Absolute identification with simple and complex stimuli

It is well known that people can perfectly identify only a handful of distinct unidimensional stimuli, such as line lengths, but can identify thousands of complex stimuli, such as letters and words. This result is consistent with capacity limits in identifying unidimensional stimuli but not complex stimuli. The experiments reported here tested this theoretical dissociation using Luce's (1963) Similarity Choice Model to measure the psychological distance between stimuli in line-length-identification and letter-identification tasks. The psychological distance between line-length stimuli decreased with the number of to-be-identified stimuli; this result is concordant with capacity limits in unidimensional absolute identification. Surprisingly, the opposite result held in letter identification. Psychological distance between letters increased with an increased number of to-be-identified stimuli. This result indicates an opposite type of processing deficit: People process letters more efficiently with more choices.     

Relative judgment and knowledge of the category structure

For evenly spaced stimuli, a purely relative judgment account of unidimensional categorization performance is trivial: All that is required is knowledge of the size of stimulus difference corresponding to the width of a category. For unevenly spaced stimuli, long-term knowledge of the category structure is required. In the present article, we will argue that such knowledge does not necessitate a direct, absolute mapping between (representations of ) stimulus magnitudes and category labels. We will show that Stewart, Brown, and Chater’s (2005) relative judgment model can account for data from absolute identification experiments with uneven stimulus spacing.     

Absolute identification by relative judgment

In unidimensional absolute identification tasks, participants identify stimuli that vary along a single dimension. Performance is surprisingly poor compared with discrimination of the same stimuli. Existing models assume that identification is achieved using long-term representations of absolute magnitudes. The authors propose an alternative relative judgment model (RJM) in which the elemental perceptual units are representations of the differences between current and previous stimuli. These differences are used, together with the previous feedback, to respond. Without using long-term representations of absolute magnitudes, the RJM accounts for (a) information transmission limits, (b) bowed serial position effects, and (c) sequential effects, where responses are biased toward immediately preceding stimuli but away from more distant stimuli (assimilation and contrast).     

Stimulus-specific learning: disrupting the bow effect in absolute identification

The bow effect is ubiquitous in standard absolute identification experiments; stimuli at the center of the stimulus-set range elicit slower and less accurate responses than do others. This effect has motivated various theoretical accounts of performance, often involving the idea that end-of-range stimuli have privileged roles. Two other phenomena (practice effects and improved performance for frequently-presented stimuli) have an important but less explored consequence for the bow effect: Standard within-subjects manipulations of set size could disrupt the bow effect. We found this disruption for stimulus types that support practice effects (line length and tone frequency), suggesting that the bow effect is more fragile than has been thought. Our results also have implications for theoretical accounts of absolute identification, which currently do not include mechanisms for practice effects, and provide results consistent with those in the literature on stimulus-specific learning.     

Diversion of attention in everyday concept learning: Identification in the service of use

Many people tend to believe that natural categories have perfectly predictive defining features. They do not easily accept the family resemblance view that the features characteristic of a category are not individually sufficient to predict the category. However, common category-learning tasks do not produce this simpler-than-it-is belief. If there is no simple classification principle in a task, the participants know that fact and can report it. We argue that most category-learning tasks in which family resemblance categories are used fail to produce the everyday simpler-than-it-is belief because they encourage analysis of identification criteria during training. To simulate the learning occurring in many natural circumstances, we developed a procedure in which participants' analytic activity is diverted from the way in which the stimuli are identified to the use to which the stimuli will be put. Finally, we discuss the prevalence of this diverted analysis in everyday categorization.     

Choice and response time processes in the identification and categorization of unidimensional stimuli

Lacouture and Marley (1991, 1995, 2001) have successfully modeled the probabilities of correct responses and the mean correct response times (RTs) in unidimensional absolute identification tasks for various stimulus ranges and stimulus/response set sizes, for individual and group data. These fits include those to a set of phenomena often referred to as end-anchor effects. A revised model, with the independent accumulator decision process replaced by a leaky competing accumulator decision process, fits the probabilities of correct responses and the full distributions of RTs in unidimensional absolute identification. The revised model is also applied successfully to a particular class of unidimensional categorization tasks. We discuss possible extensions for handling sequential effects in unidimensional absolute identification, and other extensions of the given class of categorization tasks that are of potential empirical and theoretical importance as a supplement to the study of multidimensional absolute identification tasks.     

Purely relative models cannot provide a general account of absolute identification

Unidimensional absolute identificatio—identifying a presented stimulus from an ordered set—is a common component of everyday tasks. Laboratory investigations have mostly used equally spaced stimuli, and the theoretical debate has focused on the merits of purely relative versus purely absolute models. Absolute models incorporate substantial knowledge of the complete set of stimuli, whereas relative models allow only partial knowledge and assume that each stimulus is compared with recently observed stimuli. We test and refute a general prediction made by relative models, that accuracy is very low for some stimulus sequences when the stimuli are unequally spaced. We conclude that, although relative judgment processes may occur in absolute identification, a model must incorporate long-term referents to explain performance with unequally spaced stimuli. This implies that purely relative models cannot provide a general account of absolute identification.     

Comparing Exemplar- and Rule-Based Theories of Categorization

ABSTRACT— We address whether human categorization behavior is based on abstracted rules or stored exemplars. Although predictions of both theories often mimic each other in many designs, they can be differentiated. Experimental data reviewed does not support either theory exclusively. We find participants use rules when the stimuli are confusable and exemplars when they are distinct. By drawing on the distinction between simple stimuli (such as lines of various lengths) and complex ones (such as words and objects), we offer a dynamic view of category learning. Initially, categorization is based on rules. During learning, suitable features for discriminating stimuli may be gradually learned. Then, stimuli can be stored as exemplars and used to categorize novel stimuli without recourse to rules.     

On the dominance of unidimensional rules in unsupervised categorization.

In several experiments, observers tried to categorize stimuli constructed from two separable stimulus dimensions in the absence of any trial-by-trial feedback. In all of the experiments, the observers were told the number of categories (i.e., two), they were told that perfect accuracy was possible, and they were given extensive experience in the task (i.e., 800 trials). When the boundary separating the contrasting categories was unidimensional, the accuracy of all observers improved significantly over blocks (i.e., learning occurred), and all observers eventually responded optimally. When the optimal boundary was diagonal, none of the observers responded optimally. Instead they all used some sort of suboptimal unidimensional rule. In a separate feedback experiment, all observers responded optimally in the diagonal condition. These results contrast with those for supervised category learning; they support the hypothesis that in the absence of feedback, people are constrained to use unidimensional rules.     

Acquisition of a relative class concept by an African gray parrot (Psittacus erithacus): discriminations based on relative size

We report that an African gray parrot (Psittacus erithacus), Alex, responds to stimuli on a relative basis. Previous laboratory studies with artificial stimuli (such as pure tones) suggest that birds make relational responses as a secondary strategy, only after they have acquired information about the absolute values of the stimuli. Alex, however, after learning to respond to a small set of exemplars on the basis of relative size, transferred this behavior to novel situations that did not provide specific information about the absolute values of the stimuli. He responded to vocal questions about which was the larger or smaller exemplar by vocally labeling its color or material, and he responded "none" if the exemplars did not differ in size. His overall accuracy was 78.7%.     

Do bantams (Gallus gallus domesticus) amodally complete partly occluded lines? An analysis of line classification performance

Humans perceive a line touching an edge of a large rectangle longer than the reality. Kanizsa (1979) has suggested that this illusion occurs because we perceive that the line is partly "hidden" behind the rectangle and automatically completes it. We tested whether bantams (Gallus gallus domesticus) would experience this perceptual phenomenon using a line classification task on the touch monitor, which was used in our previous study with rhesus monkeys and pigeons (Fujita, 2001). We trained three bantams to classify six lengths of black target lines into two categories, "short" or "long," ignoring a gray rectangle (Experiment 1) or a gray area (i.e., a left or a right half of the monitor was filled with gray; Experiment 2) located at the same distance (8 pixels) from the target line. In the test, the gap between the line and the gray rectangle (or area) sometimes changed (0, 4, or 8 pixels; we labeled these stimuli as G0, G4, and G8 respectively). Both of the two successfully trained bantams showed an illusion for G0, but the direction of illusion was reversed; that is, they judged the line in G0 to be "shorter" than that in G4 and G8. Further analyses proved that neither the gaps between the target line and the gray rectangle nor the total widths of the stimuli could account for the bantams' responses. These results suggest that bantams do not complete the "occluded" portion even when identification of its shape is not required.     

Fechnerian metrics in unidimensional and multidimensional stimulus spaces

A new theory is proposed for subjective (Fechnerian) distances among stimuli in a continuous stimulus space of arbitrary dimensionality. Each stimulus in such a space is associated with a psychometric function that determines probabilities with which it is discriminated from other stimuli, and a certain measure of its discriminability from its infinitesimally close neighboring stimuli is computed from the shape of this psychometric function in the vicinity of its minimum. This measure of discriminability can be integrated along any path connecting any two points in the stimulus space, yielding the psychometric length of this path. The Fechnerian distance between two stimuli is defined as the infimum of the psychometric lengths of all paths connecting the two stimuli. For a broad class of models defining the dichotomy of response bias versus discriminability, the Fechnerian distances are invariant under response bias changes. In the case in which physically multidimensional stimuli are discriminated along some unidimensional subjective attribute, a systematic construction of the Fechnerian metric leads to a resolution of the long-standing controversy related to the numbers of just-noticeable differences between isosensitivity curves. It is argued that for unidimensional stimulus continua, the proposed theory is close to the intended meaning of Fechner's original theory.     

On the dominance of unidimensional rules in unsupervised categorization

In several experiments, observers tried to categorize stimuli constructed from two separable stimulus dimensions in the absence of any trial-by-trial feedback. In all of the experiments, the observers were told the number of categories (i.e., two), they were told that perfect accuracy was possible, and they were given extensive experience in the task (i.e., 800 trials). When the boundary separating the contrasting categories was umdimensional, the accuracy of all observers improved significantly over blocks (i.e., learning occurred), and all observers eventually responded optimally. When the optimal boundary was diagonal, none of the observers responded optimally. Instead they all used some sort of suboptimal unidimensional rule. In a separate feedback experiment, all observers responded optimally in the diagonal condition. These results contrast with those for supervised category learning; they support the hypothesis that in the absence of feedback, people are constrained to use unidimensional rules.     

How do people order stimuli?

People may find it easier to construct an order after first representing stimuli on a scale or categorizing them, particularly when the number of stimuli to be ordered is large or when some of them must be remembered. Five experiments tested this hypothesis. In two of these experiments (1 and 3), we asked participants to rank line lengths or to rank photographs by artistic value. The participants provided evidence of how they performed these tasks, and this evidence indicated that they often made use of some preliminary representation—either a metric or a categorization. Two further experiments (2 and 4) indicated that people rarely produced rankings when given a choice of assessment measures for either the length of lines or the artistic value of photographs. In Experiment 5, when the number of lines was larger or lines were only visible one at a time, participants were faster at estimating line lengths as a percentage of the card covered than at rank ordering the lengths. Overall, the results indicate that ordering stimuli is not an easy or natural process when the number of stimuli is large or when the stimuli are not all perceptible at once. An implication is that the psychological measures available to individuals are not likely to be purely ordinal when many of the elements being measured must be recalled.     

Bayesian generalization with circular consequential regions

Generalization–deciding whether to extend a property from one stimulus to another stimulus–is a fundamental problem faced by cognitive agents in many different settings. Shepard (1987) provided a mathematical analysis of generalization in terms of Bayesian inference over the regions of psychological space that might correspond to a given property. He proved that in the unidimensional case, where regions are intervals of the real line, generalization will be a negatively accelerated function of the distance between stimuli, such as an exponential function. These results have been extended to rectangular consequential regions in multiple dimensions, but not for circular consequential regions, which play an important role in explaining generalization for stimuli that are not represented in terms of separable dimensions. We analyze Bayesian generalization with circular consequential regions, providing bounds on the generalization function and proving that this function is negatively accelerated.     

Cognitive changes in conjunctive rule-based category learning: An ERP approach

When learning rule-based categories, sufficient cognitive resources are needed to test hypotheses, maintain the currently active rule in working memory, update rules after feedback, and to select a new rule if necessary. Prior research has demonstrated that conjunctive rules are more complex than unidimensional rules and place greater demands on executive functions like working memory. In our study, event-related potentials (ERPs) were recorded while participants performed a conjunctive rule-based category learning task with trial-by-trial feedback. In line with prior research, correct categorization responses resulted in a larger stimulus-locked late positive complex compared to incorrect responses, possibly indexing the updating of rule information in memory. Incorrect trials elicited a pronounced feedback-locked P300 elicited which suggested a disconnect between perception, and the rule-based strategy. We also examined the differential processing of stimuli that were able to be correctly classified by the suboptimal single-dimensional rule (“easy” stimuli) versus those that could only be correctly classified by the optimal, conjunctive rule (“difficult” stimuli). Among strong learners, a larger, late positive slow wave emerged for difficult compared with easy stimuli, suggesting differential processing of category items even though strong learners performed well on the conjunctive category set. Overall, the findings suggest that ERP combined with computational modelling can be used to better understand the cognitive processes involved in rule-based category learning.     

Absolute and relative perceptual codes in young children

Three experiments were conducted to ascertain whether young children's perceptual codes, as evidenced by choice reaction times, were related to either the absolute difference or the ratio between stimuli. In Experiments 1 and 2, children were shown pairs of line lengths and were asked to choose either the longer or shorter line within each pair. In Experiment 3, children chose which of two birds on a map was closer to themselves or to the experimenter. In all three experiments, children's reaction times were related to both the absolute differences and ratios between pairs of stimuli. The findings suggest that perceptual judgments in young children may be based on both absolute and relational codes.     

Increasing capacity: practice effects in absolute identification

In most of the long history of the study of absolute identification--since Miller's (1956) seminal article--a severe limit on performance has been observed, and this limit has resisted improvement even by extensive practice. In a startling result, Rouder, Morey, Cowan, and Pfaltz (2004) found substantially improved performance with practice in the absolute identification of line lengths, albeit for only 3 participants and in a somewhat atypical paradigm. We investigated the limits of this effect and found that it also occurs in more typical paradigms, is not limited to a few virtuoso participants or due to relative judgment strategies, and generalizes to some (e.g., line inclination and tone frequency) but not other (e.g., tone loudness) dimensions. We also observed, apart from differences between dimensions, 2 unusual aspects of improvement with practice: (a) a positive correlation between initial performance and the effect of practice and (b) a large reduction in a characteristic trial-to-trial decision bias with practice.     

An explanation for the presentation-order effect in the method of constant stimuli

The point of subjective equality obtained by the method of constant stimuli depends to a great extent on whether the standard (S) or the variable (V) stimulus occurs first. This presentation-order effect was studied using lines as stimuli. Successive S, V pairs were presented, with inter-stimulus and interpair intervals equal. Observers, who were not told which was S or V, reported whether a given line was longer or shorter than the immediately preceding line. Although the observers' subjective experience was of a train of lines that was not organized into pairs, the presentation-order effect still occurred. This implies that the effect does not depend on the order of presentation of the stimuli in an experienced pair. It was also shown that the observers could categorize line lengths, since they could identify stochastically the most frequent stimulus (S). We propose that the presentation-order effect depends on a decision process based on response probabilities inferred from length categories.     

Identification of tone duration, line length, and letter position: an experimental approach to timing and working memory deficits in schizophrenia

Patients with schizophrenia display numerous cognitive deficits, including problems in working memory, time estimation, and absolute identification of stimuli. Research in these fields has traditionally been conducted independently. We examined these cognitive processes using tasks that are structurally similar and that yield rich error data. Relative to healthy control participants (n = 20), patients with schizophrenia (n = 20) were impaired on a duration identification task and a probed-recall memory task but not on a line-length identification task. These findings do not support the notion of a global impairment in absolute identification in schizophrenia. However, the authors suggest that some aspect of temporal information processing is indeed disturbed in schizophrenia.