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Abstract:
Shepard (1981) theorized that perceived similarity between
stimuli decreases exponentially for generalization gradients of
similarity judgements. There are two classes of stimuli: integral
have high interactions between stimulus dimensions; and separable
have independent dimensions (Garner, 1974). Shepard also theorized
that psychological space from which similarity distance is computed
depends on stimulus type. Computed similarity depends on the
exponential similarity gradient and the appropriate metric space.
This has been the basis of human categorization models (e.g., Medin
& Schaffer, 1978). We examined Shepard's (1981) generalization
theory. The stimuli were schematic faces that were ambiguous as to
what stimulus class they belonged. A prototype face was generated,
from which 10 distortion levels were generated by adding Gaussian
noise. Results from magnitude estimates between the prototype and
exemplars showed POWER (sqrt) rather then EXPONENTIAL trends (96%
vs 94%). Experiment 2 collected pairwise similarity judgements
between all stimuli and were submitted to a Multidimensional
scaling algorithm (MDS). The judgements were best fit by an
Euclidian metric (i.e., treated as integral). The derived
similarity gradient from the MDS was fit by an EXPONENTIAL or POWER
function. The Square root function from experiment 1 also provided
an excellent fit. A model based on a NEURAL NETWORK AUTO-ASSOCIATOR
provides an approximation of the similarity functions.
Consequently, neither the exponential similarity gradient nor the
two distance metrics may be required to account for human
similarity judgements.
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