Supervised vs. unsupervised categorization: Two sides of the same coin?

Supervised and unsupervised categorization have been studied in separate research traditions. A handful of studies have attempted to explore a possible convergence between the two. The present research builds on these studies, by comparing the unsupervised categorization results of Pothos et al. (submitted; 2008) with the results from two procedures of supervised categorization. In two experiments, we tested 375 participants with nine different stimulus sets, and examined the relation between ease of learning of a classification, memory for a classification, and spontaneous preference for a classification. After taking into account the role of the number of category labels (clusters) in supervised learning, we found the three variables to be closely associated with each other. Our results provide encouragement for researchers seeking unified theoretical explanations for supervised and unsupervised categorization, but raise a range of challenging theoretical questions. 3 supervised vs. unsupervised categorization How similar are supervised processes to unsupervised ones? This debate has been central to many themes in psychology, such as associative learning (e.g., Rescorla & Wagner, 1972; Zwickel & Wills, 2002, 2005), connectionism (e.g., Kohonen, 1982; Rumelhart & McClelland, 1986), and language learning (e.g., Chater & Manning, 2006; Plunkett et al., 1997). In categorization, it concerns the distinction between supervised and unsupervised categorization. The former is about the learning of pre-specified categories. In a laboratory setting, an experimenter may have decided that certain stimuli are in one category, while other stimuli are in a different one. The objective of a participant is to learn which stimuli go to which category, usually through a process of corrective feedback (that is, a participant sees a stimulus, guesses its category membership, and receives feedback as to whether his/her guess was correct or not). In real life, arguably many linguistic categories are taught through a process of supervised categorization. For example, a child can learn that certain objects are oranges and other objects are lemons, by guessing the category membership of a relevant novel exemplar and subsequently receiving corrective feedback from an adult. A key aspect of supervised categorization is that there are no (apparent) limits on the complexity of the classifications which can be taught (e.g., Ashby, Queller, & Berretty, 1999; Maddox et al., 2004; McKinley & Nosofsky, 1995). Unsupervised categorization concerns the spontaneous impression we often have that a group of stimuli belong to the same category. Such an intuition is most obvious in perceptual grouping, whereby sometimes we have an immediate impression that there are clusters (e.g., see Figure 1; cf. Compton & Logan, 1999). With respect to real concepts, as with the perceptual grouping example of Figure 1, certain real life concepts are more coherent than others. For example, there is little ambiguity regarding membership into the 4 supervised vs. unsupervised categorization category of ‘chairs’. However, many naive observers will disagree as to what should be considered (a member of the concept) ‘literature’. In experimental studies of unsupervised categorization, participants are typically presented (sequentially or concurrently) with a set of stimuli and are asked to spontaneously classify them into either a fixed or unlimited number of groups. ---------------------------------------------------FIGURE 1--------------------------------------------------An issue of central theoretical importance in categorization research is whether a distinction between supervised and unsupervised categorization processes is meaningful. In other words, should we seek to understand and model supervised and unsupervised categorization processes in similar ways, taking into account, of course, the differences between the corresponding tasks (cf. Wills & Pothos, submitted)? Categorization researchers have mostly pursued the development of either supervised or unsupervised models of categorization (category acquisition in the former, but not the latter, is typically guided by corrective feedback to classification decisions). Hence, the implicit assumption is that supervised and unsupervised categorization processes ought to be understood in separate ways. For example, consider influential supervised categorization models, such as exemplar theory and prototype theory (Hampton, 2007; Minda & Smith, 2000; Nosofsky, 1988; see also, Kurtz, 2007; Vanpaemel & Storms, 2008), which assume that categorization of novel exemplars is driven by their similarity to either the members or the prototypes of the available categories. Similarity is typically computed as a function of distance in a putative psychological space. A key characteristic of such models is that they allow for the possibility that the process of category learning may transform the original psychological space, through the attentional weighting of different dimensions or overall stretching or compression of the space, so as to support the process 5 supervised vs. unsupervised categorization of category learning. For example, the attentional salience of a dimension would increase if it is highly diagnostic for a required classification (such transformations of the psychological space are plausibly driven by error correction mechanisms, not readily available in unsupervised categorization; cf. Goldstone, 1994). Models of unsupervised categorization also often employ a principle of similarity. For example, Pothos and Chater’s (2002) simplicity model is based on the idea of Rosch and Mervis (1975) that more obvious classifications should be ones for which within category similarity is maximum and between category similarity is minimum. Specifically, the model assumes that the similarities of all pairs of items that are in the same category should be greater than the similarities of all pairs of items that are between categories. The model predicts that if there are many and correct such ‘constraints’ then the resulting classification should be more intuitive. An alternative approach is to assume that category formation is driven by a prerogative to maximize the posterior probability of the particular feature combination of their members, given a particular category membership. For example, in the rational model classification of a novel instance depends on ( ) ( ), where P(k) is the prior probability of a category and P(F|k) the likelihood of observing the particular combination of object features given the category (Anderson, 1991; Sanborn, Griffiths, & Navarro, 2006; cf. Corter & Gluck, 1992). But, Pothos (2007) compared the rational model and the simplicity model and found that the predictions of these models converged across a wide range of stimulus sets. The above leads us to two intuitions regarding the relevant psychological principles in supervised and unsupervised categorization. First, both supervised and (some) unsupervised categorization models are based on some flavor of similarity. Second, however, in supervised categorization the similarity relations between the categorized 6 supervised vs. unsupervised categorization objects can be radically transformed, depending on the particular classification that is taught, but there has been no corresponding evidence in unsupervised classification. Regarding the latter, it only appears that in some cases the spontaneous classification of stimuli takes place on the basis of a single stimulus dimension (Ashby, Queller, & Berretty, 1999; Medin, Wattenmaker, & Hampson, 1987; Milton & Wills, 2004; Pothos & Close, 2008). SUSTAIN (Love, Medin, & Gureckis, 2004; see also Gureckis & Love, 2003) was the first attempt to provide a single computational framework for both supervised and unsupervised categorization. In SUSTAIN there are separate, but interlinked, components responsible for each type of categorization. Regarding unsupervised categorization, categories emerge for groups of items which are similar to each other. Supervised categorization is supported by a learning mechanism similar to that embodied in current versions of the exemplar theory (e.g., Nosofsky, 1988). The supervised and unsupervised components of SUSTAIN can interact with each other so that, for example, the learning of a classification can be affected by prior perceptions of how intuitive the classification is. Therefore, in SUSTAIN both supervised and unsupervised categorization are supported by a principle of similarity, but (presumably) the exemplar-based learning mechanism in the supervised component allows for greater representational flexibility in supervised categorization. SUSTAIN embodies a particular hypothesis for the relation between supervised and unsupervised categorization: they are related (because they are both based on similarity), but correspond to separate processes. A complementary possibility is that the same basic model serves both supervised and unsupervised categorization. For example, Pothos and Bailey (2009) presented such a proposal for the Generalized Context Model (GCM; Nosofsky, 1988), which is a well-known model of supervised categorization. 7 supervised vs. unsupervised categorization In summary, more recent work in categorization modeling has addressed more directly the problem of the relation between supervised and unsupervised categorization. Such work appears to favor a convergence between supervised and unsupervised categorization. However, it is exactly here that is the heart of the problem with this research: despite the excitement associated with the possibility that supervised and unsupervised categorization might be two sides of the same (psychological process) coin, there is still a paucity of relevant experimental results. In an early study, Homa and Cultice (1984) examined whether a set of categories, whose members were all distortions of the corresponding