Similarity and Taxonomy in Categorization

Similarity and Taxonomy in Categorization Timothy Verbeemen (timothy.verbeemen@psy.kuleuven.ac.be) Departement Psychologie, K.U. Leuven, Tiensestraat 102 B-3000 Leuven, Belgium Gert Storms (gert.storms@psy.kuleuven.ac.be) Departement Psychologie, K.U. Leuven, Tiensestraat 102 B-3000 Leuven, Belgium Tom Verguts (tom.verguts@ugent.be) Vakgroep Experimentele Psychologie, Ghent University, H. Dunantlaan 2 B-9000 Ghent, Belgium Abstract In this paper, a two by three approach to modeling categorization is presented. Similarity representations based upon a geometric, an additive tree and an additive cluster model are combined with an exemplar model and a prototype model in a single approach. The six models are applied to the categorization of pictorial known and unknown fruits and vegetables (Smits et al., 2002). For novel stimuli, the geometric exemplar model and the cluster models gave the best account, indicating a strategy where people compare stimuli with stored members on more general continua or a limited set of features. For well-known stimuli, the tree-based models gave the best account of the data, suggesting more elaborate taxonomic knowledge. More generally, the results show that different categorization models may perform better for different sets of stimuli, and that a systematic empirical comparison of such models is needed. Introduction A major contribution of categorization research over the last decades has been to establish the relation between similarity and categorization. Rosch and Mervis’ (1975) seminal paper on the graded structure of categories showed that categories are ill-defined, and that the extent to which an instance of a category is seen as a typical member is positively related to similarity towards the category in question and inversely related to similarity towards relevant contrast categories (e.g., Verbeemen et al., 2001). Given the importance of similarity in categorization, a formal model should take a clear stance on two issues: The nature of similarity computation and the relevant objects of comparison in this calculation. First, the model must make assumptions about the nature of similarity, especially when the structure of the stimuli under investigation is not experimentally controllable. There are two main approaches to similarity, geometric and feature-based. The geometric approach (e.g., Carroll & Arabie, 1980; Shepard, 1964) represents stimuli in abstract space where similarity is inversely related to the distance between stimuli. In the feature-based approach (e.g. Shepard & Arabie, 1979; Tversky, 1977), similarity is considered a function of feature overlap, where commonalities increase and differences decrease overall similarity. Second, a model should specify the objects used in similarity calculation. In particular, information employed in making category decisions may be stored at the category level, or it may be stored at the level of individual instances of a category. The former approach is known as the prototype view (e.g., Hampton, 1979; Smith & Minda, 1998), and the latter as the exemplar view (e.g., Medin & Schaffer, 1978; Nosofsky, 1986). In this paper, we argue for a systematic evaluation of these formal models in a two by three approach that compares prototype and exemplar models on the one hand, and geometric and feature representations on the other hand. The Generalized Context Model and a Geometric Prototype Model In the generalized context model (GCM; Nosofsky, 1984, 1986, 1992), an exemplar model, categorization is assumed to be a function of similarity towards all relevant stored exemplars. In case (physical) dimensions are unavailable, the GCM fitting procedure starts with a multidimensional scaling procedure (MDS; Borg & Groenen, 1997) on proximity measures of all stimuli involved. The coordinates of these stimuli are then used as input for the model. In the case of two categories, A and B, the probability that stimulus x is classified in category A is given by: P(A | X) = β A η XA β A η XA + ( 1 − β A ) η XB where β Α lies between 0 and 1 and serves as a response bias parameter towards category A. The parameters η XA and η XB denote the similarity measures of stimulus x toward all stored exemplars of category A and B, respectively: η XA = j ∈ A   D exp −  c  w k y xk − y jk    k = 1 1 / r  r   with y xk and y jk as the coordinates of stimulus x and the j-th stored exemplar of category A (or B for η XB , respectively) on dimension k. The weight of the k-th dimension is denoted by w k , with all weights restricted to sum to 1. The power