pcoa: Classical Multidimensional Scaling Function

Description

pcoa performs classical multidimensional scaling or principal coordinates analysis. The function uses an eigenvalue decomposition on a Gramm matrix. The data are supposed to be distances, but often dissimilarities will do fine. The data matrix contains nonnegative values, is square, symmetric, and hollow. NA's are not allowed. An additive constant may be provided, which is added to the dissimilarities. This constant might be obtained optimally with the function fastaddconst(). Error checking focuses on the data requirements.

Usage

pcoa(
  delta = NULL,
  lower = NULL,
  data = NULL,
  p = 2,
  k = NULL,
  ac = 0,
  q = NULL,
  faster = FALSE,
  error.check = FALSE
)

Value

either n by p coordinates matrix (if q == NULL) or h by p coefficients matrix b (if q != NULL), in which case z = qb

Arguments

delta: dissimilarity matrix, non-negative, square, and hollow.
lower: lower triangular part of dissimilarity matrix.
data: multivariate data matrix.
p: dimensionality (default = 2).
k: number of landmark points (default = NULL, i.e., no landmarks).
ac: additive constant (default = 0.0, i.e., no additive constant). An additive constant can be obtained with the function fastaddconst( d ) or can be user specified.
q: matrix with h independent n-sized variables ( nrow( q ) >= p ), specifying the linear restriction z = qb (coordinates = variables times coefficients)
faster: logical indicating faster but less precise procedure
error.check: extensive check validity input parameters (default = FALSE).

Author

Frank M.T.A. Busing

References

Young and Householder (1938) Torgerson (1952, 1958) Gower (1966) Carroll, Green, and Carmone (1976) De Leeuw and Heiser (1982) Ter Braak (1992) Borg and Groenen (2005)