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sklearn
- Sklearn

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type tag = [

| `FactorAnalysis

]

type t =
  [ `BaseEstimator | `FactorAnalysis | `Object | `TransformerMixin ] Obj.t

val of_pyobject : Py.Object.t -> t

val to_pyobject : [> tag ] Obj.t -> Py.Object.t

val as_transformer : t -> [ `TransformerMixin ] Obj.t

val as_estimator : t -> [ `BaseEstimator ] Obj.t

val create : 
  ?n_components:int ->
  ?tol:float ->
  ?copy:bool ->
  ?max_iter:int ->
  ?noise_variance_init:[> `ArrayLike ] Np.Obj.t ->
  ?svd_method:[ `Lapack | `Randomized ] ->
  ?iterated_power:int ->
  ?random_state:int ->
  unit ->
  t

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 :class:`PPCA`.

FactorAnalysis performs a maximum likelihood estimate of the so-called `loading` matrix, the transformation of the latent variables to the observed ones, using SVD based approach.

Read more in the :ref:`User Guide <FA>`.

.. versionadded:: 0.13

Parameters ---------- 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 log-likelihood increase.

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, default=0 Only used when ``svd_method`` equals 'randomized'. Pass an int for reproducible results across multiple function calls. See :term:`Glossary <random_state>`.

Attributes ---------- 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.

mean_ : array, shape (n_features,) Per-feature empirical mean, estimated from the training set.

Examples -------- >>> from sklearn.datasets import load_digits >>> from sklearn.decomposition import FactorAnalysis >>> X, _ = load_digits(return_X_y=True) >>> transformer = FactorAnalysis(n_components=7, random_state=0) >>> X_transformed = transformer.fit_transform(X) >>> X_transformed.shape (1797, 7)

References ---------- .. David Barber, Bayesian Reasoning and Machine Learning, Algorithm 21.1

.. Christopher M. Bishop: Pattern Recognition and Machine Learning, Chapter 12.2.4

See also -------- 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.

val fit : ?y:Py.Object.t -> x:[> `ArrayLike ] Np.Obj.t -> [> tag ] Obj.t -> t

Fit the FactorAnalysis model to X using SVD based approach

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

y : Ignored

Returns ------- self

val fit_transform : 
  ?y:[> `ArrayLike ] Np.Obj.t ->
  ?fit_params:(string * Py.Object.t) list ->
  x:[> `ArrayLike ] Np.Obj.t ->
  [> tag ] Obj.t ->
  [> `ArrayLike ] Np.Obj.t

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)

y : ndarray of shape (n_samples,), default=None Target values.

**fit_params : dict Additional fit parameters.

Returns ------- X_new : ndarray array of shape (n_samples, n_features_new) Transformed array.

val get_covariance : [> tag ] Obj.t -> [> `ArrayLike ] Np.Obj.t

Compute data covariance with the FactorAnalysis model.

``cov = components_.T * components_ + diag(noise_variance)``

Returns ------- cov : array, shape (n_features, n_features) Estimated covariance of data.

val get_params : ?deep:bool -> [> tag ] Obj.t -> Dict.t

Get parameters for this estimator.

Parameters ---------- deep : bool, default=True If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns ------- params : mapping of string to any Parameter names mapped to their values.

val get_precision : [> tag ] Obj.t -> [> `ArrayLike ] Np.Obj.t

Compute data precision matrix with the FactorAnalysis model.

Returns ------- precision : array, shape (n_features, n_features) Estimated precision of data.

val score : 
  ?y:Py.Object.t ->
  x:[> `ArrayLike ] Np.Obj.t ->
  [> tag ] Obj.t ->
  float

Compute the average log-likelihood of the samples

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

y : Ignored

Returns ------- ll : float Average log-likelihood of the samples under the current model

val score_samples : 
  x:[> `ArrayLike ] Np.Obj.t ->
  [> tag ] Obj.t ->
  [> `ArrayLike ] Np.Obj.t

Compute the log-likelihood of each sample

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

Returns ------- ll : array, shape (n_samples,) Log-likelihood of each sample under the current model

val set_params : ?params:(string * Py.Object.t) list -> [> tag ] Obj.t -> t

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form ``<component>__<parameter>`` so that it's possible to update each component of a nested object.

Parameters ---------- **params : dict Estimator parameters.

Returns ------- self : object Estimator instance.

val transform : 
  x:[> `ArrayLike ] Np.Obj.t ->
  [> tag ] Obj.t ->
  [> `ArrayLike ] Np.Obj.t

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).

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

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

val components_ : t -> [> `ArrayLike ] Np.Obj.t

Attribute components_: get value or raise Not_found if None.

val components_opt : t -> [> `ArrayLike ] Np.Obj.t option

Attribute components_: get value as an option.

val loglike_ : t -> Py.Object.t

Attribute loglike_: get value or raise Not_found if None.

val loglike_opt : t -> Py.Object.t option

Attribute loglike_: get value as an option.

val noise_variance_ : t -> [> `ArrayLike ] Np.Obj.t

Attribute noise_variance_: get value or raise Not_found if None.

val noise_variance_opt : t -> [> `ArrayLike ] Np.Obj.t option

Attribute noise_variance_: get value as an option.

val n_iter_ : t -> int

Attribute n_iter_: get value or raise Not_found if None.

val n_iter_opt : t -> int option

Attribute n_iter_: get value as an option.

val mean_ : t -> [> `ArrayLike ] Np.Obj.t

Attribute mean_: get value or raise Not_found if None.

val mean_opt : t -> [> `ArrayLike ] Np.Obj.t option

Attribute mean_: get value as an option.

val to_string : t -> string

Print the object to a human-readable representation.

val show : t -> string

Print the object to a human-readable representation.

val pp : Format.formatter -> t -> unit

Pretty-print the object to a formatter.