Attention, similarity, and the identification-categorization relationship

A unified quantitative approach to modeling subjects' identification and categorization of multidimensional perceptual stimuli is proposed and tested. Two subjects identified and categorized the same set of perceptually confusable stimuli varying on separable dimensions. The identification data were modeled using Shepard's (1957) multidimensional scaling-choice framework. This framework was then extended to model the subjects' categorization performance. The categorization model, which generalizes the context theory of classification developed by Medin and Schaffer (1978), assumes that subjects store category exemplars in memory. Classification decisions are based on the similarity of stimuli to the stored exemplars. It is assumed that the same multidimensional perceptual representation underlies performance in both the identification and categorization paradigms. However, because of the influence of selective attention, similarity relationships change systematically across the two paradigms. Some support was gained for the hypothesis that subjects distribute attention among component dimensions so as to optimize categorization performance. Evidence was also obtained that subjects may have augmented their category representations with inferred exemplars. Implications of the results for theories of multidimensional scaling and categorization are discussed.     

The relative sensitivities of same-different and identification judgment models to perceptual dependence

Probabilistic models of same-different and identification judgments are compared (within each paradigm) with regard to their sensitivity to perceptual dependence or the degree to which the underlying psychological dimensions are correlated. Three same-different judgment models are compared. One is a step function or decision bound model and the other two are probabilistic variants of a similarity model proposed by Shepard. Three types of identification models are compared: decision bound models, a probabilistic multidimensional scaling model, and probabilistic models based on the Shepard-Luce choice rule. The decision bound models were found to be most sensitive to perceptual dependence, especially when there is considerable distributional overlap. The same-different model based on the city-block metric and an exponential decay similarity function, and the corresponding identification model were found to be particularly insensitive to perceptual dependence. These results suggest that if a Shepard-type similarity function accurately describes behavior, then under typical experimental conditions it should be difficult to see the effects of perceptual dependence. This result provides strong support for a perceptualindependence assumption when using these models. These theoretical results may also play an important role in studying different decision rules employed at different stages of identification training.We thank Robert Melara, Jerome Busemeyer and three anonymous reviewers for comments on an earlier draft of this paper.     

Recognition memory for realistic synthetic faces

A series of experiments examined short-term recognition memory for trios of briefly presented, synthetic human faces derived from three real human faces. The stimuli were a graded series of faces, which differed by varying known amounts from the face of the average female. Faces based on each of the three real faces were transformed so as to lie along orthogonal axes in a 3-D face space. Experiment 1 showed that the synthetic faces' perceptual similarity structure strongly influenced recognition memory. Results were fit by a noisy exemplar model (NEMO) of perceptual recognition memory. The fits revealed thatrecognition memory was influenced both by the similarity of the probe to the series items and by the similarities among the series items themselves. Nonmetric multidimensional scaling (MDS) showed that the faces' perceptual representations largely preserved the 3-D space in which the face stimuli were arrayed. NEMO gave a better account of the results when similarity was defined as perceptual MDS similarity, rather than as the physical proximity of one face to another. Experiment 2 confirmed the importance of within-list homogeneity directly, without mediation of a model. We discuss the affinities and differences between visual memory for synthetic faces and memory for simpler stimuli.     

Predicting similarity and categorization from identification.

In this article, the relation between the identification, similarity judgment, and categorization of multidimensional perceptual stimuli is studied. The theoretical analysis focused on general recognition theory (GRT), which is a multidimensional generalization of signal detection theory. In one application, 2 Ss first identified a set of confusable stimuli and then made judgments of their pairwise similarity. The second application was to Nosofsky's (1985b, 1986) identification-categorization experiment. In both applications, a GRT model accounted for the identification data better than Luce's (1963) biased-choice model. The identification results were then used to predict performance in the similarity judgment and categorization conditions. The GRT identification model accurately predicted the similarity judgments under the assumption that Ss allocated attention to the 2 stimulus dimensions differently in the 2 tasks. The categorization data were predicted successfully without appealing to the notion of selective attention. Instead, a simpler GRT model that emphasized the different decision rules used in identification and categorization was adequate.     

A stochastic multidimensional scaling procedure for the empirical determination of convex indifference curves for preference/choice analysis

The vast majority of existing multidimensional scaling (MDS) procedures devised for the analysis of paired comparison preference/choice judgments are typically based on either scalar product (i.e., vector) or unfolding (i.e., ideal-point) models. Such methods tend to ignore many of the essential components of microeconomic theory including convex indifference curves, constrained utility maximization, demand functions, et cetera. This paper presents a new stochastic MDS procedure called MICROSCALE that attempts to operationalize many of these traditional microeconomic concepts. First, we briefly review several existing MDS models that operate on paired comparisons data, noting the particular nature of the utility functions implied by each class of models. These utility assumptions are then directly contrasted to those of microeconomic theory. The new maximum likelihood based procedure, MICROSCALE, is presented, as well as the technical details of the estimation procedure. The results of a Monte Carlo analysis investigating the performance of the algorithm as a number of model, data, and error factors are experimentally manipulated are provided. Finally, an illustration in consumer psychology concerning a convenience sample of thirty consumers providing paired comparisons judgments for some fourteen brands of over-the-counter analgesics is discussed.     

Identification of own-race and other-race faces: Implications for the representation of race in face space

Own-race faces are recognized more easily than faces of a different, unfamiliar race. According to the multidimensional space (MDS) framework, the poor discriminability of other-race faces is due to their being more densely clustered in face space than own-race faces. Multidimensional scaling analyses of similarity ratings (Caucasian participants, n = 22) showed that other-race (Chinese) faces are more densely clustered in face space. We applied a formal model to test whether the spatial location of face stimuli could account for identification accuracy of another group of Caucasian participants (n = 30). As expected, own-race (Caucasian) faces were identified more accurately (higher hit rate, lower false alarms, and higher A) than other-race faces, which were more densely clustered than ownrace faces. A quantitative model successfully predicted identification performance from the spatial locations of the stimuli. The results are discussed in relation to the standard MDS account of race effects and also an alternative “race-feature” hypothesis.     

ConPar: a method for identifying groups of concordant subject proximity matrices for subsequent multidimensional scaling analyses

A common representation of data within the context of multidimensional scaling (MDS) is a collection of symmetric proximity (similarity or dissimilarity) matrices for each of M subjects. There are a number of possible alternatives for analyzing these data, which include: (a) conducting an MDS analysis on a single matrix obtained by pooling (averaging) the M subject matrices, (b) fitting a separate MDS structure for each of the M matrices, or (c) employing an individual differences MDS model. We discuss each of these approaches, and subsequently propose a straightforward new method (CONcordance PARtitioning—ConPar), which can be used to identify groups of individual-subject matrices with concordant proximity structures. This method collapses the three-way data into a subject×subject dissimilarity matrix, which is subsequently clustered using a branch-and-bound algorithm that minimizes partition diameter. Extensive Monte Carlo testing revealed that, when compared to K-means clustering of the proximity data, ConPar generally provided better recovery of the true subject cluster memberships. A demonstration using empirical three-way data is also provided to illustrate the efficacy of the proposed method.     

Multidimensional letter similarity derived from recognition errors

In order to provide a reliable measure of the similarity of uppercase English letters, a confusion matrix based on 1,200 presentations of each letter was established. To facilitate an analysis of the perceived structural characteristics, the confusion matrix was decomposed according to Luce’s choice model into a symmetrical similarity matrix and a response bias vector. The underlying structure of the similarity matrix was assessed with both a hierarchical clustering and a multidimensional scaling procedure. This data is offered to investigators of visual information processing as a valuable tool for controlling not only the overall similarity of the letters in a study, but also their similarity on individual feature dimensions.     

Further tests of an exemplar-similarity approach to relating identification and categorization

Further tests were provided of an exemplar-similarity model for relating the identification and categorization of separable-dimension stimuli (Nosofsky, 1986). On the basis of confusion errors in an identification paradigm, a multidimensional scaling (MDS) solution was derived for a set of 16 separable-dimension stimuli. This MDS solution was then used in conjunction with the exemplar-similarity model to accurately predict performance in four separate categorization paradigms with the same stimuli. A key to achieving the accurate quantitative fits was the assumption that a selective attention process systematically modifies similarities among exemplars across different category structures. The tests reported go well beyond earlier ones (Nosofsky, 1986) in demonstrating the generalizability and utility of the theoretical approach. Implications of the results for alternative quantitative models of classification performance, including Ashby and Perrin's (1988) general recognition theory, were also considered.     

A multidimensional scaling approach to mental multiplication

Adults consistently make errors in solving simple multiplication problems. These errors have been explained with reference to the interference between similar problems. In this paper, we apply multidimensional scaling (MDS) to the domain of multiplication problems, to uncover their underlying similarity structure. A tree-sorting task was used to obtain perceived dissimilarity ratings. The derived representation shows greater similarity between problems containing larger operands and suggests that tie problems (e.g., 7 x 7) hold special status. A version of the generalized context model (Nosofsky, 1986) was used to explore the derived MDS solution. The similarity of multiplication problems made an important contribution to producing a model consistent with human performance, as did the frequency with which such problems arise in textbooks, suggesting that both factors may be involved in the explanation of errors.     

Similarity, kernels, and the triangle inequality

Similarity is used as an explanatory construct throughout psychology and multidimensional scaling (MDS) is the most popular way to assess similarity. In MDS, similarity is intimately connected to the idea of a geometric representation of stimuli in a perceptual space. Whilst connecting similarity and closeness of stimuli in a geometric representation may be intuitively plausible, Tversky and Gati [Tversky, A., & Gati, I. (1982). Similarity, separability, and the triangle inequality. Psychological Review, 89(2), 123-154] have reported data which are inconsistent with the usual geometric representations that are based on segmental additivity. We show that similarity measures based on Shepard’s universal law of generalization [Shepard, R. N. (1987). Toward a universal law of generalization for psychologica science. Science, 237(4820), 1317-1323] lead to an inner product representation in a reproducing kernel Hilbert space. In such a space stimuli are represented by their similarity to all other stimuli. This representation, based on Shepard’s law, has a natural metric that does not have additive segments whilst still retaining the intuitive notion of connecting similarity and distance between stimuli. Furthermore, this representation has the psychologically appealing property that the distance between stimuli is bounded.     

Tests of an exemplar model for relating perceptual classification and recognition memory

Experiments were conducted in which Ss made classification, recognition, and similarity judgments for 34 schematic faces. A multidimensional scaling (MDS) solution for the faces was derived on the basis of the similarity judgments. This MDS solution was then used in conjunction with an exemplar-similarity model to accurately predict Ss' classification and recognition judgments. Evidence was provided that Ss allocated attention to the psychological dimensions differentially for classification and recognition. The distribution of attention came close to the ideal-observer distribution for classification, and some tendencies in that direction were observed for recognition. Evidence was also provided for interactive effects of individual exemplar frequencies and similarities on classification and recognition, in accord with the predictions of the exemplar model. Unexpectedly, however, the frequency effects appeared to be larger for classification than for recognition.     

Mapping the similarity space of paintings: Image statistics and visual perception

What makes two images look similar? Here we test the hypothesis that perceived similarity of artwork is related to basic image statistics to which the early visual system is attuned. In two experiments, we employ multidimensional scaling (MDS) analysis of paired-image similarity ratings from observers for paintings. Two sets of images, classified as “landscapes” and “portraits/still-life”, are tested separately. For the landscapes, we find that one of the first two MDS scales of similarity is strongly correlated with a basic greyscale image statistic, whereas the other dimension can be accounted for by a semantic variable (representation of people). For portrait/still-life, the first two MDS scales of similarity are most highly correlated with semantic variables. Linear combinations of statistical and nonstatistical features achieve improved predictive values for the first two MDS scales for both sets. The statistics that play the largest role in shaping similarity judgements in our tests are the activity fraction measure of sparseness and the log-log slope of the spatial frequency amplitude spectrum. We discuss these results in the context of scene perception and in terms of efficient coding of statistical regularities in scenes.     

Seeing through the eyes of anxious individuals: An investigation of anxiety-related interpretations of emotional expressions

The interpretation of emotional states is necessary for successful social communication. Often individuals interpret emotional expressions intuitively and without full cognitive awareness. The aim of the present study was to test whether anxiety would influence affect interpretation in the manner suggested by interpretation bias—the tendency to interpret ambiguous cues in a threatening way. Interpretation of social cues was assessed with the similarity rating task (simtask) in two studies (n₁ = 116, n₂ = 76). The similarity ratings were analysed with a multidimensional scaling (MDS) approach, and the effects of anxiety on the interpretation of emotional expressions were analysed with multilevel modelling. The results of both studies showed evidence for an anxiety-related interpretation bias. High-anxious individuals tended to interpret milder threats as more negative than low-anxious individuals did. The consequences for anxiety research are discussed.     

Scale properties of the Holtzman inkblots

Scaling techniques were presently applied to perceptions of inkblots, to empirically delineate the relationship between their stimulus properties and the nature of verbal associations elicited in projective testing. The Holtzman Inkblot Technique (HIT) was administered in group form to a relatively diverse group of college students. Subjects also individually rated the similarity of pairs of the HIT inkblots. Similarity judgments were analyzed via a multidimensional scaling (MDS) approach which recovered dimensions of variations among blots. The MDS procedures also captured variation across subjects in their utilization of blot stimulus properties. MDS solutions generally reflected differences among the blots along dimensions of physical characteristics of the blots. Differences in responsiveness of subjects to these characteristics appeared to reliably reflect meaningful substantive distinctions among subjects, many of which were not captured by traditional HIT variables. Implications were discussed in terms of further MDS applications and possible re-evaluation of HIT variables or procedures.     

Similarity and categorization of environmental sounds

Four experiments investigated the acoustical correlates of similarity and categorization judgments of environmental sounds. In Experiment 1, similarity ratings were obtained from pairwise comparisons of recordings of 50 environmental sounds. A three-dimensional multidimensional scaling (MDS) solution showed three distinct clusterings of the sounds, which included harmonic sounds, discrete impact sounds, and continuous sounds. Furthermore, sounds from similar sources tended to be in close proximity to each other in the MDS space. The orderings of the sounds on the individual dimensions of the solution were well predicted by linear combinations of acoustic variables, such as harmonicity, amount of silence, and modulation depth. The orderings of sounds also correlated significantly with MDS solutions for similarity ratings of imagined sounds and for imagined sources of sounds, obtained in Experiments 2 and 3--as was the case for free categorization of the 50 sounds (Experiment 4)--although the categorization data were less well predicted by acoustic features than were the similarity data.