Decomposition nmf transform

Development build. This page describes main, not a released package. The latest published Lodestar.Decomposition is 0.2.0 — read its documentation.

Home › Decomposition › Factorization

Nmf.Transform

W for an unseen matrix, with this fit's H held fixed.

public double[] Transform(CsrMatrix matrix)

Parameters — matrix holds the rows to factorize against this fit, and must have exactly FeatureCount columns. It does not have to be the matrix that was fitted, and usually is not.

Returns — double[], row-major and ComponentCount wide: matrix.RowCount × ComponentCount values, row i's mix of components starting at i * ComponentCount.

Exceptions — ArgumentNullException when matrix is null. ArgumentException when matrix has no row, does not have FeatureCount columns, or holds a negative value, a NaN or an infinity.

Example — one unseen document scored against the fit from Nmf.Fit's own example.

using Lodestar.Abstractions;
using Lodestar.Decomposition;

CsrMatrix matrix = new(
    4, 3,
    [3.0, 1.0, 2.0, 1.0, 1.0, 4.0, 2.0, 3.0],
    [0, 1, 0, 2, 1, 2, 0, 2],
    [0, 2, 4, 6, 8]);

Nmf fitted = Nmf.Fit(matrix, 2);

// A document the fit never saw, over the same three terms.
CsrMatrix unseen = new(1, 3, [2.0, 5.0], [0, 2], [0, 2]);

double[] weights = fitted.Transform(unseen);

double firstComponent = Math.Round(weights[0], 3);    // => 2.046
double secondComponent = Math.Round(weights[1], 3);   // => 0.835

Remarks — this iterates where TruncatedSvd.Transform multiplies. Applying a row to an orthonormal basis is a product; applying it to a non-negative one is another factorization, with H held fixed and only W free. That is why this member costs what a small fit costs rather than what a matrix product costs, and why it honours the loss, the iteration cap and the tolerance the fit was given.

The settings are the fit's, and cannot be overridden. The reference replays its estimator's own parameters in transform, so the fitted object remembers them. A Transform that took options would let a caller score under settings the model was never fitted under, which reads as a feature and behaves as a trap.

W starts from the mean, not from a draw. The reference fills it with sqrt(matrix.mean() / ComponentCount) — the mean over every cell, the structural zeros of a sparse matrix included — and no random_state reaches it. That determinism is what lets this be frozen against scikit-learn at 1e-9, and re-implementing it by hand agreed to 1.7e-16; the Python equivalence table carries the measurement.

A row of zeros comes back as zeros, and a matrix of them comes back empty of weight: the mean of an all-zero matrix is zero, so W starts at zero and a multiplicative update leaves it there. The reference answers the same way rather than refusing.

H is not touched. The fit's Components are the same after a transform as before it, which is what "held fixed" means and what makes a fitted Nmf reusable across as many batches as a caller has.

Applies to — net10.0, netstandard2.0.

See also — Nmf, Nmf.Fit, TruncatedSvd.Transform, the factorization index, the Python equivalence table.