PowerTransformer

class cuml.preprocessing.PowerTransformer(*args, **kwargs)

Apply a power transform featurewise to make data more Gaussian-like.

Power transforms are a family of parametric, monotonic transformations that are applied to make data more Gaussian-like. This is useful for modeling issues related to heteroscedasticity (non-constant variance), or other situations where normality is desired.

Currently, PowerTransformer supports the Box-Cox transform and the Yeo-Johnson transform. The optimal parameter for stabilizing variance and minimizing skewness is estimated through maximum likelihood.

Box-Cox requires input data to be strictly positive, while Yeo-Johnson supports both positive or negative data.

By default, zero-mean, unit-variance normalization is applied to the transformed data.

Parameters:

methodstr, (default=’yeo-johnson’)

The power transform method. Available methods are:

• ‘yeo-johnson’ [1], works with positive and negative values

• ‘box-cox’ [2], only works with strictly positive values

standardizeboolean, default=True

Set to True to apply zero-mean, unit-variance normalization to the transformed output.

copyboolean, optional, default=True

Set to False to perform inplace computation during transformation.

Attributes:

lambdas_array of float, shape (n_features,)

The parameters of the power transformation for the selected features.

Methods

fit(X[, y])	Estimate the optimal parameter lambda for each feature.
fit_transform(X[, y])	Fit to data, then transform it.
inverse_transform(X)	Apply the inverse power transformation using the fitted lambdas.
transform(X)	Apply the power transform to each feature using the fitted lambdas.

See also

power_transform

Equivalent function without the estimator API.

QuantileTransformer

Maps data to a standard normal distribution with the parameter output_distribution='normal'.

Notes

NaNs are treated as missing values: disregarded in fit, and maintained in transform.

References

[1]

I.K. Yeo and R.A. Johnson, “A new family of power transformations to improve normality or symmetry.” Biometrika, 87(4), pp.954-959, (2000).

[2]

G.E.P. Box and D.R. Cox, “An Analysis of Transformations”, Journal of the Royal Statistical Society B, 26, 211-252 (1964).

Examples

>>> import cupy as cp
>>> from cuml.preprocessing import PowerTransformer
>>> pt = PowerTransformer()
>>> data = cp.array([[1, 2], [3, 2], [4, 5]])
>>> print(pt.fit(data))
PowerTransformer()
>>> print(pt.lambdas_)
[ 1.386... -3.100...]
>>> print(pt.transform(data))
[[-1.316... -0.707...]
 [ 0.209... -0.707...]
 [ 1.106...  1.414...]]

fit(X, y=None) → PowerTransformer

Estimate the optimal parameter lambda for each feature.

The optimal lambda parameter for minimizing skewness is estimated on each feature independently using maximum likelihood.

Parameters:

Xarray-like, shape (n_samples, n_features)

The data used to estimate the optimal transformation parameters.

yIgnored

Returns:

selfobject

fit_transform(X, y=None) → CumlArray

Fit to data, then transform it.

Fits transformer to X and y with optional parameters fit_params and returns a transformed version of X.

Parameters:

X{array-like, sparse matrix, dataframe} of shape (n_samples, n_features)

yndarray of shape (n_samples,), default=None

Target values.

**fit_paramsdict

Additional fit parameters.

Returns:

X_newndarray array of shape (n_samples, n_features_new)

Transformed array.

inverse_transform(X) → CumlArray

Apply the inverse power transformation using the fitted lambdas.

The inverse of the Box-Cox transformation is given by:

if lambda_ == 0:
    X = exp(X_trans)
else:
    X = (X_trans * lambda_ + 1) ** (1 / lambda_)

The inverse of the Yeo-Johnson transformation is given by:

if X >= 0 and lambda_ == 0:
    X = exp(X_trans) - 1
elif X >= 0 and lambda_ != 0:
    X = (X_trans * lambda_ + 1) ** (1 / lambda_) - 1
elif X < 0 and lambda_ != 2:
    X = 1 - (-(2 - lambda_) * X_trans + 1) ** (1 / (2 - lambda_))
elif X < 0 and lambda_ == 2:
    X = 1 - exp(-X_trans)

Parameters:

Xarray-like, shape (n_samples, n_features)

The transformed data.

Returns:

Xarray-like, shape (n_samples, n_features)

The original data

transform(X) → CumlArray

Apply the power transform to each feature using the fitted lambdas.

Parameters:

Xarray-like, shape (n_samples, n_features)

The data to be transformed using a power transformation.

Returns:

X_transarray-like, shape (n_samples, n_features)

The transformed data.