Multidimensional analysis of complex structure: Mixtures of class and quantitative variation

For certain kinds of structure consisting of quantitative dimensions superimposed on a discrete class structure, spatial representations can be viewed as being composed of two subspaces, the first of which reveals the discrete classes as isolated clusters and the second of which contains variation along the quantitative attributes. A numerical method is presented for rotating a multi-dimensional configuration or factor solution so that the first few axes span the space of classes and the remaining axes span the space of quantitative variation. The use of this method is then illustrated in the analysis of some experimental data.

[1]  A. Householder,et al.  Discussion of a set of points in terms of their mutual distances , 1938 .

[2]  P. Halmos Finite-Dimensional Vector Spaces , 1960 .

[3]  G. A. Miller,et al.  An Analysis of Perceptual Confusions Among Some English Consonants , 1955 .

[4]  W. L. Sawrey,et al.  An Objective Method of Grouping Profiles by Distance Functions and its Relation to Factor Analysis , 1960 .

[5]  D. Brillinger,et al.  Multivariate Procedures for the Behavioral Sciences. , 1964 .

[6]  W. A. Wickelgren,et al.  Distinctive features and errors in short-term memory for English consonants. , 1966, The Journal of the Acoustical Society of America.

[7]  J. B. Kruskal,et al.  A geometric interpretation of diagnostic data from a digital machine: Based on a study of the morris, illinois electronic central office , 1966 .

[8]  S. C. Johnson Hierarchical clustering schemes , 1967, Psychometrika.

[9]  J. Rubin Optimal classification into groups: an approach for solving the taxonomy problem. , 1967, Journal of theoretical biology.

[10]  Louis L. McQuitty,et al.  A Novel Application of the Coefficient of Correlation in the Isolation of Both Typal and Dimensional Constructs , 1967 .

[11]  Bennett L. Fox,et al.  Scientific Applications: An algorithm for identifying the ergodic subchains and transient states of a stochastic matrix , 1967, Commun. ACM.

[12]  L. Guttman A general nonmetric technique for finding the smallest coordinate space for a configuration of points , 1968 .

[13]  Forrest W. Young Computer program abstracts , 1968 .

[14]  E. Pollack THE ROLE AND METHODOLOGY OF CLASSIFICATION IN PSYCHIATRY AND PSYCHOPATHOLOGY , 1969 .