Multidimensional Scaling Solutions Research Articles

The representation of auditory source characteristics: simple geometric form.

Two experiments examined listeners' ability to discriminate the geometric shape of simple resonating bodies on the basis of their corresponding auditory attributes. In cross-modal matching tasks, subjects listened to recordings of pairs of metal bars (Experiment 1) or wooden bars (Experiment 2) struck in sequence and then selected a visual depiction of the bar cross sections that correctly represented their relative widths and heights from two opposing pairs presented on a computer screen. Multidimensional scaling solutions derived from matching scores for metal and wooden bars indicated that subjects' performance varied directly with increasing differences in the width/height (W/H) ratios of both sets of bars. Subsequent acoustic analyses revealed that the frequency components from torsional vibrational modes and the ratios of frequencies of transverse bending modes in the bars correlated strongly with both the bars' W/H ratios and bar coordinates in the multidimensional configurations. The results suggest that listeners can encode the auditory properties of sound sources by extracting certain invariant physical characteristics of their gross geometric properties from their acoustic behavior.

The texture lexicon: Understanding the categorization of visual texture terms and their relationship to texture images

In this paper we present the results of two experiments. The first is on the categorization of texture words in the English language. The goal was to determine whether there is a common basis for subjects' groupings of words related to visual texture, and if so, to identify the underlying dimensions used to categorize those words. Eleven major clusters were identified through hierarchical cluster analysis, ranging from ‘random’ to ‘repetitive’. These clusters remained intact in a multidimensional scaling solution. The stress for a three-dimensional solution obtained through multidimensional scaling was 0.18, meaning that 82% of the variance in the data is explained through the use of three dimensions. It appears that the major dimensions of texture descriptors are repetitive versus nonrepetitive; linearly oriented versus circularly oriented; and simple versus complex. In the second experiment we measured the strength of association between texture words and texture images. The goal was to determine whether there is any systematic correspondence between the domains of texture words and texture images. Pearson's coefficient of contingency, a measure of the strength of association, was found to be 0.63 for words corresponding to given images and 0.56 for images corresponding to given words. Thus the texture categories in the verbal space and those in the visual space are strongly tied. In sum, our two experiments show (a) that despite the tremendous variety in the words we have to describe textures, there is an underlying structure to the lexical space which can be derived from the experimental data; and (b) that the association between a category of words and a category of images was strongest when both categories represent the same underlying property. This suggests that subjects' organizations of texture terms are systematically tied to their organization of texture images.

The Texture Lexicon: Understanding the Categorization of Visual Texture Terms and Their Relationship to Texture Images

In this paper we present the results of two experiments. The first is on the categorization of texture words in the English language. The goal was to determine whether there is a common basis for subjects' groupings of words related to visual texture, and if so, to identify the underlying dimensions used to categorize those words.Eleven major clusters were identified through hierarchical cluster analysis, ranging from “random” to “repetitive”. These clusters remained intact in a multidimensional scaling solution. The stress for a three‐dimensional solution obtained through multidimensional scaling was 0.18, meaning that 82% of the variance in the data is explained through the use of three dimensions. It appears that the major dimensions of texture descriptors are repetitive versus nonrepetitive; linearly oriented versus circularly oriented; and simple versus complex.In the second experiment we measured the strength of association between texture words and texture images. The goal was to determine whether there is any systematic correspondence between the domains of texture words and texture images. Pearson's coefficient of contingency, a measure of the strength of association, was found to be 0.63 for words corresponding to given images and 0.56 for images corresponding to given words. Thus the texture categories in the verbal space and those in the visual space are strongly tied.In sum, our two experiments show (a) that despite the tremendous variety in the words we have to describe textures, there is an underlying structure to the lexical space which can be derived from the experimental data; and (b) that the association between a category of words and a category of images was strongest when both categories represent the same underlying property. This suggests that subjects' organizations of texture terms are systematically tied to their organization of texture images.

A multi-method analysis of work-related preferences in three nations: implications for inter-and intra-national human resource management

This study explores the structure of the work-related preferences (WRPs) of 175 Australian, 283 Mexican and 159 USA respondents through multidimensional scaling and a covariance structure analytic approach. The complexities inherent in interpreting multidimensional scaling solutions and the contribution confirmatory factor analysis can make in testing hypothesized WRP structures are highlighted. Empirical support is found for a six-factor structure of WRPs that is common (or etic) across samples, although more restrictive tests identified equivalence between the Australian and Mexican samples but, surprisingly, not the USA sample. These empirical findings have implications for international HRM policies and practices of multinational enterprises, as well as intra-national human resource management. Importantly, the present study provides quantitative empirical evidence supporting the aphorism in the international management literature 'think global, act local'.

The representation of auditory source characteristics: Simple geometric form

Two experiments examined listeners’ ability to discriminate the geometric shape of simple resonating bodies on the basis of their corresponding auditory attributes. In cross-modal matching tasks, subjects listened to recordings of pairs of metal bars (experiment 1) or wooden bars (experiment 2) struck in sequence, and then selected a visual depiction of the bar cross sections that correctly represented their relative widths and heights from two opposing pairs presented on a computer screen. Multidimensional scaling solutions derived from matching scores for metal and wooden bars indicated that subjects’ performance varied directly with increasing differences in the width–height ratios of both sets of bars. Subsequent acoustic analyses revealed that the frequency components from torsional vibrational modes and the ratios of frequencies of transverse bending modes in the bars correlated strongly with both of the bars’ width–height ratios and bar coordinates in the multidimensional configurations. The results suggest that listeners can encode the auditory properties of sound sources by extracting certain invariant physical characteristics of their gross geometric properties from their acoustic behavior. [Work supported by CNRS.]

Dimensions of the impact of cancer pain in a four country sample: new information from multidimensional scaling

We investigated the question of how cultural and linguistic backgrounds affect relationships among ratings (reported by patients with metastatic cancer) of pain's reference with such functions as activity, mood, and sleep. Multidimensional scaling (MDS) was used to analyze ratings of pain interference from a sample consisting of four culturally and linguistically different groups from the US ( n = 1106), France ( n = 324), the Philippines ( n = 267), and China ( n = 146). Patients all completed the Brief Pain Inventory, a self-report measure of pain and its interference with function. For each of these samples, MDS solutions consistently revealed two interpretable dimensions. In all samples, one dimension represented affect and the other dimension represented activity. The dimensions were consistently interpretable across all four samples and across three levels of pain severity (‘mild’, ‘moderate’, and ‘severe’). The dimensions were most prominent when pain was moderate, rather than mild (when little interference was produced) or severe (when all domains were highly interfered with). These dimensions may have utility in the study of the epidemiology of pain and of the effectiveness of pain treatment. They may also be useful in clinical assessment to describe different patterns of pain interference.

An investigation of data collection methods for auditory stimuli: Paired comparisons versus a computer sorting task

Two experiments were performed to determine whether a computer sorting task could be used to collect data for auditory stimuli. Within each experiment, subjects were assigned to either a paired comparison task or a computer sorting task. For the first experiment, the stimuli were 18 graph representations constructed to vary on three parameters (shape, frequency, and amplitude). The stimuli for the second experiment were 30 sentences produced by actors portraying five emotions (anger, fear, happiness, sadness, and neutral). Multidimensional scaling solutions were produced and comparisons were made between the paired comparison and computer sorting task in each experiment. The results suggest that the computer sorting task is a viable alternative to the paired comparison task traditionally used for the investigation of the perception of auditory stimuli.

Towards a texture naming system: Identifying relevant dimensions of texture

Recently, researchers have started using texture for data visualization. The rationale behind this is to exploit the sensitivity of the human visual system to texture in order to overcome the limitations inherent in the display of multidimensional data. A fundamental issue that must be addressed is what textural features are important in texture perception, and how they are used. We designed an experiment to help identifiy the relevant higher order features of texture perceived by humans. We used twenty subjects, who were asked to rate 56 pictures from Brodatz's album on 12 nine-point Likert scales. Each subject was also asked to group these pictures into as many classes as desired. We applied the techniques of hierarchical cluster analysis and non-parametric multidimensional scaling (MDS) to the pooled similarity matrix generated from the subjects' groupings. We used Classification and Regression Tree Analysis (CART), discriminant analysis, and principal component analysis on the data from the scale ratings. The clusters generated from hierarchical cluster analysis remained intact in the MDS plots. We found that the MDS solutions fit the data well. The stress in the three-dimensional case is 0.12. The CART and discriminant analyses provided further justification for our interpretation. The three orthogonal dimensions we identified for texture are repetitive vs non-repetitive; high-contrast and non-directional vs low-contrast and directional; granular, coarse and low-complexity vs non-granular, fine and high-complexity.

Frequency, ordinal position and semantic distance as measures of cross-cultural stability and hierarchies for action verbs

Swedish and English (American) speaking subjects were given a superordinate description for a general class of actions that depict bodily movement. Based on a listing task similar to the one used in Battig and Montague (1969), the subjects were instructed to list all the actions that conformed to the superordinate. The results of the task indicate graded structure for the superordinate category as well as hierarchical relations between a basic and subordinate level as shown by measures of response frequencies and mean ordinal positions. These measures also correlated highly between the Swedish and American samples for the most frequently listed verbs, indicating a strong degree of cross-cultural stability. In an additional test of this stability, the ordinal positions of the verbs were used as proximity data in multidimensional scaling analyses in order to obtain a measure of the semantic distance between the different verbs. A correlation between the Swedish and American samples, using the derived distances for all possible pairs of the verbs, revealed a significant degree of stability. Furthermore, groupings of locomotory and vocal actions in the 3-dimensional multidimensional scaling solutions showed a tendency towards a much stronger stability. A speculative account of these results is proposed in terms of the physical constraints in human motion and the frequency of performing or seeing others perform actions around us.

The relationship between leisure theory and recreation practice

The purpose of this study was to examine the relationship between leisure theory and recreation practice, using a cognitive approach. Seventeen male and 3 female public leisure service managers took part in the investigation. A pile‐sort technique was used to ascertain the structure of the conceptual domain consisting of the Accreditation Standards of the National Recreation and Park Association (1991). The pile‐sort data were used to generate hierarchical clustering (HC) and multidimensional scaling (MDS) solutions. Both the HC and the MDS solutions indicated that these practitioners associate leisure theory and philosophy primarily with the programming process and that this area of knowledge is used most by mid‐level managers and front‐line staff. This investigation demonstrated a relationship between leisure theory and recreation practice for these practitioners and that researchers and practitioners may hold different meanings for the concepts of leisure theory and philosophy. Implications for future ...

The timbre of compound tones consisting of four amplitude modulated waves of different frequency regions.

The timbre of compound tones consisting of four amplitude modulated waves is examined by psychoacoustical experiments using a similarity judgement of timbre. The obtained data are analyzed by a multi-dimensional scaling (MDS) method. The MDS solutions are different according to the frequency regions of the AM waves. When the frequency region is low and there is one AM wave within the bandwidth of the auditory filter, envelope correlations between AM waves are a determinant factor of timbre. However, the three dimensional MDS solution suggests that all the envelopes do not affect the timbre in the same manner. The effect of the lowest AM wave is not clear. As the frequency region is higher, the effect of the envelope correlation is less dominant. The effect of thedepth of amplitude modulation of the compound waves then becomes dominant. When there are two AM waves within the bandwidth of the auditory filter, we no longer see the effect of the envelope correlation between AM waves. In this case, the correspondence of the shape of the compound envelopes of two AM waves affect the timbre.

The effects of alternative methods of collecting similarity data for Multidimensional Scaling

In this paper, we study differences between the four data collection methods sorting, paired comparisons, conditional rankings, and triadic combinations. Effects of the judgment task on fatigue, boredom, and learning, on similarity data, and on perceptual maps derived with Multidimensional Scaling (MDS) are investigated. The data are analyzed with MAXSCAL. For each data collection method, subjects responding to the task become fatigued and bored, whereas increases in stimulus knowledge and task insight do not occur. The amount of fatigue and boredom differs between the data collection methods. Moreover, the type of data collection method used affects both the similarity data and the MDS solution.

Individual Differences in Metacognitive Decision Making and Situation Assessment

28 senior naval officers (experts) and 48 junior naval officers (novices) (1) categorized tactical situations, (2) performed pairwise similarity ratings of them, and (3) represented their metacognitive models of tactical decision making as graphic weighted networks. Multidimensional scaling was conducted employing subjects’ pairwise similarity ratings of tactical situations. Using classification measures and multidimensional weights as dependent variables and salient metacognitive link weights as independent variables, two one-way multivariate analyses of covariance between experts and novices and associated statistics were computed. Some of the results of canonical and regression analyses and product-moment correlations validated an important aspect of a metacognitive model of naturalistic schema-driven tactical decision making. They established significant associations of the two link weights connecting event sequence and similarity recognition to situation assessment with actual performances on the two experimental tasks requiring situation assessment. These findings demonstrated (1) the importance of event sequence and similarity recognition as necessary input to situation assessment, and (2) these two metacognitive links are significantly associated with the recognition of similar scenarios. Experts and novices did not differ significantly in (1) the number of categories, scenarios per category, and times to classify the tactical situations during sorting and resorting, and (2) their derived weights along the two dimensions, warfare tempo and reaction time, of the multidimensional scaling solution.

Using Subject-Matter Experts to Assess Content Representation: An MDS Analysis

Demonstration of content domain representation is of central importance in test validation. An expanded version of the method of content evaluation proposed by Sireci & Geisinger (1992) was evaluated with respect to a national licensure examination and a nationally standardized social studies achievement test. Two groups of 15 subject-matter experts (SMEs) rated the similarity of all item pairs comprising a test, and then rated the relevance of the items to the con tent domains listed in the test blueprints. The similar ity ratings were analyzed using multidimensional scaling (MDS); the item relevance ratings were ana lyzed using procedures proposed by Hambleton (1984) and Aiken (1980). The SMES' perceptions of the underlying content structures of the tests emerged in the MDS solutions. All dimensions were germane to the content domains measured by the tests. Some of these dimensions were consistent with the content structure specified in the test blueprint, others were not. Correlation and regression analyses of the MDS item coordinates and item relevance ratings indicated that using both item similarity and item relevance data provided greater information of content repre sentation than did using either approach alone. The implications of the procedure for test validity are dis cussed and suggestions for future research are provided.

The effect of amplitude envelopes of each amplitude modulated wave on the timbre of compound tones consisting of three amplitude modulated waves.

The timbre of compound tones consisting of three amplitude modulated waves is examined by psychoacoustical experiments using a similarity judgement. The obtained data are analyzed by a multi-dimensional scaling (MDS) method. The MDS solutions are interpreted by the regression equations as a function of the envelope correlation coefficients between the AM waves. In particular, the envelope correlations between adjacent AM waves are the determinant factor. When the modulation rate is slow enough, the fine structure of amplitude envelopes of each AM wave affects the timbre. However, the modulation rate is faster than the auditory temporal resolving power, the fine structure has no effect and the timbre is determined by only the envelope correlations. The auditory system has a function to detect the amplitude envelope correlation between the output signals of the different auditory filters. The present study shows how this function contributes to timbre perception.

Mapping the perceptual magnet effect for speech using signal detection theory and multidimensional scaling.

Recent experiments have demonstrated that the category goodness of speech sounds strongly influences perception in both adult and infants [Kuhl, Percept. Psychophys. 50, 93-107 (1991); Kuhl et al., Science 255, 606-608 (1992)]. Stimuli judged as exceptionally good instances of phonetic categories (prototypes) make neighboring tokens in the vowel space seem more similar, exhibiting a perceptual magnet effect. Three experiments further examined the perceptual magnet effect in adults. Experiment 1 collected goodness and identification judgments for 13 variants of the vowel /i/. Experiment 2 used signal detection theory to assess the discrimination of these tokens using a bias-free measure (d'). Experiment 3 employed multidimensional scaling (MDS) to geometrically model the distortion of the perceptual space due to the magnet effect. The results demonstrated a strong relationship between category goodness and discrimination. Vowel tokens receiving high goodness ratings in experiment 1 were more difficult to discriminate in experiment 2 and were more tightly clustered in the MDS solutions of experiment 3. These findings support the existence of a perceptual magnet effect, and may help explain some aspects of first language learning in infants and second language learning in adults.

Classification and perceived similarity of compound gratings that differ in relative spatial phase.

Discrimination studies suggest that two, and only two, channels encode relative spatial phase shifts in compound gratings (Bennett & Banks, 1991; Field & Nachmias, 1984). The more sensitive channel consists of even-symmetric filters and responds best to cosine phase shifts (e.g., 0 degree-180 degrees); the other consists of odd-symmetric filters and responds best to sine phase shifts (e.g., 90 degrees-270 degrees). The present experiments investigated whether the two-channel model generalizes to suprathreshold perceptual tasks. Experiment 1 examined classification learning of compound gratings, consisting of a fundamental (f) and second harmonic (2f), that differed in 2f contrast and relative phase. Experiments 2 and 3 measured the perceived similarity of f + 2f gratings. The results of Experiment 1 were broadly consistent with the predictions of the two-channel model. Specifically, the classification data were best explained by assuming that classification was based on the responses of differentially sensitive even- and odd-symmetric filters. In Experiments 2 and 3, two-dimensional multidimensional scaling solutions provided a good account for the similarity judgments. In Experiment 2, Dimension 1 was strongly correlated with cosine phase, and Dimension 2 was moderately correlated with sine phase. In Experiment 3, cosine phase was again strongly related to Dimension 1, whereas the absolute value of sine phase was strongly related to Dimension 2. Overall, these results suggest that the two-channel model of phase discrimination provides a useful framework for interpreting classification and similarity judgments of compound gratings.

Musical timbre perception: The influence of onset transients

Previous research on musical timbre has suggested that onsets are particularly important for the perception of musical timbre; identification is poor if listeners do not hear onsets, and dimensions of MDS solutions tend to correspond to attack length. However, more recent research has demonstrated that the dynamic attributes that influence similarity judgments cannot be localized to onset transients [P. Iverson and C. L. Krumhansl, J. Acoust. Soc. Am. 94, 2595–2603 (1993)]. In separate experiments, subjects rated the similarity of complete tones, the onsets of those tones, and tones with the onsets removed (remainders). Multidimensional scaling solutions revealed that judgments on all three sets of tones were quite similar, demonstrating that the attributes that influence timbre in complete tones are present both at onsets and remainders. Results from acoustic analyses suggested that similarity judgments may rely on global acoustic comparisons rather than on the isolation of specific acoustic attributes. In contrast, identification judgments may rely on specific acoustic attributes present only at the onsets. This research will be reviewed in light of new research on musical timbre perception.

Statistical analysis of neural organization

1. The responses of 32 taste neurons in the solitary nucleus of the rat to 12 stimuli were analyzed with multidimensional scaling (MDS) and cluster analysis (CA) procedures. These analyses of empirical taste data were compared with similar analyses of two model data sets of known configuration to help clarify the implications of these methods commonly used in forming conclusions about the organization of the taste system. 2. To relate to possible conclusions about groupings in taste, both model data sets were chosen as the best possible examples of ungrouped data, the first being completely regular (in the form of a checkerboard) across the taste space, the second randomly arranged. The analysis of the present empirical data appear to be similar to the present ungrouped models, more so the random than the regular model, in the sense that all are amenable to grouping. 3. Because of the similarity of these model MDS and CA solutions to the present empirical solutions and to most published analyses of this sort, the idea is suggested that the appearance of the plots per se for empirical data does not support the conclusion of grouping. And, technically, MDS and CA do not have the statistical power to provide conclusions about issues of neural organization. 4. MDS and CA analyses have two very powerful roles relating to their ability to disclose the hidden organization of complex data sets; they may lend support for or refute theories about the data sets developed from other considerations, and may help generate theories for further consideration. The question of groupings is only one of many such issues. 5. Because data in the present and other reports are quite adequately accounted by MDS solutions of low dimensionality, it is suggested that their organization is characterized as continuous (i.e., rather than belonging to several disjoint spaces). 6. The use of correlations as distance measures in MDS and CA procedures distorts the spatial solutions, making analysis by visual inspection misleading. For example, using correlations, the true or natural spatial arrangements of data sets are probably less circular or spherical than shown in published MDS solutions. Also they are probably more evenly distributed across the space in the sense that the points are actually more concentrated toward the centers of the spaces; this may have strong influences on interpretations of the general form of the solutions. CA solutions can be influenced in analogous fashion. These problems of distortion of the solutions can be avoided with use of direct, linear estimates of distances. (ABSTRACT TRUNCATED AT 400 WORDS)

Preorderings, monotone functions, and best rank r approximations with applications to classical MDS

This paper extends the classical results of Eckart and Young (Psychometrika 1, 1936) and Mirsky (Quarterly Journal of Mathematics in Oxford, Series 2, 11, 1960) concerning the best rank r matrix approximation with respect to certain preorderings defined on the space of complex n x k matrices. A note on some related work of Jensen ( J. Stat. Sim. Com. 39 , No. 3, 1991) is included, his assertions, though, are shown to be flawed. In a second part we turn to the problem of approximating a Hermitian matrix by a positive semidefinite matrix of given rank which is of major relevance in the context of multidimensional scaling (MDS). Further universally optimal properties of the classical MDS solution are provided.