BiplotML implements methods for fitting logistic biplot models to multivariate binary data. A logistic biplot represents individuals as points and binary variables as directed vectors in a low-dimensional subspace. The orthogonal projection of each individual's point onto a variable's vector approximates the expected probability that the corresponding characteristic is present, providing an intuitive simultaneous visualization of observations and variables.

The package provides several fitting algorithms:

MM — Coordinate descent Majorization-Minimization algorithm (fast, recommended default).
PDLB — Block coordinate descent algorithm based on data projection; handles matrices with missing values and allows new individuals to be projected as supplementary rows without refitting the model.
CG — Conjugate gradient algorithms (Fletcher–Reeves, Polak–Ribière, Beale–Sorenson, Dai–Yuan).
BFGS — Broyden–Fletcher–Goldfarb–Shanno quasi-Newton method.

A k-fold cross-validation function (cv_LogBip) is included to help select the number of dimensions.

Installation

Install the released version from CRAN:

install.packages("BiplotML")

Or install the development version from GitHub:

# install.packages("devtools")
devtools::install_github("jgbabativam/BiplotML")

Usage

library(BiplotML)
data("Methylation")
# Fit a logistic biplot using the MM algorithm (default)
res_MM <- LogBip(x = Methylation, method = "MM", maxit = 1000)
# Fit using the PDLB algorithm (supports missing data and supplementary rows)
set.seed(12345)
n <- nrow(Methylation); p <- ncol(Methylation)
miss <- matrix(rbinom(n * p, 1, 0.2), n, p)
miss <- ifelse(miss == 1, NA, miss)
x_miss <- Methylation + miss
res_PDLB <- LogBip(x = x_miss, method = "PDLB", maxit = 1000)
# Select the number of dimensions via cross-validation
cv_result <- cv_LogBip(data = Methylation, k = 0:5, method = "MM")
# Bootstrap confidence ellipses
set.seed(02052020)
res_boot <- bootBLB(x = Methylation, ellipses = TRUE)

Main functions

Function	Description
`LogBip()`	Fit a logistic biplot using a chosen algorithm
`sdv_MM()`	Coordinate descent MM algorithm (called internally by `LogBip`)
`proj_LogBip()`	Block coordinate descent with data projection and missing-data support
`cv_LogBip()`	Cross-validation to select the number of dimensions
`bootBLB()`	Bootstrap logistic biplot with confidence ellipses
`plotBLB()`	Plot a logistic biplot from a `BiplotML` object
`pred_LB()`	Predict binary responses and compute optimal per-variable thresholds
`fitted_LB()`	Extract fitted values on the logit or probability scale
`performanceBLB()`	Compare convergence and speed across multiple optimization algorithms
`gradientDesc()`	Fit a logistic biplot via simple gradient descent
`simBin()`	Simulate a binary data matrix from a latent variable model

Citation

If you use BiplotML in your research, please cite:

Babativa-Márquez, J. G., & Vicente-Villardón, J. L. (2021). Logistic biplot by conjugate gradient algorithms and iterated SVD. Mathematics, 9(16), 2015. https://doi.org/10.3390/math9162015

Author

Maintained by Jose Giovany Babativa-Marquez — jgbabativam@unal.edu.co