An Exemplar-Based Random Walk Model of Perceptual Categorization

The Exemplar-Based Random Walk (EBRW) model (Nosofsky & Palmeri, 1997; Palmeri, 1997) incorporates elements of Nosofsky’s (1986) generalized context model (GCM) of categorization and Logan’s (1988) instance theory of automaticity. The model assumes that categories are represented in terms of stored exemplars. Exemplars are represented as points in a multidimensional psychological space with similarity a decreasing function of distance in the space. During categorization, exemplars race to be retrieved from memory with rates determined by their similarity to the presented object. Memory retrieval drives a random walk decision process. The model accounts for categorization response times and accuracies in a variety of tasks. Moreover, it accounts for the development of automaticity in categorization and for categorization in cluttered environments. Recent years have seen tremendous progress developing powerful psychological theories of perceptual categorization. However, as competing theories have become increasingly sophisticated it has become increasingly difficult to contrast their predictions − theories which differ rather markedly in their assumptions about category representations and decision processes can nevertheless make strikingly similar predictions of categorization response probabilities. One fundamental limitation of most current theories is that they offer no account of the time course of categorization judgments. Therefore, one aim of recent theoretical work has been to develop dynamic theories which can account for categorization response times (RTs) as well as categorization accuracies. In addition to addressing the need to develop more complete theories of categorization, examination of response times may prove to be fertile territory for testing the representational and processing assumptions of various theories. In this article, I describe a recently developed model of categorization, the Exemplar-Based Random Walk (EBRW) model (Nosofsky & Palmeri, 1997; Palmeri, 1997). The model assumes that categories are represented in term of the individual instances which have been experienced; in this way, it differs markedly from theories of categorization which posit that prototypes, rules, or other forms of abstract knowledge underlie categorization. Categorization decisions are determined by the similarity between a presented item and stored category exemplars. In this article, I begin by providing an overview of the EBRW and describing several successful applications of the model. I then describe some recent extensions of the model to categorization tasks involving multiple objects in the visual field. Theoretical Background The EBRW (Nosofsky & Palmeri, 1997; Palmeri, 1997) combines elements of the Generalized Context Model (GCM) of categorization (Nosofsky, 1986) and the Instance Theory of automaticity (Logan, 1988). The theoretical claim of the EBRW is that both categorization and automaticity are manifestations of the same exemplar-based memory retrieval processes. Below, I briefly discuss these two models and then describe the EBRW in some detail. The Generalized Context Model (GCM) The GCM (Nosofsky, 1986) is an exemplar-based model of categorization. The model assumes that people represent categories in memory in terms of fairly detailed information about specific instances (exemplars) they have experienced. When judging whether an object is a member of some category, a person compares the object with similar stored exemplars. The object is classified according to its relative similarity to the objects in the various categories. The GCM stands as one of the most successful theories of categorization in the field today. Not only has the GCM accounted for fundamental categorization phenomena, but it has provided an integrated theory of recognition memory, stimulus identification, and typicality judgments. However, although powerful in its ability to predict accuracy in a wide variety of tasks, the GCM is limited in providing no account of how processing unfolds over time − that is, the theory cannot predict the amount of time it takes to make a categorization response. The Instance Theory of Automaticity According to Logan’s (1988) instance theory, automaticity in some aspect of cognition reflects shifts from algorithmic or strategic processes to memory-based processes. People are assumed to start with some set of general algorithms, strategies, or rules that solve a particular task, such as categorization. Every time some cognitive skill is performed, a trace of the instance of that action is stored in memory. When a new object is encountered to be categorized or judged in some way, a race ensues between Published in Proceedings of the Interdisciplinary Workshop On Similarity And Categorisation (1997) University of Edinburgh, Scotland 2 the strategy and retrieval of previously stored instances. Initially, performance is governed solely by strategic processing. Memory retrieval is assumed to get faster as more repetitions of a particular instance are stored whereas the time for strategic processing is assumed to remain constant. Soon, memory retrieval begins to dominate the race over strategic processing. In essence, novices must solve the task using explicit strategies whereas experts simply remember what they did before. Qualitative changes in performance are due to shifts from strategic processing to memory retrieval. Quantitative changes in processing speed, often characterized by a power law of practice, are due to more instances being added to memory (Logan, 1992). However, although elegant in its simplicity, and powerful in its predictions, instance theory is limited by not taking into account graded similarities among exemplars and not allowing for response competition to emerge. The Exemplar-Based Random Walk Model The EBRW combines elements of the GCM and instance theory. It embeds a dynamic similarity-based memory retrieval mechanism within a competitive random walk decision process. The EBRW is one of the first models to make quantitative predictions of both categorization response time (RT) and accuracy. It is also unique in providing a unified account of a variety cognitive tasks. Following the GCM, exemplars are represented as points in a multidimensional psychological space. Typically, this psychological space is derived through multidimensional scaling or other techniques (Shepard, 1980). Similarity between objects is a decreasing function of distance in the space. Distance between exemplars i and j is given by