pb_basis: Principal balance basis

In coda.base: A Basic Set of Functions for Compositional Data Analysis

Principal balance basis

Description

Construct a basis of principal balances for a compositional data set.

Usage

pb_basis(
  X,
  method,
  constrained.criterion = "variance",
  cluster.method = "ward.D2",
  ordering = TRUE,
  ...
)

Arguments

X	Compositional data set.
method	Method used to construct the principal balances. One of '"exact"', '"constrained"', or '"cluster"'.
constrained.criterion	Criterion used by the constrained method. Either '"variance"' (default) or '"angle"'.
cluster.method	Linkage criterion passed to hclust when 'method = "cluster"'.
ordering	Logical; if 'TRUE', reorder balances by decreasing explained variance.
...	Additional arguments passed to hclust.

Details

Several methods are available:

• '"exact"': exact computation of principal balances,

• '"constrained"': constrained approximation based on a target criterion,

• '"cluster"': approximation based on hierarchical clustering.

Value

A matrix whose columns are principal balances.

References

Martín-Fernández, J. A., Pawlowsky-Glahn, V., Egozcue, J. J., & Tolosana-Delgado, R. (2018). Advances in Principal Balances for Compositional Data. Mathematical Geosciences, 50, 273–298.

Examples

set.seed(1)
X <- matrix(exp(rnorm(5 * 100)), nrow = 100, ncol = 5)

v1 <- apply(coordinates(X, "pc"), 2, var)
v2 <- apply(coordinates(X, pb_basis(X, method = "exact")), 2, var)
v3 <- apply(coordinates(X, pb_basis(X, method = "constrained")), 2, var)
v4 <- apply(coordinates(X, pb_basis(X, method = "cluster")), 2, var)

barplot(
  rbind(v1, v2, v3, v4),
  beside = TRUE,
  ylim = c(0, 2),
  legend = c(
    "Principal Components",
    "PB (Exact method)",
    "PB (Constrained)",
    "PB (Ward approximation)"
  ),
  names = paste0("Comp.", 1:4),
  args.legend = list(cex = 0.8),
  ylab = "Variance"
)

coda.base documentation built on March 4, 2026, 9:06 a.m.