Lodestar.Decomposition 0.2.0. This page is frozen at that release. Read the current documentation for what main says now. A link to a decision or a migration page follows main, and leaves the archive.

NmfBetaLoss

What Nmf.Fit is asked to minimise, and therefore what "a good factorization" means for the data in hand.

The beta divergence is one family with a parameter; this package ships the two members of it that solver="mu" computes in closed form. They are not two ways of reaching one answer. Each is the maximum-likelihood fit under a different noise model, so they disagree about which errors are worth trading against which — and a matrix of counts and a matrix of measurements do not want the same trade.

Members

Member	Value	What it does
Frobenius	0	Half the squared Frobenius norm of X − W H, β = 2. The Gaussian noise model, and what a matrix of continuous measurements wants. scikit-learn's beta_loss="frobenius".
KullbackLeibler	1	The generalised Kullback–Leibler divergence, β = 1. The Poisson noise model, and what counts want — a term-document matrix included, which is why it is here. scikit-learn's beta_loss="kullback-leibler".

The choice changes the arithmetic and not only the objective. Frobenius updates W through two dense products; Kullback–Leibler divides X by W H where X is non-zero and broadcasts a row of sums as the denominator, which is why it is the slower of the two on a wide matrix and why it snaps H below machine epsilon to zero where Frobenius does not.

ReconstructionError is reported in the loss that produced it, so numbers from two different members are not comparable — a Kullback–Leibler fit of a corpus is routinely the "larger" of the two and is not the worse one. Compare a loss against itself, across ranks or across initialisations, and never across this enum.

Other β values — Itakura–Saito at β = 0, or anything between — are not offered. They cost a general power in the inner loop, and neither of the two data shapes this package targets asks for one.