gradientDesc: Gradient function for Binary Logistic Biplot

In jgbabativam/BiplotML: Biplots Estimation with Algorithms ML

Gradient function for Binary Logistic Biplot

Description

This function computes the parameters of A and B in Binary Logistic Biplot under algorithm of Descendent Gradient.

Usage

gradientDesc(
  x,
  k = 2,
  rate = 0.001,
  converg = 0.001,
  max_iter,
  plot = FALSE,
  ...
)

Arguments

x	Binary matrix.
k	Dimensions number. By default k = 2.
rate	The value of the rate of descent α in the algorithm of descending gradient. By default α = 0.001.
converg	Tolerance limit to achieve convergence. By default converg = 0.001
max_iter	Maximum iterations number.
plot	Plot the Logistic Biplot.
...	other arguments

Details

We note that the Binary Logistic Biplot is defined as:

logit(π_{ij})= log≤ft( \frac{π_{ij}}{1-π_{ij}} \right)=μ_{j}+∑_{s=1}^kb_{js}a_{is} = μ_{j}+\mathbf{a_i^{T}b_j}

Also, note that the gradient is:

\nabla \ell= ≤ft(\frac{\partial \ell}{\partial μ}, \frac{\partial \ell}{\partial \mathbf{A}}, \frac{\partial \ell}{\partial \mathbf{B}}\right)== ≤ft( (Π - \mathbf{X})^T, (Π - \mathbf{X})\mathbf{B}, (Π - \mathbf{X})^TA \right)

Value

The coefficients of A and B matrix.

Author(s)

Giovany Babativa <[e-mail]>

References

Vicente-Villardon, J.L. and Galindo, M. Purificacion (2006), Multiple Correspondence Analysis and related Methods. Chapter: Logistic Biplots. Chapman-Hall

See Also

plotBLB, performanceBLB

Examples

data('Methylation')
set.seed(02052020)
MatGD <- gradientDesc(x = Methylation, k=2, max_iter=10000)
outGD <- gradientDesc(x = Methylation, k=2, max_iter=10000, plot = TRUE)

jgbabativam/BiplotML documentation built on July 31, 2022, 11:10 a.m.