Preprocessing quantiletransformer transform

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QuantileTransformer.Transform

Maps each value onto its rank.

public double[] Transform(ReadOnlySpan<double> samples)

Parameters — samples is the matrix to transform, row-major, FeatureCount values per row.

Returns — a new matrix of the same shape: each value's position in the fitted distribution, on [0, 1] under QuantileOutput.Uniform, or the standard normal quantile of that position under Normal.

Exceptions — ArgumentException when samples holds a partial row or a non-finite value.

Example — the same column, uniform and normal.

using Lodestar.Preprocessing;

double[] skew = [1.0, 1.0, 2.0, 3.0, 5.0, 8.0, 13.0, 21.0, 34.0, 100.0];

QuantileTransformer uniform = QuantileTransformer.Fit(skew, 1);
QuantileTransformer normal = QuantileTransformer.Fit(
    skew, 1, new QuantileTransformerOptions { Output = QuantileOutput.Normal });

double middleUniform = uniform.Transform([8.0])[0];   // => 0.5555555555555556
double middleNormal = normal.Transform([8.0])[0];     // => 0.13971029888186234

Remarks — a value outside the fitted range is clamped. Anything below the smallest fitted value maps to 0 and anything above the largest to 1, so a later row cannot leave the interval. Under Normal those two ends would be infinite, so they are clipped at the quantile of 1e-7 one ulp in — the reference's own threshold and the reason its output stops near ±5.2 rather than running to infinity.

A tie maps to the average of its two interpolations. The mapping is computed forwards and backwards through the fitted quantiles and averaged, which is what puts a repeated value in the middle of the range its copies occupy instead of at one end of it. The reference does the same, and it is why the first two entries of a column starting 1, 1 both map to 0 rather than to 0 and 0.111.

Applies to — net10.0, netstandard2.0.

See also — QuantileTransformer.InverseTransform, QuantileOutput.