NEWS.md

In BiplotML: Logistic Biplot Estimation Using Machine Learning Algorithms

BiplotML 1.1.1

Resubmission to CRAN

This version restores the package to CRAN after it was archived on 2023-10-29 due to a dependency on the optimr package, which was removed from CRAN at the maintainer's request. All calls to optimr() now use optimx::optimr(), which is the current home of that function.

Dependency changes

• The optimr package has been removed from Imports. Its function optimr() is now imported from optimx, which absorbed it.
• optimr, optimx, and shapes moved from Depends to Imports, in line with CRAN policy.
• RSpectra moved from Suggests to Imports, since it is unconditionally required for large matrices in proj_LogBip().

Bug fixes

• bootBLB(): fixed a column-naming bug that caused plotBLB() to fail with "Column 'Dim1' not found" after bootstrap aggregation.
• bootBLB(): suppressed verbose control messages printed to the console by optimx::optimr() when using the CG method.
• Fixed typo Sensitivy -> Sensitivity in the confusion-matrix output of bootBLB() and pred_LB().

Internal changes

• All non-ASCII characters (typographic dashes, accented letters) in R source files replaced with portable ASCII equivalents, as required by CRAN.
• utils::globalVariables() declaration moved to R/zzz.R to prevent a roxygen2 block error in plotBLB.R.
• Removed incorrect importFrom(stats, svd) and importFrom(stats, eigen) from NAMESPACE: both functions belong to base R.
• All ggplot2::aes() calls updated to use .data[[]] tidy evaluation, eliminating R CMD check NOTEs about undefined global variables.
• inst/CITATION updated from the deprecated citEntry() to bibentry().
• sdv_MM(): loop variable j initialised before the loop to prevent a potential "object not found" error on zero iterations.
• RoxygenNote updated to 7.3.3.

BiplotML 1.1.0

New algorithm: projection-based logistic biplot with missing data

Version 1.1.0 introduced a major new fitting method for the logistic biplot model, described in:

Babativa-Marquez, J. G., & Vicente-Villardon, J. L. (2022). A coordinate descent MM algorithm for logistic biplot model with missing data. In process.

The problem addressed

All previous logistic biplot algorithms (alternating, external logistic, and the conjugate gradient / iterated SVD methods introduced in v1.0.0) share a structural limitation: each row of the data matrix has its own parameter vector theta_i = mu_i + sum_s a_is * b_s. Consequently:

• The number of parameters to estimate grows with the number of rows, making the model computationally impractical for large datasets.
• Projecting new individuals as supplementary rows requires re-running the full optimisation, because the row markers are free parameters. This introduces a risk of overfitting.
• None of the previous algorithms handled missing data directly.

The new approach

The new method reformulates the logistic biplot using Pearson's (1901) data projection idea, extended to the logistic case by Landgraf & Lee (2020). Instead of treating each row's coordinates as independent free parameters, the row markers are expressed as a projection of the (centred) data matrix onto a low-rank subspace V:

A = (X - 1 * mu') * V

This single change has three important consequences:

1. The number of parameters no longer depends on n. Only the p x k matrix V (column markers) and the p-vector mu (intercepts) need to be estimated, regardless of how many rows the data matrix has.

2. New individuals can be projected without refitting. Given estimated V and mu, the row markers of any new observation x_new are simply: a_new = (x_new - mu') * V. No optimisation is required.

3. Missing data are handled natively. A weight matrix W (W_ij = 1 if x_ij is observed, 0 if missing) is incorporated into the loss function. Missing entries are imputed at each iteration using the current fitted values and a per-variable threshold that minimises the Balanced Accuracy (BACC), ensuring that classification performance is optimised throughout fitting.

The algorithm

The objective function -- the negative log-likelihood weighted by W -- is non-convex. To avoid dealing with it directly, it is majorized at each iteration by a quadratic surrogate (the MM step), following the approach of Babativa-Marquez & Vicente-Villardon (2021). The surrogate is then minimised using a block coordinate descent algorithm:

• Update V: Fix mu; the optimal V consists of the k leading eigenvectors of a symmetric matrix derived from the surrogate, computed via eigendecomposition (using RSpectra::eigs_sym() for large matrices).
• Update mu: Fix V; the optimal mu has a closed-form solution as a weighted column mean.
• Impute missing values: Replace missing entries with binary predictions from the current fitted model, using per-variable BACC-optimal thresholds.
• Repeat until the relative decrease in the loss function falls below the convergence tolerance (default 1e-5).

Because each MM step reduces the surrogate, and the surrogate upper-bounds the true loss, the algorithm guarantees that the negative log-likelihood is non-increasing across iterations.

New and updated functions

LogBip() -- updated

The main fitting function now accepts method = "PDLB" (Projection-based logistic biplot with block coordinate Descent) in addition to the existing "MM", "CG", and "BFGS" methods.

When method = "PDLB":

• The binary matrix x may contain NA values.
• The returned object includes an impute_x component: the completed binary matrix with missing entries replaced by the model's fitted values.
• If the matrix contains missing values and a non-PDLB method is requested, a warning is issued and the method is automatically switched to "PDLB".

# Complete data -- coordinate descent MM algorithm (fast, no missing values)
res_MM <- LogBip(x = Methylation, method = "MM", maxit = 1000)

# Matrix with missing data -- projection-based block coordinate descent
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)
imputed_data <- res_PDLB$impute_x   # completed matrix

proj_LogBip() -- new

Low-level function that implements the projection-based block coordinate descent algorithm directly. It is called internally by LogBip(method = "PDLB") but is also exported for advanced users who need direct control over the algorithm.

out <- proj_LogBip(x = x_miss, k = 2, max_iters = 1000, epsilon = 1e-5)
# out$mu      -- estimated intercept vector (length p)
# out$A       -- row-marker matrix (n x k)
# out$B       -- column-marker matrix (p x k)
# out$x_est   -- imputed binary matrix
# out$iter    -- number of iterations
# out$loss_funct -- loss function values per iteration

cv_LogBip() -- updated

Cross-validation now supports method = "PDLB", allowing selection of the optimal number of dimensions k for datasets with missing values.

cv_result <- cv_LogBip(data = x_miss, k = 0:5, method = "PDLB", maxit = 1000)

References

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

Landgraf, A. J., & Lee, Y. (2020). Dimensionality reduction for binary data through the projection of natural parameters. Journal of Multivariate Analysis, 180, 104668. https://doi.org/10.1016/j.jmva.2020.104668

Pearson, K. (1901). On lines and planes of closest fit to systems of points in space. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 2(11), 559-572.

Vicente-Villardon, J. L., & Galindo, M. P. (2006). Logistic biplots. In M. Greenacre & J. Blasius (Eds.), Multiple Correspondence Analysis and Related Methods (pp. 503-521). Chapman & Hall.

BiplotML 1.0.0

Initial CRAN release

First release of BiplotML, providing methods for fitting logistic biplot models to multivariate binary data.

Functions

• LogBip() -- fit a logistic biplot using conjugate gradient ("CG") or BFGS ("BFGS") optimization methods.
• sdv_MM() -- fit a logistic biplot via the coordinate descent Majorization-Minimization algorithm (method = "MM" in LogBip()).
• bootBLB() -- bootstrap logistic biplot with optional confidence ellipses for row markers.
• plotBLB() -- ggplot2-based biplot visualization with directed variable vectors and optional confidence ellipses.
• pred_LB() -- predict binary responses and compute per-variable optimal classification thresholds minimising the Balanced Error Rate.
• fitted_LB() -- extract fitted values on the logit or probability scale.
• cv_LogBip() -- k-fold cross-validation for selecting the number of dimensions.
• performanceBLB() -- compare convergence speed and accuracy across multiple optimization algorithms.
• gradientDesc() -- fit a logistic biplot via simple gradient descent (pedagogical / benchmarking use).
• simBin() -- simulate a binary data matrix from a latent variable model for benchmarking and cross-validation studies.

Data

• Methylation -- a binary matrix of DNA methylation data (50 individuals, 13 CpG sites) used in examples throughout the package.

Reference

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

BiplotML documentation built on May 8, 2026, 5:06 p.m.