Is Competitive Learning an Adequate Account of Free Classification?

Is Competitive Learning an Adequate Account of Free Classification? Jan Zwickel (jzwickel@ix.urz.uni-hd.de) Department of Psychology, Hauptstrase 47-51 69117 Heidelberg, Germany A.J. Wills (a.j.wills@ex.ac.uk) School of Psychology, University of Exeter Perry Road, Exeter. EX4 4QG. England. Abstract Rumelhart & Zipser's (1986) competitive learning algorithm is an account of unsupervised learning and, as such, might be considered a potential model of free classification behavior in humans. However, selective learning effects (e.g. Dickinson, Shanks & Evenden, 1984) suggest that human learning, at least under conditions of feedback, may be better characterized by an error-correcting system. An experiment is reported that provides preliminary evidence for the existence of a selective learning effect in free classification. Simulations indicate that Rumelhart & Zipser's algorithm does not provide an adequate account of the behavior observed, whilst an error-correcting variant of competitive learning does. Introduction Free classification, or free sorting as it is also called, is a procedure in which human participants are presented with a set of stimuli and are asked to group them in any way that seems sensible or reasonable to them (e.g. Bersted, Brown & Evans, 1969; Regehr & Brooks, 1995; Wills & McLaren, 1998). It may be contrasted with the more standard experimental task of category learning via trial-specific feedback that has been the dominant mode of enquiry into humans' categorization abilities for the last fifty years (e.g. Bruner, Goodnow & Austin, 1956; Medin & Schaffer, 1978; Wills, Reimers, Stewart, Suret & McLaren, 2000). The study of categorization under conditions where each decision receives immediate feedback from a totally reliable source has allowed psychologists great control over the structure of the categories participants acquire. As a methodology, it has been successful in broadening our understanding of the category learning process. However, the level of feedback available in such tasks seems higher than that available in many real-world situations, begging the question of whether what we have learned about the categorization process will generalize to situations where the feedback is absent or scarce. An interesting parallel may be drawn with the sort of connectionist systems that have been proposed for learning in the presence or absence of feedback. For example, Rumelhart & Zipser's (1986) competitive learning model is an unsupervised system. It extracts statistical regularities in the input to form categorical representations, and does so in the absence of feedback. In contrast, McClelland & Rumelhart's (1985) model is a supervised system. It can be taught multiple categories (cat vs. dog vs. bagel in their example) but learns to categorize because each stimulus is accompanied by an externally-provided category label. One of the differences between these two models is the nature of the weight-update algorithms they employ. McClelland & Rumelhart (1985) employ an error- correcting algorithm, where the size of the weight change is proportional to the mismatch between an external teaching signal and internal inputs. In other words, learning only occurs when the system fails to fully predict the teaching signal. Specifically, ∆ w ij = η ( e i − i i ) a j where ∆w ij is the change in the strength of the connection from unit j to unit i, e i is the external teaching signal to unit i, a j is the activity of unit j, and i i is the total internal input to unit i, this being calculated as i i = ∑ a j w ij j In contrast, Rumelhart & Zipser's algorithm does not employ error-correction in this sense. Rumelhart & Zipser use the internal input to determine which unit is the winner and then change weights to the winning unit by an amount proportional to the difference between the current weight of that connection and an asymptote 1 . Specifically, the change in weight from unit j to the winning unit is Rumelhart & Zipser (1986) also discuss a variant where connections to the losing unit are also changed via Equation 3, but with a much lower learning rate. The current article concentrates on the winner-only version, although the conclusions drawn are valid for both variants.