factor_analyzer.factor_analyzer_rotator

factor_analyzer.factor_analyzer_rotator

Class to perform various rotations of factor loading matrices.

Classes

Name	Description
Rotator	Perform rotations on an unrotated factor loading matrix.

Rotator

factor_analyzer.factor_analyzer_rotator.Rotator(
    method='varimax',
    normalize=True,
    power=4,
    kappa=0,
    gamma=0,
    delta=0.01,
    max_iter=500,
    tol=1e-05,
)

Perform rotations on an unrotated factor loading matrix.

The Rotator class takes an (unrotated) factor loading matrix and performs one of several rotations.

Parameters

Name	Type	Description	Default
method	str	The factor rotation method. Options include: (a) varimax (orthogonal rotation) (b) promax (oblique rotation) (c) oblimin (oblique rotation) (d) oblimax (orthogonal rotation) (e) quartimin (oblique rotation) (f) quartimax (orthogonal rotation) (g) equamax (orthogonal rotation) (h) geomin_obl (oblique rotation) (i) geomin_ort (orthogonal rotation) Defaults to ‘varimax’.	`'varimax'`
normalize	bool	Whether to perform Kaiser normalization and de-normalization prior to and following rotation. Used for ‘varimax’ and ‘promax’ rotations. If None, default for ‘promax’ is False, and default for ‘varimax’ is True. Defaults to None.	`True`
power	int	The exponent to which to raise the promax loadings (minus 1). Numbers should generally range from 2 to 4. Defaults to 4.	`4`
kappa	float	The kappa value for the ‘equamax’ objective. Ignored if the method is not ‘equamax’. Defaults to 0.	`0`
gamma	int	The gamma level for the ‘oblimin’ objective. Ignored if the method is not ‘oblimin’. Defaults to 0.	`0`
delta	float	The delta level for ‘geomin’ objectives. Ignored if the method is not ’geomin_*’. Defaults to 0.01.	`0.01`
max_iter	int	The maximum number of iterations. Used for ‘varimax’ and ‘oblique’ rotations. Defaults to 1000.	`500`
tol	float	The convergence threshold. Used for ‘varimax’ and ‘oblique’ rotations. Defaults to 1e-5.	`1e-05`

Attributes

Name	Type	Description
loadings_	numpy.ndarray	The loadings matrix. Shape (n_features, n_factors).
rotation_	numpy.ndarray	The rotation matrix. Shape (n_factors, n_factors).
phi_	numpy.ndarray or None	The factor correlations matrix. This only exists if method is ‘oblique’.

Notes

Most of the rotations in this class are ported from R’s GPARotation package.

References

[1] https://cran.r-project.org/web/packages/GPArotation/index.html

Examples

>>> import pandas as pd
>>> from spotoptim.factor_analyzer import FactorAnalyzer, Rotator
>>> df_features = pd.read_csv('test02.csv')
>>> fa = FactorAnalyzer(rotation=None)
>>> fa.fit(df_features)
>>> rotator = Rotator()
>>> rotator.fit_transform(fa.loadings_)
array([[-0.07693215,  0.04499572,  0.76211208],
       [ 0.01842035,  0.05757874,  0.01297908],
       [ 0.06067925,  0.70692662, -0.03311798],
       [ 0.11314343,  0.84525117, -0.03407129],
       [ 0.15307233,  0.5553474 , -0.00121802],
       [ 0.77450832,  0.1474666 ,  0.20118338],
       [ 0.7063001 ,  0.17229555, -0.30093981],
       [ 0.83990851,  0.15058874, -0.06182469],
       [ 0.76620579,  0.1045194 , -0.22649615],
       [ 0.81372945,  0.20915845,  0.07479506]])

Methods

Name	Description
fit	Compute the factor rotation.
fit_transform	Compute the factor rotation, and return the new loading matrix.

fit

factor_analyzer.factor_analyzer_rotator.Rotator.fit(X, y=None)

Compute the factor rotation.

Parameters

Name	Type	Description	Default
X	array - `like`	The factor loading matrix. Shape (n_features, n_factors).	required
y	`ignored`	Ignored.	`None`

Returns

Name	Type	Description
self	Rotator	The rotator object.

Examples

>>> import pandas as pd
>>> from spotoptim.factor_analyzer import FactorAnalyzer, Rotator
>>> df_features = pd.read_csv('test02.csv')
>>> fa = FactorAnalyzer(rotation=None)
>>> fa.fit(df_features)
>>> rotator = Rotator()
>>> rotator.fit(fa.loadings_)

fit_transform

factor_analyzer.factor_analyzer_rotator.Rotator.fit_transform(X, y=None)

Compute the factor rotation, and return the new loading matrix.

Parameters

Name	Type	Description	Default
X	array - `like`	The factor loading matrix. Shape (n_features, n_factors).	required
y	`ignored`	Ignored.	`None`

Returns

Name	Type	Description
loadings_	numpy.ndarray	The loadings matrix. Shape (n_features, n_factors).

Raises

Name	Type	Description
	ValueError	If `method` is not in the list of acceptable methods.

Examples

>>> import pandas as pd
>>> from spotoptim.factor_analyzer import FactorAnalyzer, Rotator
>>> df_features = pd.read_csv('test02.csv')
>>> fa = FactorAnalyzer(rotation=None)
>>> fa.fit(df_features)
>>> rotator = Rotator()
>>> rotator.fit_transform(fa.loadings_)
array([[-0.07693215,  0.04499572,  0.76211208],
       [ 0.01842035,  0.05757874,  0.01297908],
       [ 0.06067925,  0.70692662, -0.03311798],
       [ 0.11314343,  0.84525117, -0.03407129],
       [ 0.15307233,  0.5553474 , -0.00121802],
       [ 0.77450832,  0.1474666 ,  0.20118338],
       [ 0.7063001 ,  0.17229555, -0.30093981],
       [ 0.83990851,  0.15058874, -0.06182469],
       [ 0.76620579,  0.1045194 , -0.22649615],
       [ 0.81372945,  0.20915845,  0.07479506]])