Trajectory Mapping: A New Nonmetric Scaling Technique

Trajectory mapping is a new scaling technique designed to recover the parameterizations, axes, and paths used to traverse a feature space. Unlike with multidimensional scaling, there is no assumption that the space is homogeneous or metric. Although some metric ordering information is obtained with trajectory mapping, the main output is the feature parameterizations that partition the given domain of object samples into different categories. After an introductory example, the technique is further illustrated by using first a set of colors and then a collection of textures.

[1]  Amos Tversky,et al.  Studies of similarity , 1978 .

[2]  J. W. Hutchinson,et al.  Nearest neighbor analysis of psychological spaces. , 1986 .

[3]  D JAMESON,et al.  Some quantitative aspects of an opponent-colors theory. IV. A psychological color specification system. , 1956, Journal of the Optical Society of America.

[4]  R W BURNHAM Comparison of color systems with respect to uniform visual spacing. , 1949, Journal of the Optical Society of America.

[5]  D. Gentner,et al.  Respects for similarity , 1993 .

[6]  R. Shepard The analysis of proximities: Multidimensional scaling with an unknown distance function. II , 1962 .

[7]  J. Kruskal Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis , 1964 .

[8]  U EBBECKE,et al.  [Goethe's color theory]. , 1949, Experientia.

[9]  J. M. Rubin,et al.  Color Vision: Representing Material Categories , 1984 .

[10]  M. Zigler,et al.  Color in business, science and industry. , 1953 .

[11]  D. L. Macadam Uniform color scales. , 1974, Journal of the Optical Society of America.

[12]  W. Torgerson Multidimensional scaling: I. Theory and method , 1952 .

[13]  R. Shepard The analysis of proximities: Multidimensional scaling with an unknown distance function. I. , 1962 .

[14]  A. Ravishankar Rao,et al.  Identifying High Level Features of Texture Perception , 1993, CVGIP Graph. Model. Image Process..

[15]  David L. MacAdam,et al.  Colorimetric data for samples of OSA uniform color scales , 1978 .