Our current goal is not to argue that caricatures or prototypes are better categorized, but to identify experimental factors that modulate the benefit of one over the other. Specifically, experimental factors that promote relatively isolated concepts should tend to promote an advantage for prototypes over caricatures. In the absence of interconceptual influences, the representation that best exemplifies a concept will be its central tendency. If we try to represent Category B and do not know anything about Category A, then our best representation of Category B will be the point marked “X” in Figure 1. However, if a concept is characterized relative to other simultaneously acquired concepts, then characterizations of the form “Concept B members have relatively large Dimension 1 values compared to Concept A” will be formed. Caricatures fit these relational descriptions better than do prototypes. Nosofsky (1991) argued that classification of an object into a category depends on both its absolute similarity to members of the category, and its relative similarity to members of all of the candidate categories. The current experiments explore factors that affect the relative importance of these absolute and relative determinants of categorization.
We instantiate caricatures and prototypes by face stimuli that are formed using automatic morphing software developed by Steyvers (1999). An example of caricaturization using this software is shown in Figure 2. A prototypical bald head was generated by combining together 62 bald heads taken from Kayser (1997). To create this prototype without the blurred quality typical of superimposed face photographs (Busey, 1998; Galton, 1878), 127 defining points were found for each of the 62 heads, and the average location for each point was assigned to the average face. The gray scale values of corresponding pixels across the 62 heads were blended to create the gray scale values for the average face. The caricature (shown on the right in Figure 2) of a particular face (shown in the middle of Figure 2) was generated by taking each of the 127 defining points on the face, and distorting them by 20% away from the defining points on the average face. According to the framework of interrelated and isolated concepts, a representation of the actual face in Figure 2 that is relatively isolated from other face representations would tend to resemble the actual face itself. Conversely, if the actual face is represented relative to other faces, then its internal representation would tend to more resemble the caricature.
------INSERT FIGURE 2 ABOUT HERE ------
Manipulations of Conceptual Interrelatedness
The relative ease of categorizing prototypes and caricatures will be used as the measure of concept interrelatedness. The other main task is to develop experimental manipulations that are predicted to affect the interrelatedness of concepts. There already exists a literature suggesting such manipulations. Goldstone (1996) found that interrelated categories were promoted when 1) participants were encouraged to look for features that discriminated between the learned categories, 2), categories were alternated frequently, 3) participants were practiced categorizers, and 4) stimuli were relatively undistorted versions of the categories’ prototypes. In contrast, isolated categories were promoted when 1) participants were encouraged to form images of the categories, 2) categories were alternated rarely, 3) participants were relatively unpracticed, and 4) stimuli were highly distorted versions of the categories’ prototypes. Niedenthal and Beike (1997) explored whether people’s self-concepts were relatively independent of other people, or relationally defined. They found that self-concepts were relatively interrelated when participants were asked to consider their distinctive attributes, and when participants were younger siblings comparing themselves to older siblings rather than vice versa. McKenzie (1998, 1999) has explored the conditions under which finding out information about one hypothesis affects mutually exclusive alternative hypotheses. Even in situations where participants are told that a patient has one and only one of two candidate diseases, evidence that increases participants’ confidence that the patient has one disease does not always decrease confidence that the patient has the other disease. Presenting the two diseases concurrently rather than successively makes the diagnoses of the diseases more (negatively) dependent on one another, as does mentioning both diseases when participants make confidence judgments about each disease.
The current research explores two experimental manipulations that might be expected to affect concept interrelatedness. Experiment 1 manipulates the labels given to categories being acquired. One category is given a positive label (Club A) and the other category is given a negation label (Not Club A). Although this manipulation was used by Goldstone (1996), it has never been used with the caricature versus prototype measure of interrelatedness, and never used with naturalistic stimuli. Experiment 2 manipulates the order of learning categories, testing the hypothesis that the first learned category will be relatively isolated, while the second category tends to be characterized relative to the first category.
Experiment 1
Numerous studies have shown that the labels given to categories of objects influence the characterization of those categories (Harnad, 1987; Malt et al., 1999; Waxman, 1990; Wisniewski & Medin, 1994). One example that is particularly related to concept interrelatedness is the mutual exclusivity hypothesis (Markman, 1990; Waxman, Chambers, Yntema, & Gelman, 1989). Children adopting this hypothesis determine the referent of a noun by assuming that nouns are mutually exclusive, and consequently, if a new term is applied to one of two objects and one object already has a name, children will tend to assume that the term refers to the other object. Similar to Saussure’s (1915/1959) notion of competition between concepts, the mutual exclusivity hypothesis assumes that as one concept gains control of a conceptual region, its competitor concepts lose control of the region. This is the same competition that is predicted to make interrelated concepts increasingly characterized by their caricatures rather than prototypes. In both cases, a category is displaced away from another category.
Labeling may make pairs of concepts asymmetrically dependent on one another. One concept can be labeled “Category A” while another concept is labeled “not Category A.” In this case, the concept labeled “Not Category A” is predicted to be more influenced by “Category A” than vice versa (Clark, 1990). The concept that has a label that refers to another concept is predicted to be highly influenced by the referenced concept. Even though the category structures are symmetric, and the labels are randomly assigned to two categories, the “Not Category A” concept is predicted to be characterized more in terms of a caricature than the “Category A” concept. More precisely, there should be a tendency to associate the “Not Category A” concept with a stimulus that is more of a caricature than the stimulus associated with the “Category A” concept. There may be a bias to associate both categories with caricatures rather than prototypes (Goldstone, 1996; Palmeri & Nosofsky, 2001; Rhodes, Brennan, & Carey, 1987), but the extent of caricaturization is predicted to be greater for the “Not Category A” concept. The basis for this prediction comes from a combination of two assumptions: 1) the more dependent Concept A is on a mutually exclusive Concept B, the more Concept A’s characterization will be caricatured away from Concept B, and 2) explicitly labeling Concept A as not being Concept B makes Concept A dependent on Concept B.
Method
Participants. Sixty-two undergraduate students from IndianaUniversity served as participants in order to fulfill a course requirement. The students were split evenly into the two labeling conditions.
Materials. The stimuli were faces that were generated by morphing between photographs of two bald heads selected from Kayser (1997). Previous research has suggested that morphs generated from the two selected faces did not introduce conspicuous non-linearities between physical and psychological scalings (Goldstone & Steyvers, 2001). The morph sequence of 10 faces used is shown in Figure 3. Each of the morphs was automatically generated using a morphing technique described by Steyvers (1999). Applying this technique, the main contours in the face images were delineated by 127 control lines. These control lines served to align the features of the four faces. In the warping phase of this morphing algorithm, correspondences were calculated between the pixels of all the images to be morphed. Then, in the cross-dissolving phase, the gray scale values of corresponding pixels were blended to create the gray scale values of the resulting morph image. The faces on the left and right ends of Figure 3 are actual faces, and the 8 intermediate faces are blends of the two actual faces, with the proportion of the left face shifting from 10% to 90% along the series in equal 10% increments.