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Дата: April 12, 2006 09:38PM
В хэлпе к программе STATISTICA 6.0 всё написано ))))))
MDS - Notes and Technical Information
Multidimensional Scaling is an implementation of non-metric multidimensional scaling. Comprehensive introductions to the computational approach used in this module can be found in Borg and Lingoes (1987), Borg and Shye (in press), Guttman (1968), Schiffman, Reynolds, and Young (1981), Young and Hamer (1987), and in Kruskal and Wish (1978).
As the starting configuration, principal components of the similarity/dissimilarity matrix are computed. STATISTICA will then begin iterations under steepest descent (see, for example, Schiffman, Reynolds, and Young, 1981). The goal of these iterations is to minimize the raw stress (or raw Phi) and the coefficient of alienation (see Guttman, 1968). The raw stress is defined as:
where dij are the reproduced distances, given the current number of dimensions, and f(dij) represents the monotone transformation of the observed input data dij (Deltaij).
The coefficient of alienation K is defined as:
In general, STATISTICA attempts to minimize the differences between the reproduced distances and a monotone transformation of the input data, that is, the program attempts to reproduce the rank-ordering of the input distances or similarities (hence, also the name nonmetric multidimensional scaling).
Note that under steepest descent the fitted values are calculated via the rank-image permutation procedure (see Guttman, 1968; or Schiffman, Reynolds, & Young, 1981, pp. 368-369).After each iteration under steepest descent the program will perform up to five iterations using the monotone regression transformation procedure (see Kruskal, 1964; or Schiffman, Reynolds, & Young, 1981, pp. 367-368). This procedure is aimed at minimizing the standardized stress (S):
Before final convergence, STATISTICA performs several monotone regression transformation iterations.
D-Stars and D-Hats. D-stars are calculated via a procedure known as the rank-image permutation procedure (see Guttman, 1968; or Schiffman, Reynolds, & Young, 1981, pp. 368-369). In general, this procedure attempts to reproduce the rank order of differences in the similarity or dissimilarity matrix. D-hats are calculated via a procedure referred to as the monotone regression transformation procedure (see Kruskal, 1964;Schiffman, Reynolds, & Young, 1981, pp. 367-368). In this procedure, the program attempts to determine the best monotone (regression) transformation to reproduce the similarities (or dissimilarities) in the input matrix.