# FactorAnalysis¶

class ibex.sklearn.decomposition.FactorAnalysis(n_components=None, tol=0.01, copy=True, max_iter=1000, noise_variance_init=None, svd_method='randomized', iterated_power=3, random_state=0)

Bases: sklearn.decomposition.factor_analysis.FactorAnalysis, ibex._base.FrameMixin

Note

The documentation following is of the class wrapped by this class. There are some changes, in particular:

Note

The documentation following is of the original class wrapped by this class. This class wraps the attribute components_.

Example:

>>> import pandas as pd
>>> import numpy as np
>>> from ibex.sklearn import datasets
>>> from ibex.sklearn.decomposition import PCA as PdPCA

>>> iris = datasets.load_iris()
>>> features = iris['feature_names']
>>> iris = pd.DataFrame(
...     np.c_[iris['data'], iris['target']],
...     columns=features+['class'])

>>> iris[features]
sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)
0                5.1               3.5                1.4               0.2
1                4.9               3.0                1.4               0.2
2                4.7               3.2                1.3               0.2
3                4.6               3.1                1.5               0.2
4                5.0               3.6                1.4               0.2
...

>>> PdPCA(n_components=2).fit(iris[features], iris['class']).transform(iris[features])
comp_0    comp_1
0   -2.684207 ...0.326607
1   -2.715391 ...0.169557
2   -2.889820 ...0.137346
3   -2.746437 ...0.311124
4   -2.728593 ...0.333925
...


Factor Analysis (FA)

A simple linear generative model with Gaussian latent variables.

The observations are assumed to be caused by a linear transformation of lower dimensional latent factors and added Gaussian noise. Without loss of generality the factors are distributed according to a Gaussian with zero mean and unit covariance. The noise is also zero mean and has an arbitrary diagonal covariance matrix.

If we would restrict the model further, by assuming that the Gaussian noise is even isotropic (all diagonal entries are the same) we would obtain PPCA.

FactorAnalysis performs a maximum likelihood estimate of the so-called loading matrix, the transformation of the latent variables to the observed ones, using expectation-maximization (EM).

Read more in the User Guide.

n_components : int | None
Dimensionality of latent space, the number of components of X that are obtained after transform. If None, n_components is set to the number of features.
tol : float
Stopping tolerance for EM algorithm.
copy : bool
Whether to make a copy of X. If False, the input X gets overwritten during fitting.
max_iter : int
Maximum number of iterations.
noise_variance_init : None | array, shape=(n_features,)
The initial guess of the noise variance for each feature. If None, it defaults to np.ones(n_features)
svd_method : {‘lapack’, ‘randomized’}
Which SVD method to use. If ‘lapack’ use standard SVD from scipy.linalg, if ‘randomized’ use fast randomized_svd function. Defaults to ‘randomized’. For most applications ‘randomized’ will be sufficiently precise while providing significant speed gains. Accuracy can also be improved by setting higher values for iterated_power. If this is not sufficient, for maximum precision you should choose ‘lapack’.
iterated_power : int, optional
Number of iterations for the power method. 3 by default. Only used if svd_method equals ‘randomized’
random_state : int, RandomState instance or None, optional (default=0)
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random. Only used when svd_method equals ‘randomized’.
components_ : array, [n_components, n_features]
Components with maximum variance.
loglike_ : list, [n_iterations]
The log likelihood at each iteration.
noise_variance_ : array, shape=(n_features,)
The estimated noise variance for each feature.
n_iter_ : int
Number of iterations run.
PCA: Principal component analysis is also a latent linear variable model
which however assumes equal noise variance for each feature. This extra assumption makes probabilistic PCA faster as it can be computed in closed form.
FastICA: Independent component analysis, a latent variable model with
non-Gaussian latent variables.
fit(X, y=None)[source]

Note

The documentation following is of the class wrapped by this class. There are some changes, in particular:

Fit the FactorAnalysis model to X using EM

X : array-like, shape (n_samples, n_features)
Training data.

y : Ignored.

self

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

Note

The documentation following is of the class wrapped by this class. There are some changes, in particular:

Fit to data, then transform it.

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

X : numpy array of shape [n_samples, n_features]
Training set.
y : numpy array of shape [n_samples]
Target values.
X_new : numpy array of shape [n_samples, n_features_new]
Transformed array.
score(X, y=None)[source]

Note

The documentation following is of the class wrapped by this class. There are some changes, in particular:

Compute the average log-likelihood of the samples

X : array, shape (n_samples, n_features)
The data

y : Ignored.

ll : float
Average log-likelihood of the samples under the current model
score_samples(X)[source]

Note

The documentation following is of the class wrapped by this class. There are some changes, in particular:

Compute the log-likelihood of each sample

X : array, shape (n_samples, n_features)
The data
ll : array, shape (n_samples,)
Log-likelihood of each sample under the current model
transform(X)[source]

Note

The documentation following is of the class wrapped by this class. There are some changes, in particular:

Apply dimensionality reduction to X using the model.

Compute the expected mean of the latent variables. See Barber, 21.2.33 (or Bishop, 12.66).

X : array-like, shape (n_samples, n_features)
Training data.
X_new : array-like, shape (n_samples, n_components)
The latent variables of X.