A generalization of the interpoint distance model

Psychometrika ◽  
1964 ◽  
Vol 29 (2) ◽  
pp. 167-176 ◽  
Author(s):  
John Ross ◽  
Norman Cliff
1986 ◽  
Vol 23 (3) ◽  
pp. 271-280 ◽  
Author(s):  
J. Douglas Carroll ◽  
Paul E. Green ◽  
Catherine M. Schaffer

Correspondence anal/sis is a metric technique for finding a spatial representation of data that has particular applicability to the analysis of cross tabulations (or contingency tables). The authors focus on some of the geometric underpinnings of the procedure and the kinds of statements that can be made about interobject similarity based on a distance model. In particular, a rationale is developed, along with a scaling of coordinates, that enables one to compare both between-set and within-set squared distances. This scaling differs from the conventional scaling currently used in correspondence analysis, where only one set of distances usually are compared.


2005 ◽  
Vol 5 (3-4) ◽  
pp. 293-348 ◽  
Author(s):  
Kimberly Jameson

AbstractExisting research in color naming and categorization primarily reflects two opposing views: A Cultural Relativist view that posits color perception is greatly shaped by culturally specific language associations and perceptual learning, and a Universalist view that emphasizes panhuman shared color processing as the basis for color naming similarities within and across cultures. Recent empirical evidence finds color processing differs both within and across cultures. This divergent color processing raises new questions about the sources of previously observed cultural coherence and cross-cultural universality. The present article evaluates the relevance of individual variation on the mainstream model of color naming. It also presents an alternate view that specifies how color naming and categorization is shaped by both panhuman cognitive universals and socio-cultural evolutionary processes. This alternative view, expressed, in part, using an Interpoint Distance Model of color categorization, is compatible with new empirical results showing divergent color processing within and across cultures. It suggests that universalities in color naming and categorization may naturally arise across cultures because color language and color categories primarily reflect culturally modal linguistic mappings, and categories are shaped by universal cognitive constructs and culturally salient features of color. Thus, a shared cultural representation of color based on widely shared cognitive dimensions may be the proper foundation for universalities of color naming and categorization. Across cultures this form of representation may result from convergent responses to similar pressures on color lexicon evolution.


1977 ◽  
Vol 5 (1) ◽  
pp. 21-39 ◽  
Author(s):  
Christopher Winship
Keyword(s):  

1983 ◽  
Vol 20 (3) ◽  
pp. 513-528 ◽  
Author(s):  
Richard J. Kryscio ◽  
Roy Saunders

For stationary Poisson or Poisson cluster processes ξ on R2 we study the distribution of the interpoint distances using the interpoint distance function and the nearest-neighbor indicator function . Here Sr (x) is the interior of a circle of radius r having center x, I(t) is that subset of D which has x ∊ D and St(x) ⊂ D and χ is the usual indicator function. We show that if the region D ⊂ R2 is large, then these functions are approximately distributed as Poisson processes indexed by and , where µ(D) is the Lebesgue measure of D.


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