Project Non-Negative Matrix with Controllable Orthonormality

Iteratively projects a non-negative matrix towards the intersection of non-negative matrices and matrices with orthonormal columns. Allows control over the degree of orthonormality enforced.

project_to_partially_orthonormal_nonnegative(
  X,
  max_iter = 100,
  tol = 1e-06,
  constraint = "positive",
  ortho_strength = 1,
  epsilon = 1e-04
)

Arguments

X

A square or rectangular numeric matrix with non-negative entries.

max_iter

Maximum number of iterations for the alternating projection.

tol

Tolerance for convergence (Frobenius norm of change).

constraint

'positive' or 'either' (influences initial data preprocessing).

ortho_strength

A value between 0 and 1, controlling the degree of orthonormality enforced. 0 means no orthonormality enforcement (only non-negativity), 1 means full orthonormality.

epsilon

very small value for stability.

Value

A matrix Y that is non-negative and has columns that are controlled in their orthonormality by ortho_strength.

Examples

# Example matrix (non-negative)
X_sample <- matrix(c(
  1, 2, 0.1,
  0.5, 1, 0.8,
  0.2, 0.5, 1
), nrow=3, byrow=TRUE)

# Full orthonormality (ortho_strength = 1)
Y_full_ortho = project_to_partially_orthonormal_nonnegative(
  X_sample, ortho_strength = 1, max_iter = 5)

# No orthonormality enforcement (ortho_strength = 0) - 
    # should just be pmax(X, 0)
Y_no_ortho <- project_to_partially_orthonormal_nonnegative(
   X_sample, ortho_strength = 0, max_iter = 5) # Low iter for speed