Multidimensional similarity: an experimental and theoretical comparison of vector, distance, and set theoretical models

Eisler, Hannes; Roskam, Edward E.

doi:10.1016/0001-6918(77)90009-9

Cited by 55 publications

(22 citation statements)

References 37 publications

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“…In addition, we further expect that Model 1 fits best if p= 1, because there is ample evidence (e.g., Eisler & Roskam, 1977;Shepard, 1964;Torgerson, 19S8) that the city-block metric is the adequate distance function for "analyzable" stimuli, such as rectangles. "Fits best" does not necessarily mean, however, that the stress has to be lowest for p = 1.…”

mentioning

confidence: 99%

Dimensional models for the perception of rectangles

Borg

Leutner

1983

Perception & Psychophysics

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Krantz and Tversky (1975), Takane (1981), Wender (1971), and others have suggested that it is impossible to explain similarity judgments for rectangles by a simple dimensional model of the Minkowski distance type, because the psychologically compelling dimensions are not independent and interact, For reasons never made explicit, the relevant dimensions were assumed to be area and shape, rather than width and height. Reanalyses show, however, that the latter dimensions, appropriately scaled, eliminate interaction effects. To test these conclusions empirically, an experiment was carried out with two sets of rectangles. Each set was a complete 4X4 design, one in width X height coordinates, and one in area X shape coordinates. For each stimulus set, 21 subjects judged the dissimilarities of all pairs of rectangles twice. All subjects were reliable. Apart from one extreme subject in each group, all data lead to very similar MDS solutions. These solutions correspond closely to the predictions, that is, they can be well approximated with physical width and height coordinates rescaled such that the units decrease increasingly as one moves away from the origin. No interaction effects are found, but some indications for a more complicated composition rule are observed.

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confidence: 99%

Dimensional models for the perception of rectangles

Borg

Leutner

1983

Perception & Psychophysics

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“…For example. in the experiments reported by Eissler and Roskam (1977) and Roskam (1979). the stimuli were vectors of various lengths and orientation .…”

Section: Quadratic Transformationsmentioning

confidence: 72%

On possible psychophysical maps: I. Quadratic transformations

Schönemann

1979

Bull. Psychon. Soc.

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A certain class of quadratic transformations can be used to map multidimensional physical spaces into multidimensional perceptual spaces; their numerical representations change under various coordinate transformations in both spaces.where E denotes the physical. experimentally controllable space that is represented by a (possibly bounded) region in Re x Re = Re' • and s eRe' denotes the subjective space. The second pair. a,s, can be interpreted as log transforms of area (hw) and shape (h /w), Krantz and Tversky found decomposability violated for both Equations I and 2. This means that neither pair can give rise to Minkowsky metrics monotone with the observed dissimilarities. Krantz and Tversky then processed the observed dissimilarities with two multidimensional scaling programs. They accepted a fit of the INDSCAL model (1. D. Carroll & Chang. 1970) in two dimensions. but without testing it with any stringency. If the assumptions of the model are met. then the coordinate axes in S. that is. the "psychological dimensions ." are uniquely identified by the data.1 The main result of this scaling analysis was a distortion of the design configuration that seemed to corroborate the resultsThe problem of relating two or more multidimensional spaces arises both in scaling and in factor analysis. The technology for fitting such transformations optimally in some sense (usually a least squares sense) is reasonably well understood for the group of affine transformations and its subgroups : similarities. rigid motions, and rotations ("Procrustes" problems, e.g

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“…Thus, the degree of adaptation, measured by using a common test stimulus 5 sec after the end of adaptation, can be described as a linear function of the logarithm ofthe adapting concentration. The mean difference between observed and calculated data is 6.3% for D M E , and 4.9% for D RT • As a further test ofgoodness of fit, the proportion of explained variance-the coefficient U-as suggested by Eisler and Roskam (1977), was…”

Section: Resultsmentioning

confidence: 99%

Influence of the intensity of NaCl solutions on adaptation degree and recovery time course

Szabó

Bujas²,

Ajduković

et al. 1997

Perception & Psychophysics

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and MARIJAN VODANOVIC HAZU, Zagreb, CroatiaThe degree of adaptation and the time course of recovery after adaptation to NaCl solutions of various intensities were examined by magnitude estimation and simple sensory reaction time using a test stimulus of constant intensity. The results show that the degree of adaptation increased with the adapting concentration following a negatively accelerated function. Similarly,all recovery curves were negatively accelerated functions of the recovery time. The relation between the recovery constant (time necessary to attain two-thirds of normal responsivity) and adapting concentration approximates with both criteria more or less a linear function. Thus the recovery constant is a positively accelerated function of the degree of adaptation. The relationship between concentration and degree of adaptation can be approximated by Beidler's equation of taste stimulation, while the time course of recovery can be expressed by an exponential equation that can also be related to Beidler's theory. The two criteria used showed similar deteriorating effects of taste adaptation, indicating that reaction time can also be a useful criterion of the level of sensory responsivity.Prolonged steady stimulation of taste receptors results in changes in the response level of the gustatory system. These changes, known as adaptation phenomena, generally consist of some reduction in the taste response, and are therefore used as criteria ofadaptation effects. The criteria are various: threshold values, sensation intensity, time necessary for the disappearance of taste, total taste effect, reaction time, and speed of recovery. With the neurophysiological approach, taste adaptation was assessed according to changes in the transient and tonic portions of the inte-

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Multidimensional similarity: an experimental and theoretical comparison of vector, distance, and set theoretical models

Cited by 55 publications

References 37 publications

Dimensional models for the perception of rectangles

Dimensional models for the perception of rectangles

On possible psychophysical maps: I. Quadratic transformations

Influence of the intensity of NaCl solutions on adaptation degree and recovery time course

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