Binary Monotone Regression (2026-06-24)

In the file monotone.R in the github repository

https://github.com/deleeuw/voronoi

there is a new routine binaryMonotoneRegression() for the special case of least squares monotone regression in which the partial order is defined by a partition of the target into two sets. All elements in the first set are required to be smaller than or equal to all elements in the second set. Previously I used Kruskal’s primary approach to ties to handle this case, which requires a lot of sorting and index manipulation in each iteration.

The new algorithm reduces the monotone regression problem to minimizing a differentiable and piecewise quadratic convex function of a single variable. We sort the target and use the fact that the function is quadratic between each interval of successive values in the sorted vector. We start at one end of the scale, evaluate the derivative at successive values until it changes sign, and then interpolate linearly to find the zero.

The new function is used in the voronoiHomogeneityAnalysis(), voronoiCentroidAnalysis(), and voronoiSphericalAnalysis() functions for unfolding categorical data that can be found in the same github repository.