mprod.MeanDeviationForm

class mprod.MeanDeviationForm

Standardize the data by subtracting the mean (or empiric mean) sample The mean deviation form of a tensor \(X \in \mathbb{R}^{m \times p \times n}\) is calculated as:

Z = X - U

where U is the mean sample of X , calculated as follows:

\[U = \frac{1}{m} \sum_{i=1}^{m} X[i,:,:]\]

and for the empiric mean deviation form:

\[U = \frac{1}{m-1} \sum_{i=1}^{m} X[i,:,:]\]

Attributes

_mean_samplendarray of shape (p_features, n_repeats), or None

The mean sample of the dataset

Methods

fit:	Fits a MeanDeviationForm transformer by computing the mean sample of a training dataset
transform:	Shift dataset by fitted sample mean
fit_transform:	Compute the mean sample of a dataset and transform it to its mean deviation form
inverse_transform:	Add precomputed mean sample to a dataset

fit(X, y=None, **fit_param)

Compute the mean (or empiric mean) sample of a tensor

Parameters

X{array-like} of shape (m_samples, p_features, n_repeats)

The data used to compute the mean sample used for later cantering along the features-repeats axes.

yNone

Ignored.

Returns

selfobject

Fitted MeanDeviationForm object

Examples

>>> from mprod import MeanDeviationForm
>>> import numpy as np
>>> X = np.random.randn(10,20,4)
>>> mdf = MeanDeviationForm()
>>> mdf = mdf.fit(X)

fit_transform(X, y=None, **fit_params)

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

Xarray-like of shape (n_samples, n_features)

Input samples.

yarray-like of shape (n_samples,) or (n_samples, n_outputs), default=None

Target values (None for unsupervised transformations).

**fit_paramsdict

Additional fit parameters.

Returns

X_newndarray array of shape (n_samples, n_features_new)

Transformed array.

inverse_transform(Y)

Undo the centering of X according to mean sample.

Parameters

Xarray-like of shape (m_samples, p_features, n_repeats)

Input data that will be transformed.

Returns

Xtndarray of shape (m_samples, p_features, n_repeats)

Transformed data.

Examples

>>> from mprod import MeanDeviationForm
>>> import numpy as np
>>> X = np.random.randn(10,20,4)
>>> mdf = MeanDeviationForm()
>>> Xt = mdf.fit_transform(X)
>>> mdf.inverse_transform(Xt) - X

transform(X, y=None)

Perform standardization by centering.

Parameters

Xarray-like of shape (k_samples, p_features, n_repeats)

The data used to center along the features-repeats axes.

Returns

X_trndarray of shape (k_samples, p_features, n_repeats)

Transformed tensor.

Examples

>>> from mprod import MeanDeviationForm
>>> import numpy as np
>>> X = np.random.randn(10,20,4)
>>> y = np.random.randn(50,20,4)
>>> mdf = MeanDeviationForm()
>>> mdf_fit = mdf.fit(X)
>>> yt = mdf.transform(yt)