Mathematical Social Sciences 38 1999 295–313
Modelling the dynamics of visual classification learning
¨ Alexander Unzicker , Martin Juttner, Ingo Rentschler
¨ ¨
¨ ¨
Institut f ur Medizinische Psychologie , Universitat Munchen, Munchen FRG, Goethestrasse 31, D-80336
Munich , Germany
Accepted 1 March 1998
Abstract
Classification learning of grey-level images is severely degraded in extrafoveal relative to foveal vision. Using a probabilistic virtual prototype PVP model we have recently demonstrated that
this deficit is related to a reduced perceptual dimensionality of extrafoveally acquired class ¨
concepts relative to that of foveally developed representations [Juttner, M., Rentschler, I., 1996. Reduced perceptual dimensionality in extrafoveal vision. Vision Research 36, 1007–1021]. Here
we show how the PVP technique can be extended to capture the dynamics of classification learning. Unlike former attempts at such a description our approach does not primarily aim at
modelling a learning curve, i.e., the gradual change of a global error measure. Rather it provides a means to trace the learning status of the observer by visualizing the changing pattern of
classification errors. This allows one to assess the cognitive strategies observers employ during concept learning.
1999 Elsevier Science B.V. All rights reserved.
Keywords : Classification learning; Dynamics; Virtual prototype; Cognitive stereotypes
1. Introduction
Psychophysical approaches to human vision have been endeavouring, over a long time, to characterize visual performance in terms of acuity measures, visual field and
contrast sensitivity. From a paradigmatic viewpoint, such a notion of visual processing can be related to tasks of detection or discrimination which are intrinsically character-
ized by a one-dimensional processing of stimulus information. Even in psychophysical models of spatial vision Thomas, 1985; Olzack and Thomas, 1986 which inherently
involve multidimensional representations in terms of multiple channel outputs, these
Corresponding author. Tel.: 149-89-5996-202; fax: 149-89-5996-615. E-mail address
: sascha.imp.med.uni-muenchen.de A. Unzicker 0165-4896 99 – see front matter
1999 Elsevier Science B.V. All rights reserved.
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. Unzicker et al. Mathematical Social Sciences 38 1999 295 –313
representations are typically reduced by some form of vector normalization to a single response variable, which then provides an index of visibility or discriminability. By
contrast, cognitive psychologists have traditionally preferred to define pattern recogni- tion as the ability to assign perceived objects to previously acquired categorical concepts
Bruner, 1957; Rosch, 1978. Such classifications in general require a simultaneous consideration of stimulus information along multiple stimulus dimensions Watanabe,
1985.
The distinction between the tasks of discrimination or detection on the one side and classification on the other seems to be more than a mere epistemological differentiation.
This has become evident in recent psychophysical studies on perceptual learning across ¨
the visual field Juttner and Rentschler, in preparation. Here for a common set of grey-level patterns compound-sinewave gratings, cf. Fig. 1 classification and discrimi-
nation performance were compared in foveal and extrafoveal 2.58 eccentric viewing. Whereas for a foveal presentation of the stimuli learning speed for the two types of tasks
was found to be equal, there was a clear dissociation in case of an extrafoveal presentation. Learning duration for pattern classification now increased by a factor of
five relative to the foveal condition, while it remained unaffected for pattern discrimina- tion. Such a divergence suggests that internal representations underlying pattern
classification and discrimination arise at distinct cortical levels in the brain, and that the former are normally developed within an extremely narrow visual field delimited to the
fovea.
To some extent these results bolster earlier psychophysical findings concerning foveal and extrafoveal character recognition Strasburger and Harvey Jr., 1991; Strasburger and
Rentschler, 1996. However, their novel contribution lies in that they provide an approach to pattern recognition from the perspective of concept learning, where subjects
are trained to assign hitherto unfamiliar patterns into predefined classes. Methodo- logically, this paradigm raises two major issues, namely: 1 how the internal class
concepts acquired during the training period can be related to physical stimulus properties; and 2 how the evolution of such mental concepts, i.e. the dynamics of
learning, can be adequately described.
In order to analyze the structure of the categorical concepts underlying classification we have developed a probabilistic virtual prototype PVP model Rentschler et al.,
1994. This model provides a technique for reconstructing internal representations of categories which observers develop during learning. More specifically, the PVP
approach assumes that human classification behaviour is based on internal feature states which can be linked to physical feature vectors. Physical and internal feature states are
coupled by additive stochastic error signals that can be estimated on the basis of the experimental classification data. Within this parametric approach adopted from technical
pattern classification Duda and Hart, 1973 pattern classes are represented as a distribution of feature vectors around a mean vector, the so-called class prototype.
Analogously, perceptual concepts of classes are described by corresponding distributions of internal feature states, the mean values of which are referred to as virtual prototypes.
Human classification behaviour, then, is described in terms of a Bayesian classifier operating on such internal class representations.
A . Unzicker et al. Mathematical Social Sciences 38 1999 295 –313
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The PVP approach provides a parsimonious description of classification behaviour based on a similarity concept which, on the one hand, is based on a stimulus-dependent
physical signal description, and on the other hand includes observer-dependent cognitive biases. As an important property it allows inferences about the dimensionality or the
degrees of freedom characterizing internal class concepts. In particular, it was shown that the perceptual dimensionality of extrafoveally acquired class concepts is distinctive-
¨ ly reduced relative to foveally developed representations Juttner and Rentschler, 1996.
The adequateness of the PVP model within the domain of psychophysical classification also has been demonstrated by Unzicker et al. 1998 in a comparative evaluation of
various standard models in the classification literature, including prototype approaches, exemplar-based models, General Recognition Theory and HyperBf-Networks.
In all non-trivial cases, the learning of class concepts does not occur instantaneously. A certain limitation of the current version of the PVP approach can be seen in that so far
it has been mainly applied to experimental classification data cumulated across the entire training procedure. Consequently, the data base only provides some sort of average error
profile an observer reveals during the learning process. In the concrete case of extrafoveal classification the training often extends over several hours, and learning
often proceeds in a seemingly non-continuous and irregular manner. Such a behaviour makes it desirable to find ways for analyzing classification data beyond the standard
method of visualization in form of a learning curve. What is needed is a method to track the evolution of class concepts as they emerge during the training.
In this article we propose how such a description concerning the dynamics of learning can be obtained. The primary scope of the paper is to achieve this goal within the
framework of the PVP model. However, it should be clear that the basic issue of modelling learning processes also arises in the context of other standard models in the
classification literature although this problem so far has been largely ignored. In the following, we will first restate the basic assumptions of the PVP approach. On this basis
we show how such an analysis can be extended to capture the dynamics of learning. The method will be illustrated by applying it to samples of psychophysical classification data.
Finally, the results will be discussed in the context of alternative approaches to perceptual classification and learning.
2. The probabilistic virtual prototype approach
