On the Need for A General Quantitative Theory of Pattern Similarity

Perceptual interactions of facial dimensions in speeded classification and identification

“…In addition to invariance in performance for the relevant component while the irrelevant component varies, absolute separability should also include the case in which it does not matter whether the opposing dimension exists or not (Garner, 1974;Townsend & Thomas, 1993), at least in such cases where this is possible. Ashby and Townsend (1986) claim that their definition of perceptual separability (PS) applies equally to the case in which features are either present or absent to the case in which the feature is always present but varies along a continuous dimension.…”

A Differential Geometric Description of the Relationships among Perceptions

“…In short, the existence of a metric is a significant experimental question, above and beyond the existence of an affine connection. The method presented in this paper does not assume that the observer has such a sense of``distance,'' unlike certain variants of multidimensional scaling (Shepard, 1964;Beals, Krantz 6 Tversky, 1968;Baird 6 Noma, 1978;Lindman 6 Caelli, 1978;Carroll 6 Arabie, 1980;Townsend 6 Thomas, 1993). The approach in this paper differs significantly from that of Dzhafarov and Colonius (1999) who also proposed a multidimensional generalization of Fechnerian psychophysics.…”

“…This way of describing psychological spaces is different from that provided by multidimensional scaling or MDS (Shepard, 1964;Beals, Krantz, 6 Tversky, 1968;Rumelhart 6 Abrahamson, 1973;Baird 6 Noma, 1978;Lindman 6 Caelli, 1978;Holman, 1978;Carroll 6 Arabie, 1980;Townsend 6 Thomas, 1993). Both methods attempt to describe a psychological manifold that is populated by internal states of the observer (e.g., perceptions).…”

Maximum Entropy Inference and Stimulus Generalization

“…The Minkowski r-metric is often found to fit generalization data closely and is defined as In particular, the city-block metric (r=1) better describes data obtained for stimuli differing along separable dimensions, such as size and orientation of shapes, whereas the Euclidean metric (r=2) better describes data obtained for stimuli differing along integral dimensions, such as saturation and lightness of colors (for reviews see Garner, 1974, andShepard, 1991; for a critical review of related issues, see Townsend 6 Thomas, 1993). There is some evidence, however, that generalization data may be better described by a Minkowski r-metric with a non-integer r-value between 1 and 2, or greater than 2, or even less than 1 (see, e.g., Kruskal, 1964;Shepard, 1964;Tversky 6 Gati, 1982;and Shepard, 1991).…”