The R Project SVN – R – Diff – /trunk/src/library/stats/man/cmdscale.Rd



  A set of Euclidean distances on \eqn{n} points can be represented
  exactly in at most \eqn{n - 1} dimensions.  \code{cmdscale} follows
  the analysis of Mardia (1978), and returns the best-fitting
  \eqn{k}-dimensional representation, where \eqn{k} may be less than the
  argument \code{k}.
 
  The representation is only determined up to location (\code{cmdscale}
  takes the column means of the configuration to be at the origin),
  rotations and reflections.  The configuration returned is given in
  principal-component axes, so the reflection chosen may differ between
  \R platforms (see \code{\link{prcomp}}).
 
  When \code{add = TRUE}, a minimal additive constant \eqn{c*} is
  computed such that the the dissimilarities \eqn{d_{ij} + c*}{d[i,j] +
  c*} are Euclidean and hence can be represented in \code{n - 1}
  dimensions.  Whereas S (Becker \emph{et al.}, 1988) computes this
  constant using an approximation suggested by Torgerson, \R uses the

 
  Cox, T. F. and Cox, M. A. A. (2001)
  \emph{Multidimensional Scaling}.  Second edition.
  Chapman and Hall.
 
  Gower, J. C. (1966)
  Some distance properties of latent root and vector
  methods used in multivariate analysis.
  \emph{Biometrika} \bold{53}, 325--328.
 
  Krzanowski, W. J. and Marriott, F. H. C. (1994)
  \emph{Multivariate Analysis. Part I. Distributions, Ordination and
  Inference.}  London: Edward Arnold. (Especially pp. 108--111.)
 
  Mardia, K.V. (1978)
  Some properties of classical multidimensional scaling.
  \emph{Communications on Statistics -- Theory and Methods}, \bold{A7},
  1233--41.
 
  Mardia, K. V., Kent, J. T. and Bibby, J. M. (1979).  Chapter 14 of
  \emph{Multivariate Analysis}, London: Academic Press.
 
  Seber, G. A. F. (1984).
  \emph{Multivariate Observations}.

The R Project SVN R

(root)/trunk/src/library/stats/man/cmdscale.Rd – Rev 59039 → 61433

Rev 59039		Rev 61433
Line 38...		Line 38...
38	`A set of Euclidean distances on \eqn{n} points can be represented`	38	`A set of Euclidean distances on \eqn{n} points can be represented`
39	`exactly in at most \eqn{n - 1} dimensions. \code{cmdscale} follows`	39	`exactly in at most \eqn{n - 1} dimensions. \code{cmdscale} follows`
40	`the analysis of Mardia (1978), and returns the best-fitting`	40	`the analysis of Mardia (1978), and returns the best-fitting`
41	`\eqn{k}-dimensional representation, where \eqn{k} may be less than the`	41	`\eqn{k}-dimensional representation, where \eqn{k} may be less than the`
42	`argument \code{k}.`	42	`argument \code{k}.`
43		43
44	`The representation is only determined up to location (\code{cmdscale}`	44	`The representation is only determined up to location (\code{cmdscale}`
45	`takes the column means of the configuration to be at the origin),`	45	`takes the column means of the configuration to be at the origin),`
46	`rotations and reflections. The configuration returned is given in`	46	`rotations and reflections. The configuration returned is given in`
47	`principal-component axes, so the reflection chosen may differ between`	47	`principal-component axes, so the reflection chosen may differ between`
48	`\R platforms (see \code{\link{prcomp}}).`	48	`\R platforms (see \code{\link{prcomp}}).`
49		49
50	`When \code{add = TRUE}, a minimal additive constant \eqn{c*} is`	50	`When \code{add = TRUE}, a minimal additive constant \eqn{c*} is`
51	`computed such that the the dissimilarities \eqn{d_{ij} + c*}{d[i,j] +`	51	`computed such that the the dissimilarities \eqn{d_{ij} + c*}{d[i,j] +`
52	`c*} are Euclidean and hence can be represented in \code{n - 1}`	52	`c*} are Euclidean and hence can be represented in \code{n - 1}`
53	`dimensions. Whereas S (Becker \emph{et al.}, 1988) computes this`	53	`dimensions. Whereas S (Becker \emph{et al.}, 1988) computes this`
54	`constant using an approximation suggested by Torgerson, \R uses the`	54	`constant using an approximation suggested by Torgerson, \R uses the`
Line 90...		Line 90...
90		90
91	`Cox, T. F. and Cox, M. A. A. (2001)`	91	`Cox, T. F. and Cox, M. A. A. (2001)`
92	`\emph{Multidimensional Scaling}. Second edition.`	92	`\emph{Multidimensional Scaling}. Second edition.`
93	`Chapman and Hall.`	93	`Chapman and Hall.`
94		94
95	`Gower, J. C. (1966)`	95	`Gower, J. C. (1966)`
96	`Some distance properties of latent root and vector`	96	`Some distance properties of latent root and vector`
97	`methods used in multivariate analysis.`	97	`methods used in multivariate analysis.`
98	`\emph{Biometrika} \bold{53}, 325--328.`	98	`\emph{Biometrika} \bold{53}, 325--328.`
99		99
100	`Krzanowski, W. J. and Marriott, F. H. C. (1994)`	100	`Krzanowski, W. J. and Marriott, F. H. C. (1994)`
101	`\emph{Multivariate Analysis. Part I. Distributions, Ordination and`	101	`\emph{Multivariate Analysis. Part I. Distributions, Ordination and`
102	`Inference.} London: Edward Arnold. (Especially pp. 108--111.)`	102	`Inference.} London: Edward Arnold. (Especially pp. 108--111.)`
103		103
104	`Mardia, K.V. (1978)`	104	`Mardia, K.V. (1978)`
105	`Some properties of classical multidimensional scaling.`	105	`Some properties of classical multidimensional scaling.`
106	`\emph{Communications on Statistics -- Theory and Methods}, \bold{A7},`	106	`\emph{Communications on Statistics -- Theory and Methods}, \bold{A7},`
107	`1233--41.`	107	`1233--41.`
108		108
109	`Mardia, K. V., Kent, J. T. and Bibby, J. M. (1979). Chapter 14 of`	109	`Mardia, K. V., Kent, J. T. and Bibby, J. M. (1979). Chapter 14 of`
110	`\emph{Multivariate Analysis}, London: Academic Press.`	110	`\emph{Multivariate Analysis}, London: Academic Press.`
111		111
112	`Seber, G. A. F. (1984).`	112	`Seber, G. A. F. (1984).`
113	`\emph{Multivariate Observations}.`	113	`\emph{Multivariate Observations}.`