Status: accepted · Date: 2026-09-12 · Applies: 0074, 0075, 0076

docs/equivalence.md:314 has carried the same row since the package shipped:

PCA, SparsePCA, DictionaryLearning — no counterpart yet. The truncated SVD and NMF are what ships in 0.1.0. PCA in particular is not the SVD with centring bolted on.

That sentence is correct and is the reason the row exists: centring a CsrMatrix subtracts a column mean from every stored zero, so PCA over sparse input is a different computation rather than a preprocessing step in front of the one that ships. scikit-learn refuses it for the same reason — TruncatedSVD exists precisely because PCA will not take a sparse matrix.

What the row did not say is whether .NET has PCA at all. #685 asked, and decision 0074 says how: read the exported surface, never the README.

Run with tools/survey.cs, which decision 0110 built so a reading is re-runnable rather than retyped. Both licences read from the artefact, per decision 0075.

dotnet run tools/survey.cs -- Microsoft.ML 5.0.0 'PrincipalComponent|Pca' --assembly Microsoft.ML.PCA
dotnet run tools/survey.cs -- NumFlat 1.3.4 'Pca|PrincipalComponent'

Two things follow, and neither was guessable from the outside.

NumFlat is maintained, MIT and complete — and cannot be reached below net8.0. Its lib/ holds one folder. Every core package here ships netstandard2.0 (decision 0001), so a .NET Framework, Mono or Unity caller has no NumFlat at all.

ML.NET does reach netstandard2.0, and cannot say how much variance a component explains. That was the surprise. The argument that looked strongest before the reading — PCA is missing below net8.0 — is false: Microsoft.ML.PCA.dll is in a netstandard2.0 package and projects perfectly well. What it will not tell you is explained_variance_ratio_, the number a scree plot is made of and the one every "how many components?" decision is taken on.

Lodestar.Decomposition does not write a projection, and the gap it may fill later is the explained variance. The row in docs/equivalence.md stops saying no counterpart and starts saying which of the two to reach for.

• Sparse input stays with TruncatedSvd, and PCA is refused for it by name. Not an omission: centring densifies, and a package whose subject is CsrMatrix offering an operation that destroys sparsity would be offering a trap. docs/reference/decomposition/ says so where a reader looks for PCA.
• Dense projection is delegated. Microsoft.ML on any target this repository supports; NumFlat when a caller is on net8.0 or above and wants a matrix API rather than a pipeline. Both get a docs/migration/ row with the constraint that picks between them.
• The explained variance is left open, scoped, and not taken here. It is one lot — eigenvalues of the covariance of a centred dense block, the ratios, and the cumulative curve — and it has no incumbent on netstandard2.0. It waits for a caller, under decision 0095's rule rather than being written on the strength of a gap alone.

Nmf.Transform(X_new) is deferred with it, and for a reason of its own: docs/equivalence.md:325 already calls it "a factorization with H held fixed rather than a projection, so it is a solve and not a product". It is not part of the PCA question and it does not become one by being adjacent in the table.

• Write a dense PCA here. The honest case for it is real: explained variance below net8.0 exists nowhere, and a framework-free call is what README.md already sells against ML.NET for metrics. Refused for this package rather than for ever — Lodestar.Decomposition's stated subject is decompositions over a CsrMatrix, and a dense-only member would be the first thing in it that does not take one. Where the explained variance lands is a question for the lot that writes it, and putting it here by default would settle that question by accident.
• Delegate to NumFlat alone. Cleaner as a sentence, and wrong for a third of the targets this repository supports. A migration row naming one library that a netstandard2.0 caller cannot install is a row that fails exactly the readers docs/migration/ exists for.
• Say "ML.NET has PCA" and close the row. It would have been true and useless. The member count is what stops that: fourteen members, GetEigenVectors and GetMean among them, and no eigenvalue anywhere — a reader told "ML.NET has PCA" reaches for a scree plot and finds nothing.

• README.md's incumbent table gains the reading for Lodestar.Decomposition, which previously said only "not like-for-like" against ProjectToPrincipalComponents. It is still not like-for-like, and now the row says what ML.NET does and does not report.
• tools/survey.cs gained an --assembly argument on the way, because it could not read this one otherwise: Microsoft.ML installs no Microsoft.ML.dll, its surface is spread over eight assemblies, and Microsoft.ML.PCA is not a package id anyone can install. Deriving the target from the package id made that surface unreadable — found on the tool's second use.
• The reopening condition is written down rather than implied: a caller who needs the explained variance. Two of the three refusals above turn on it, and a package that cannot say how much variance it captured is the finding, not the projection.