On the spatial distribution of visual attention

An implication of the data analysis and presentation of Podgorny and Shepard (1983) is that subjects are able to attend simultaneously to more than one square of a grid display when the squares are separated by unattended areas: Attention to such nonunitary areas produces similar benefits as attention to unitary areas. These benefits are reflected in reaction times (RTs), which were reported by Podgorny and Shepard (1983) as being related to a measure of spatial dispersion (compactness) of the attended areas, but this measure does not signify whether these areas are unitary or not. A reanalysis of part of Podgorny and Shepard's (1983) data shows that RTs to attended and unattended squares are almost identical when the attended areas are nonunitary. This reanalysis also shows that RTs are related to compactness for unitary attended areas but that this relation breaks down when attention is focused on nonunitary areas. In addition, Podgorny and Shepard's (1983) data are presented in a way that demonstrates the importance of the actual grid location of probes on RTs. The failure of compactness to reflect these aspects of the spatial nature of attention suggests that this metric is deficient when applied to the study of the spatial determinants of attention.     

Stimulus complexity effects in visual comparisons: the effects of practice and learning context.

This study examined visual comparison performance for 6-24-point random polygon stimuli (Cooper & Podgorny, 1976). Stimulus complexity effects decreased with practice, consistent with Bethell-Fox and Shepard (1988). A difficult discrimination context produced greater complexity effects than an easy discrimination context, consistent with Folk and Luce (1987). The difficult discrimination context also led to more stimulus-specific learning and diminished stimulus complexity effects. Increased stimulus learning resulted in continued skill acquisition, better transfer, and less performance disruption when the task context was equated for all Ss. It is argued that improvements in performance in a perceptual comparison task are not solely a function of the amount of practice provided in responding to particular stimuli. The context in which responses are elicited is equally important and must be accommodated in theories of skill acquisition.     

Shifting of attentional focus within and about a visual display

If several positions must be attended in a large visual display, does the efficiency of performance vary as a function of the display distance between these to-be-attended positions? Two previous experiments (Podgorny & Shepard, 1983; Shaw, 1978) gave conflicting answers. In the present experiments, eight-letter circular displays were briefly presented. On each trial one, two, or three positions of the display were cued or precued. The number of noncued display positions intervening between the cued locations varied from zero to three. The subjects' task was to rapidly discriminate between two target letters. Although reaction time was found to increase with increases in the number of cued locations, no significant or suggestive effects were found for the spacing or distance between the cued locations. The evidence strongly suggests that the subjects serially searched the cued locations, which further implies that attention can index locations in the visual field at a speed that is independent of the distance between these locations.     

Neural nets for generalization and classification: comment on Staddon and Reid (1990)

The neural net model of Staddon and Reid (1990) explains exponential and Gaussian generalization gradients in the same way as the diffusion model of Shepard (1958). The "cognitive" generalization theory of Shepard (1987), which also has been implemented as a connectionist network, goes beyond both of these models in accounting for classification learning.     

Mental rotation and perceptual uprightness

Performance in Cooper and Shepard’s (1973) mental rotation task was examined in the context of a model that defined the extent to which alphabet letters could be tilted from their normal orientation and still be perceptually upright. For letters with a broad range of orientations for which they remain perceptually upright, a nonlinear effect of orientation on reaction time was obtained (as in Cooper and Shepard). However, for letters with a narrow range of orientations for which they remain perceptually upright, reaction time was linearly related to orientation. The results supported the hypothesis that subjects in the Cooper and Shepard task would mentally rotate alphabet letters only when they were presented in orientations for which they were not perceptually upright.     

Relative attention in judgments of heterogeneous similarity

Shepard’s (1964) study on similarity of stimuli with clearly discernible dimensions was repeated with some modifications, the most important being that the Os had to make numerical similarity estimates of the stimulus pairs. The overall outcome did not deviate much from Shepard’s findings. By using quantitative estimates and choosing stimulus series so that the two dimensions were negatively correlated, data for each 0 could be analyzed separately with a partial correlation technique. It was found that the more an 0 attended to one dimension the less he attended to the other. The shifts in attention seemed to be random rather than regular. Consequently, the meaningfulness of a contention like Shepard’s as to the nonexistence of a metric is questioned.     

Netscal: A network scaling algorithm for nonsymmetric proximity data

A simple property of networks is used as the basis for a scaling algorithm that represents nonsymmetric proximities as network distances. The algorithm determines which vertices are directly connected by an arc and estimates the length of each arc. Network distance, defined as the minimum pathlength between vertices, is assumed to be a generalized power function of the data. The derived network structure, however, is invariant across monotonic transformations of the data. A Monte Carlo simulation and applications to eight sets of proximity data support the practical utility of the algorithm.I am grateful to Roger Shepard and Amos Tversky for their helpful comments and guidance throughout this project. The work was supported by National Science Foundation Grant BNS-75-02806 to Roger Shepard and a National Science Foundation Graduate Fellowship to the author. Parts of this paper were drawn from a doctoral dissertation submitted to Stanford University (Hutchinson, 1981).     

Circularity in relative pitch judgments for inharmonic complex tones: The Shepard demonstration revisited,again

The Shepard illusion, in which the presentation of a cyclically repetitive sequence of complex tones composed of partials separated by octave intervals (Shepard, 1964) gives the illusion of an endlessly increasing sequence of pitch steps, is often cited as evidence for octave equivalence. In this paper, evidence is presented which demonstrates that this illusion can be produced using (inharmonic) complex tones whose partials are separated by equal ratios other than octaves. Therefore, the illusion is not evidence for octave equivalence.     

Sex differences and the factor of time in solving Vandenberg and Kuse mental rotation problems

In accounting for the well-established sex differences on mental rotation tasks that involve cube stimuli of the Shepard and Metzler (Shepard & Metzler, 1971) kind, performance factors are frequently invoked. Three studies are presented that examine performance factors. In Study 1, analyses of the performance of a large number of subjects (n=1765) that performed the Vandenberg and Kuse (1976) mental rotation test (MRT) under standard conditions showed that the magnitude of the sex differences increases as subjects proceed through the sequence of problems, and that fewer females than males reach the last problems in a problem set. This supports the role of time constraints in sex differences on the MRT. Study 2 compared the magnitude of sex differences for subjects (n=212) who did the MRT under standard conditions (T1), and with double the time (T2) allowed for the test. No significant reduction in the magnitude of sex differences was observed-even though the overall scores under T2 increased markedly for both sexes. Study 3 examined the suggestion by that mental rotation differences arise because females spend more time than males in assuring that stimuli that do not match do indeed not match, with no sex differences for matching stimuli. This hypothesis was not supported for a sample of 20 males and 26 females. We conclude that performance factors may play a role in sex difference on mental rotation tasks, but do not account for all of the differences.     

A parallel-process model of mental rotation

It is argued that some of the phenomena identified with analog processes by Shepard can be understood as resulting from a parallel-process algorithm running on a processor having many individual processing elements and a restricted communication structure. In particular, an algorithm has been developed and implemented which models human behavior on Shepard's object rotation and comparison task. The algorithm exhibits computation times which increase linearly with the angle of rotation. Shepard found a similar linear function in his experiments with human subjects. In addition, the intermediate states of the computation are such that if the rotation process were to be interrupted at any point, the object representation would correspond to that of the actual object at a position along the rotation trajectory. The computational model presented here is governed by three constraining assumptions: (a) that it be parallel: (b) that the communication between processors be restricted to immediate neighbors: (c) that the object representation be distributed across a large fraction of the available processors. A method of diagnosing the correct axis of rotation is also presented.     

Internalization: a metaphor we can live without

Shepard has supposed that the mind is stocked with innate knowledge of the world and that this knowledge figures prominently in the way we see the world. According to him, this internal knowledge is the legacy of a process of internalization; a process of natural selection over the evolutionary history of the species. Shepard has developed his proposal most fully in his analysis of the relation between kinematic geometry and the shape of the motion path in apparent motion displays. We argue that Shepard has made a case for applying the principles of kinematic geometry to the perception of motion, but that he has not made the case for injecting these principles into the mind of the percipient. We offer a more modest interpretation of his important findings: that kinematic geometry may be a model of apparent motion. Inasmuch as our recommended interpretation does not lodge geometry in the mind of the percipient, the motivation of positing internalization, a process that moves kinematic geometry into the mind, is obviated. In our conclusion, we suggest that cognitive psychologists, in their embrace of internal mental universals and internalization may have been seduced by the siren call of metaphor.     

Interactive clustering

An interactive strategy for applying cluster-analytic techniques in behavioral research is presented. The two-part approach stresses the use of on-line computers for both data collection and analysis. In data collection, an extension of multidimensional unfolding to clustering reduces the number of judgments required of subjects by as much as 50%, During data analysis, the interactive procedures described permit the testing of multiple clustering models from an extensive family. With each selection, the goodness of fit of the model to the data can be tested. In addition to improving efficiency, the interactive strategy promoted here combines the advantages of the original nonmetric clustering procedures (e.g., Johnson, 1967) with those of the latest linear additive models (e.g., Sattath & Tversky, 1977; Shepard & Arabie, 1979).     

A model for detection and recognition with signal uncertainty

A model for signal detectability suggested by Luce is extended to situations in which the observer is uncertain of some important characteristic of the signal, such as frequency. By making a single assumption concerning the observer's covert response behavior, two solutions are obtained corresponding to qualitatively different behavior. Decrements in detectability and in recognition with uncertainty are shown to be particular functions of discriminability and detectability of the stimuli in other situations. Relevant experimental data are considered.This work was supported by grant NSF-G5544 from the National Science Foundation. The author is indebted to R. Duncan Luce for critical discussion of the content and helpful suggestions concerning the form of this paper. Useful comments have been made by David M. Green, Francis W. Irwin, Roger M. Shepard, and W. P. Tanner, Jr.     

A theory of visual attention

A unified theory of visual recognition and attentional selection is developed by integrating the biased-choice model for single-stimulus recognition (Luce, 1963; Shepard, 1957) with a choice model for selection from multielement displays (Bundesen, Pedersen, & Larsen, 1984) in a race model framework. Mathematically, the theory is tractable, and it specifies the computations necessary for selection. The theory is applied to extant findings from a broad range of experimental paradigms. The findings include effects of object integrality in selective report, number and spatial position of targets in divided-attention paradigms, selection criterion and number of distracters in focused-attention paradigms, delay of selection cue in partial report, and consistent practice in search. On the whole, the quantitative fits are encouraging.     

Category learning in rhesus monkeys: a study of the Shepard, Hovland, and Jenkins (1961) tasks

In influential research, R. N. Shepard, C. I. Hovland, and H. M. Jenkins (1961) surveyed humans' categorization abilities using tasks based in rules, exclusive-or (XOR) relations, and exemplar memorization. Humans' performance was poorly predicted by cue-conditioning or stimulus-generalization theories, causing Shepard et al. to describe it in terms of hypothesis selection and rule application that were possibly supported by verbal mediation. The authors of the current article surveyed monkeys' categorization abilities similarly. Monkeys, like humans, found category tasks with a single relevant dimension the easiest and perceptually chaotic tasks requiring exemplar memorization the most difficult. Monkeys, unlike humans, found tasks based in XOR relations very difficult. The authors discuss the character and basis of the species difference in categorization and consider whether monkeys are the generalization-based cognitive system that humans are not.     

Working memory capacity and categorization: individual differences and modeling

Working memory is crucial for many higher-level cognitive functions, ranging from mental arithmetic to reasoning and problem solving. Likewise, the ability to learn and categorize novel concepts forms an indispensable part of human cognition. However, very little is known about the relationship between working memory and categorization, and modeling in category learning has thus far been largely uninformed by knowledge about people's memory processes. This article reports a large study (N = 113) that related people's working memory capacity (WMC) to their category-learning performance using the 6 problem types of Shepard, Hovland, and Jenkins (1961). Structural equation modeling revealed a strong relationship between WMC and category learning, with a single latent variable accommodating performance on all 6 problems. A model of categorization (the Attention Learning COVEring map, ALCOVE; Kruschke, 1992) was fit to the individual data and a single latent variable was sufficient to capture the variation among associative learning parameters across all problems. The data and modeling suggest that working memory mediates category learning across a broad range of tasks.     

Mapclus: A mathematical programming approach to fitting the adclus model

We present a new algorithm, MAPCLUS (MAthematicalProgrammingCLUStering), for fitting the Shepard-Arabie ADCLUS (forADditiveCLUStering) model. MAPCLUS utilizes an alternating least squares method combined with a mathematical programming optimization procedure based on a penalty function approach, to impose discrete (0,1) constraints on parameters defining cluster membership. This procedure is supplemented by several other numerical techniques (notably a heuristically based combinatorial optimization procedure) to provide an efficient general-purpose computer implemented algorithm for obtaining ADCLUS representations. MAPCLUS is illustrated with an application to one of the examples given by Shepard and Arabie using the older ADCLUS procedure. The MAPCLUS solution uses half as many clusters to achieve nearly the same level of goodness-of-fit. Finally, we consider an extension of the present approach to fitting a three-way generalization of the ADCLUS model, called INDCLUS (INdividualDifferencesCLUStering).We are indebted to Scott A. Boorman, W. K. Estes, J. A. Hartigan, Lawrence J. Hubert, Carol L. Krumhansl, Joseph B. Kruskal, Sandra Pruzansky, Roger N. Shepard, Edward J. Shoben, Sigfrid D. Soli, and Amos Tversky for helpful discussions of this work, as well as the anonymous referees for their suggestions and corrections on an earlier version of this paper. We are also grateful to Pamela Baker and Dan C. Knutson for technical assistance. The research reported here was supported in part by LEAA Grant 78-NI-AX-0142 and NSF Grants SOC76-24512 and SOC76-24394.     

Effects of stimulus color, pattern, and practice on sex differences in mental rotations task performance.

Redundant color information improved performance for both sexes on the Shepard Mental Rotations Task (MRT; Shepard & Metzler, 1971). Absolute score gains for women were larger than those for men; therefore, relative improvement was greater. Substantial practice effects, also favoring women, were apparent in both studies. Study 1 showed that redundant color improved performance by 0.25 SD. Study 2 demonstrated that redundant black-and-white pattern information did not have any effect; a second visuospatial channel, redundant color, was a critical factor in improving scores of men and women on difficult mental rotations tasks.     

Second-order isomorphism of internal representations of familiar faces

Following a suggestion by Shepard and Chipman (1970), photographs and names of 15 well-known faces were used as stimuli in judgments of similarity. Ss ranked all pairs of stimuli in terms of facial similarity either from memory when presented with pairs of names, or from photographs. There was a highly significant positive correlation between these two types of judgment. A simple classificatory analysis of the 15 faces in terms of the physical features provided evidence that judgments based on the internal representation of the faces utilized pictorial information. These results extend the generality of Shepard and Chipman’s findings and confirm the usefulness of an approach to the problem of mental images based on the concept of second-order isomorphism.