CrissCross: Alternated Least Squares Biplot

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/CrissCross.R

Description

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

Usage

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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

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MultBiplotR documentation built on April 6, 2021, 9:08 a.m.