gradientDesc {BiplotML} R Documentation

## 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 <gbabativam@gmail.com>

### References

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

plotBLB, performanceBLB
data('Methylation')