CrissCross: Alternated Least Squares Biplot

In MultBiplotR: Multivariate Analysis Using Biplots in R

Alternated Least Squares Biplot

Description

Alternated Least Squares Biplot with any choice of weigths for each element of the data matrix

Usage

CrissCross(x, w = matrix(1, dim(x)[1], dim(x)[2]), dimens = 2, a0 = NULL, 
b0 = NULL, maxiter = 100, tol = 1e-04, addsvd = TRUE, lambda = 0)

Arguments

x	Data Matrix to be analysed
w	Weights matrix. Must be of the same size as X.
dimens	Dimension of the solution.
a0	Starting row coordinates. Random coordinates are calculated if the argument is NULL.
b0	Starting column coordinates. Random coordinates are calculated if the argument is NULL.
maxiter	Maximum number of iterations
tol	Tolerance for the algorithm to converge.
addsvd	Calculate an additional SVD at the end of the algorithm. That meakes the final solution more readable
lambda	Constant to add to the diagonal of the natrices to be inverted in order to improve stability when the matrices are ill-conditioned.

Details

The function calculates Alternated Least Squares Biplot with any choice of weigths for each element of the data matrix. The function is useful when we want a low rank approximation of a data matrix in which each element of the matrix has a different weight, for example, all the weights are 1 except for the missing elements that are 0, or to model the logarithms of a frequency table using the frequencies as weights.

Value

An object of class .Biplot" with the following components:

n	Number of Rows
p	Number of Columns
dim	Dimension of the Biplot
EigenValues	Eigenvalues
Inertia	Explained variance (Inertia)
CumInertia	Cumulative Explained variance (Inertia)
RowCoordinates	Coordinates for the rows
ColCoordinates	Coordinates for the columns
RowContributions	Contributions for the rows
ColContributions	Contributions for the columns
Scale_Factor	Scale factor for the traditional plot with points and arrows. The row coordinates are multiplied and the column coordinates divided by that scale factor. The look of the plot is better without changing the inner product. For the HJ-Biplot the scale factor is 1.

Author(s)

Jose Luis Vicente Villardon

References

GABRIEL, K.R. and ZAMIR, S. (1979). Lower rank approximation of matrices by least squares with any choice of weights. Technometrics, 21: 489-498.

See Also

LogFrequencyBiplot

Examples

data(Protein)
X=as.matrix(Protein[,3:11])
X = InitialTransform(X, transform=5)$X
bip=CrissCross(X)

MultBiplotR documentation built on Nov. 21, 2023, 5:08 p.m.