Preprocessing normalizer transform

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Normalizer.Transform

Scales each row of a row-major matrix to unit norm.

public static double[] Transform(ReadOnlySpan<double> samples, int featureCount, RowNorm norm = RowNorm.L2)

public static CsrMatrix Transform(CsrMatrix matrix, RowNorm norm = RowNorm.L2)

Parameters — samples is the matrix, row-major, featureCount values per row; the span is read, never modified. matrix is the sparse form, also read and never modified. norm says which norm each row is scaled by.

Returns — a new matrix of the same shape; the sparse overload returns a new CsrMatrix with the same stored positions, since scaling a row by a positive number turns no stored value into a zero that was not one already.

Exceptions — ArgumentOutOfRangeException when featureCount is not positive or norm is not a defined value. ArgumentException when samples holds no row, a partial one, or a non-finite value.

Example — three documents as word counts, each scaled to unit Euclidean length, which is what makes a dot product between two of them a cosine.

using Lodestar.Preprocessing;

double[] counts = [2.0, 0.0, 1.0, 0.0, 4.0, 4.0, 1.0, 1.0, 1.0];

double[] scaled = Normalizer.Transform(counts, featureCount: 3);

double first = Math.Round(scaled[0], 4);    // => 0.8944
double second = Math.Round(scaled[4], 4);   // => 0.7071

Remarks — a row of zeros is left alone rather than divided by its own norm. There is no direction to preserve, and the reference makes the same choice; the row comes back as zeros rather than as NaNs.

using Lodestar.Preprocessing;

double[] withEmptyRow = [3.0, 4.0, 0.0, 0.0];

double[] scaled = Normalizer.Transform(withEmptyRow, featureCount: 2);

double emptyStaysEmpty = scaled[2];   // => 0

The sparse overload returns a new matrix rather than scaling one in place. CsrMatrix carries a NormalizeRows that mutates, which is the right shape for a caller who owns the matrix and wants it changed; it is the wrong shape here, where every member leaves its input alone so a caller can transform the same data twice. It also carries no maximum norm, which this does.

Applies to — net10.0, netstandard2.0.

See also — RowNorm, StandardScaler.Transform for the column-wise counterpart, the Python equivalence table.