categories. That is, since cue validity is the probability of being in some category given some property, this probability will increase (or at worst not decrease) as the size of the category increases (e.g. the probability of being an animal given the property of flying is greater than the probability of bird given flying, since there must be more animals that fly than birds that fly).6 The idea that cohesive categories maximize the probability of particular properties given the category fares no better. In this case, the most specific categories will always be picked out. Medin (1982) has analyzed a variety of formal measures of category cohe­ siveness and pointed out problems with all of them. For example, one possible principle is to have concepts such that they minimize the similarity between contrasting categories; but minimizing between-category similarity will always lead one to sort a set of n objects into exactly two categories. Similarly, functions based on maximizing within-category similarity while minimizing between-category similarity lead to a variety of problems and counterintuitive expectations about when to accept new members into existent categories versus when to set up new categories. At a less formal but still abstract level, Sternberg (1982) has tried to translate some of Goodman's (e.g. 1983) ideas about induction into possible constraints on natural concepts. Sternberg suggests that the apparent naturalness of a concept increases with the familiarity of the concept (where familiarity is related to Goodman's notion of entrenchment), and decreases with the number of transformations specified in the concept (e.g. aging specifies certain trans­

Concepts and Concept Formation

Similarity, Separability, and the Triangle Inequality

This state of the art report focuses on glyph-based visualization, a common form of visual design where a data set is depicted by a collection of visual objects referred to as glyphs. Its major strength is that patterns of multivariate data involving more than two attribute dimensions can often be more readily perceived in the context of a spatial relationship, whereas many techniques for spatial data such as direct volume rendering find difficult to depict with multivariate or multi-field data, and many techniques for non-spatial data such as parallel coordinates are less able to convey spatial relationships encoded in the data. This report fills several major gaps in the literature, drawing the link between the fundamental concepts in semiotics and the broad spectrum of glyph-based visualization, reviewing existing design guidelines and implementation techniques, and surveying the use of glyph-based visualization in many applications.

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Glyph-based Visualization: Foundations, Design Guidelines, Techniques and Applications

https://groups.psych.northwestern.edu/gentner/papers/GoldstoneMedinGentner91.pdf

Relational similarity and the nonindependence of features in similarity judgments.

In this article, the relation between the identification, similarity judgment, and categorization of multidimensional perceptual stimuli is studied. The theoretical analysis focused on general recognition theory (CRT), which is a multidimensional generalization of signal detection theory. In one application, 2 Ss first identified a set of confusable stimuli and then made judgments of their painvise similarity. The second application was to Nosofsky's (1985b, 1986) identificationcategorization experiment. In both applications, a GRT model accounted for the identification data better than Luce's (1963) biased-choice model. The identification results were then used to predict performance in the similarity judgment and categorization conditions. The GRT identification model accurately predicted the similarity judgments under the assumption that Ss allocated attention to the 2 stimulus dimensions differently in the 2 tasks. The categorization data were predicted successfully without appealing to the notion of selective attention. Instead, a simpler GRT model that emphasized the different decision rules used in identificatio n and categorization was adequate. The perceptual processes involved when subjects identify, categorize, or judge the pairwise similarity of multidimensional perceptual stimuli are closely related (e.g., Ashby & Perrin, 1988; Getty, Swets, Swets, & Green, 1979; Nosofsky, 1986; Shepard & Chang, 1963; Shepard, Hovland, & Jenkins, 1961). Roughly speaking, as the similarity between a pair of stimuli increases, so too does the probability that one will be misidentified as the other and the probability that they will be assigned to the same category. This observation suggests a possible close relationship between these three tasks. During the past several years, a number of theories have been developed that attempt to simultaneousl y account for data from all three of these tasks. Such theories are important because they represent attempts to integrate a broad spectrum of psychological data within one theoretical framework. In this article, we (a) explore the empirical relation between identification, categorization, and similarity judgment and (b) examine the ability of the more powerful of these theories to predict categorization performance and judgments of perceived similarity from the confusions that subjects make in an identification task. The models that we focus most heavily on are derived from general recognition theory (GRT; Ashby & Gott, 1988; Ashby & Perrin, 1988; Ashby & Townsend, 1986). They assume that the perceptual effect associated with each presentation of a stimulus can be represented as a point in a multidimensional space but that perceptual noise causes the percept to vary over trials. Thus, GRT assumes that a distribution of percepts is the appropriate perceptual representation of a stimulus. During identification or categorization, the subject is assumed to

/pdf/predicting-similarity-and-categorization-from-identification-4f9ospkuvr.pdf

Predicting similarity and categorization from identification.

Publisher Summary This chapter discusses the relation between stimulus analyzability and perceived dimensional structure. The combination of integral dimensions yields stimuli that are phenomenologically fused or wholistic, whereas the combination of separable dimensions yields stimuli with perceptually distinct components. Operationally, integral dimensions produce a Euclidean metric in direct distance scaling, classifications based on a distance or similarity structure in a restricted classification task, a redundancy gain in speeded classification when the dimensions are correlated, and interference in a filtering task when the dimensions are orthogonal and selective attention is required. Some dimensional combinations meet these operational criteria extremely well; value and chroma of a single Munsell chip uniformly produce results that are consistent with the operational definition of integral dimensions and, similarly, size of circle and angle of radial line are clearly separable. The evaluation of the subjective independence of dimensional combinations by the algebraic properties of the additive difference model is important in drawing the distinction between integral and separable dimensions.

Willa Kay Wiener-Ehrlich

Papers

The Relation Between Stimulus Analyzability and Perceived Dimensional Structure1

An analysis of generative representation systems