Cue Preference in a Mulitdimensional Categorization Task

C ue Preference in a M ultidim ensional C ategorization Task Patricia M . Berretty (berretty@ fordham .edu) D epartm ent of Psychology, Bronx, NY 10458-5198 USA A bstract M any natural categories vary along m ultiple dim ensions. The present studies address tw o m ain questions underlying categorization w ith m ultiple dim ensions. First, how w ell can hum ans perform in a categorization task consisting of five categories varying along nine continuously valued dim ensions? Second, w hat are the properties of the cues preferred by hum ans if not all the available cues are used? Rem arkably, participants not only learned to distinguish am ong the five categories, but they also learned to do so using only the relevant dim ensions. A satisficing m odel of categorization w as bestable to account for participants’ responses. In addition, in a cue preference task, the results show ed that nearly all participants preferred to use the dim ension w ith the greatest variance w hen the num ber of dim ensions available w as restricted, in accord w ith predictions m ade by the satisficing m odel. dim ensions. Therefore, an im portant step in such algorithm s is determ ining w hich dim ensions from the set of possible dim ensions should be used. H ow ever, the different m ethods used to m odel this step usually involve com plex com putations and thus are also not psychologically plausible. W hat follow s is a brief review of tw o popular categorization m odels (exem plar m odels and decision bound theory), as w ell as a review of a satisficing m odel of categorization (categorization by elim ination). N ext, a multi-dim ension, m ulti-category task is described, including a discussion of how w ell the above three m odels can account for hum an responses in such a task. The paper concludes w ith a brief discussion on the learning of relevant cues in the m ulti-dim ension, m ulti- category task. R eview of M odels Introduction Categorization has been studied by m any disciplines including psychology and m achine learning. In the area of psychology, the psychological processes underlying hum an categorization have been investigated. O ne com m on approach to determ ining these processes has been to teach hum ans to learn novel categories based on very sim ple stim uli that vary along only a few dim ensions. In such sim ple situations, the com plex calculations involved in som e of the popular m odels of categorization (e.g., N osofsky’s (1986) generalized context m odel; A shby’s (A shby & G ott, 1988; A shby & Perrin, 1988) decision bound theory) m ay be psychologically plausible. H ow ever, the results of these experim ents are then assum ed to be generalizable to categories w hose m em bers vary along m any dim ensions. It seem s unreasonable to assum e that hum ans are capable of the even m ore com plex calculations required w ith an increase in category dim ensionality. For exam ple, N osofsky, Palm eri, and M cK inley (1994) “question the plausibility of exem plar storage processes and the vast m em ory resources that they seem to require” (p.53). M achine learning, on the other hand, has been prim arily concerned w ith developing algorithm s based on experts in specific dom ains (Q uinlan, 1986) -- although the algorithm s them selves tend to be general-purpose algorithm s (i.e., the algorithm s are intended to apply to any categorization task). These algorithm s have been developed using large data sets that vary along m any Exem plar M odels Exem plar m odels (Brooks, 1978; Estes, 1986; M edin & Schaffer, 1978; N osofsky, 1986) assum e that w hen presented w ith a novel object, hum ans com pute the sim ilarity betw een that object and all exem plars of every category in w hich the novel object could be placed. In theory, the object is placed into the category w ith w hich it is m ost sim ilar, how ever m ost exem plar m odels assum e probability m atching. N osofsky’s (1986) generalized context m odel (G CM ) allow s for variation in the am ount of attention given to different features during categorization (see also M edin & Schaffer, 1978). Therefore, it is possible that different cues w ill be used in different tasks. H ow ever, this attention w eight rem ains the sam e for the entire stim ulus set for each particular categorization task, rather than varying across different objects belonging to the sam e category. G CM uses a probabilistic response rule based on the Luce-Shepard choice m odel. The probability of placing stim ulus i into category j is com puted by sum m ing the sim ilarity betw een stim ulus i and all objects in category j along every dim ension and then w eighting the sum m ed sim ilarity by the bias to respond w ith category j. The w eighted sum m ed sim ilarity is divided by the sum of the w eighted sum m ed sim ilarity of stim ulus i to each category. Sim ilarity is usually either an exponential (for separable stim uli) or gaussian (for integral stim uli) function of psychological distance (Shepard, 1964). Psychological