Text sparsenorm

SparseNorm

Which norm CsrMatrix.NormalizeRows divides each row by.

public enum SparseNorm { L1, L2 }

Members — L1 divides each row by the sum of the absolute values of its entries, so the row sums to 1 and reads as a distribution. L2 divides by the Euclidean length, so the row lies on the unit sphere and a dot product between two rows is their cosine similarity.

Example — the same counts, normalized both ways.

using Lodestar.Text.Vectorization;

string[] docs = ["the cat eats", "the dog eats", "the cat and the dog"];

CsrMatrix byLength = new CountVectorizer().FitTransform(docs);
byLength.NormalizeRows(SparseNorm.L2);
double euclidean = byLength.RowL2Norm(0);  // => 1

CsrMatrix byMass = new CountVectorizer().FitTransform(docs);
byMass.NormalizeRows(SparseNorm.L1);
double mass = byMass.RowL1Norm(2);  // => 1

Remarks — L2 is the one to want when the vectors are going into a similarity computation, which is most of the time: it is what makes documents of different lengths comparable, and it is TfidfOptions's default for that reason. L1 is the one to want when the row should be read as "what share of this document is each term", which is a different question and a rarer one.

A row that is entirely zero has no norm to divide by and is left alone rather than producing NaN — the same choice scikit-learn makes.

Applies to — net10.0, netstandard2.0.

See also — CsrMatrix.NormalizeRows, TfidfOptions, the Python equivalence table.