Random projection

BaseRandomProjection

Module Sklearn.​Random_projection.​BaseRandomProjection wraps Python class sklearn.random_projection.BaseRandomProjection.

type t

fit

method fit

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

Generate a sparse random projection matrix

Parameters

• X : numpy array or scipy.sparse of shape [n_samples, n_features] Training set: only the shape is used to find optimal random matrix dimensions based on the theory referenced in the afore mentioned papers.

y Ignored

Returns

self

fit_transform

method fit_transform

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.

get_params

method get_params

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.

set_params

method set_params

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.

transform

method transform

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

Project the data by using matrix product with the random matrix

Parameters

• X : numpy array or scipy.sparse of shape [n_samples, n_features] The input data to project into a smaller dimensional space.

Returns

• X_new : numpy array or scipy sparse of shape [n_samples, n_components] Projected array.

to_string

method to_string

val to_string: t -> string

Print the object to a human-readable representation.

show

method show

val show: t -> string

Print the object to a human-readable representation.

pp

method pp

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

Pretty-print the object to a formatter.

GaussianRandomProjection

Module Sklearn.​Random_projection.​GaussianRandomProjection wraps Python class sklearn.random_projection.GaussianRandomProjection.

type t

create

constructor and attributes create

val create :
  ?n_components:[`I of int | `Auto] ->
  ?eps:float ->
  ?random_state:int ->
  unit ->
  t

Reduce dimensionality through Gaussian random projection

The components of the random matrix are drawn from N(0, 1 / n_components).

Read more in the :ref:User Guide <gaussian_random_matrix>.

.. versionadded:: 0.13

Parameters

• n_components : int or 'auto', optional (default = 'auto') Dimensionality of the target projection space.

  n_components can be automatically adjusted according to the number of samples in the dataset and the bound given by the Johnson-Lindenstrauss lemma. In that case the quality of the embedding is controlled by the eps parameter.

  It should be noted that Johnson-Lindenstrauss lemma can yield very conservative estimated of the required number of components as it makes no assumption on the structure of the dataset.

• eps : strictly positive float, optional (default=0.1) Parameter to control the quality of the embedding according to the Johnson-Lindenstrauss lemma when n_components is set to 'auto'.

  Smaller values lead to better embedding and higher number of dimensions (n_components) in the target projection space.

• random_state : int, RandomState instance or None, optional (default=None) Controls the pseudo random number generator used to generate the projection matrix at fit time. Pass an int for reproducible output across multiple function calls.

• See :term:Glossary <random_state>.

Attributes

• n_components_ : int Concrete number of components computed when n_components='auto'.

• components_ : numpy array of shape [n_components, n_features] Random matrix used for the projection.

Examples

>>> import numpy as np
>>> from sklearn.random_projection import GaussianRandomProjection
>>> rng = np.random.RandomState(42)
>>> X = rng.rand(100, 10000)
>>> transformer = GaussianRandomProjection(random_state=rng)
>>> X_new = transformer.fit_transform(X)
>>> X_new.shape
(100, 3947)

See Also

SparseRandomProjection

fit

method fit

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

Generate a sparse random projection matrix

Parameters

• X : numpy array or scipy.sparse of shape [n_samples, n_features] Training set: only the shape is used to find optimal random matrix dimensions based on the theory referenced in the afore mentioned papers.

y Ignored

Returns

self

fit_transform

method fit_transform

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.

get_params

method get_params

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.

set_params

method set_params

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.

transform

method transform

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

Project the data by using matrix product with the random matrix

Parameters

• X : numpy array or scipy.sparse of shape [n_samples, n_features] The input data to project into a smaller dimensional space.

Returns

• X_new : numpy array or scipy sparse of shape [n_samples, n_components] Projected array.

n_components_

attribute n_components_

val n_components_ : t -> int
val n_components_opt : t -> (int) option

This attribute is documented in create above. The first version raises Not_found if the attribute is None. The _opt version returns an option.

components_

attribute components_

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

This attribute is documented in create above. The first version raises Not_found if the attribute is None. The _opt version returns an option.

to_string

method to_string

val to_string: t -> string

Print the object to a human-readable representation.

show

method show

val show: t -> string

Print the object to a human-readable representation.

pp

method pp

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

Pretty-print the object to a formatter.

SparseRandomProjection

Module Sklearn.​Random_projection.​SparseRandomProjection wraps Python class sklearn.random_projection.SparseRandomProjection.

type t

create

constructor and attributes create

val create :
  ?n_components:[`I of int | `Auto] ->
  ?density:float ->
  ?eps:float ->
  ?dense_output:bool ->
  ?random_state:int ->
  unit ->
  t

Reduce dimensionality through sparse random projection

Sparse random matrix is an alternative to dense random projection matrix that guarantees similar embedding quality while being much more memory efficient and allowing faster computation of the projected data.

If we note s = 1 / density the components of the random matrix are drawn from:

• -sqrt(s) / sqrt(n_components) with probability 1 / 2s
• 0 with probability 1 - 1 / s
• +sqrt(s) / sqrt(n_components) with probability 1 / 2s

Read more in the :ref:User Guide <sparse_random_matrix>.

.. versionadded:: 0.13

Parameters

• n_components : int or 'auto', optional (default = 'auto') Dimensionality of the target projection space.

  n_components can be automatically adjusted according to the number of samples in the dataset and the bound given by the Johnson-Lindenstrauss lemma. In that case the quality of the embedding is controlled by the eps parameter.

  It should be noted that Johnson-Lindenstrauss lemma can yield very conservative estimated of the required number of components as it makes no assumption on the structure of the dataset.

• density : float in range ]0, 1], optional (default='auto') Ratio of non-zero component in the random projection matrix.

  If density = 'auto', the value is set to the minimum density as recommended by Ping Li et al.: 1 / sqrt(n_features).

  Use density = 1 / 3.0 if you want to reproduce the results from Achlioptas, 2001.

• eps : strictly positive float, optional, (default=0.1) Parameter to control the quality of the embedding according to the Johnson-Lindenstrauss lemma when n_components is set to 'auto'.

  Smaller values lead to better embedding and higher number of dimensions (n_components) in the target projection space.

• dense_output : boolean, optional (default=False) If True, ensure that the output of the random projection is a dense numpy array even if the input and random projection matrix are both sparse. In practice, if the number of components is small the number of zero components in the projected data will be very small and it will be more CPU and memory efficient to use a dense representation.

  If False, the projected data uses a sparse representation if the input is sparse.

• random_state : int, RandomState instance or None, optional (default=None) Controls the pseudo random number generator used to generate the projection matrix at fit time. Pass an int for reproducible output across multiple function calls.

• See :term:Glossary <random_state>.

Attributes

• n_components_ : int Concrete number of components computed when n_components='auto'.

• components_ : CSR matrix with shape [n_components, n_features] Random matrix used for the projection.

• density_ : float in range 0.0 - 1.0 Concrete density computed from when density = 'auto'.

Examples

>>> import numpy as np
>>> from sklearn.random_projection import SparseRandomProjection
>>> rng = np.random.RandomState(42)
>>> X = rng.rand(100, 10000)
>>> transformer = SparseRandomProjection(random_state=rng)
>>> X_new = transformer.fit_transform(X)
>>> X_new.shape
(100, 3947)
>>> # very few components are non-zero
>>> np.mean(transformer.components_ != 0)
0.0100...

See Also

GaussianRandomProjection

References

.. [1] Ping Li, T. Hastie and K. W. Church, 2006, 'Very Sparse Random Projections'.

• https://web.stanford.edu/~hastie/Papers/Ping/KDD06_rp.pdf

.. [2] D. Achlioptas, 2001, 'Database-friendly random projections',

• https://users.soe.ucsc.edu/~optas/papers/jl.pdf

fit

method fit

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

Generate a sparse random projection matrix

Parameters

• X : numpy array or scipy.sparse of shape [n_samples, n_features] Training set: only the shape is used to find optimal random matrix dimensions based on the theory referenced in the afore mentioned papers.

y Ignored

Returns

self

fit_transform

method fit_transform

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.

get_params

method get_params

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.

set_params

method set_params

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.

transform

method transform

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

Project the data by using matrix product with the random matrix

Parameters

• X : numpy array or scipy.sparse of shape [n_samples, n_features] The input data to project into a smaller dimensional space.

Returns

• X_new : numpy array or scipy sparse of shape [n_samples, n_components] Projected array.

n_components_

attribute n_components_

val n_components_ : t -> int
val n_components_opt : t -> (int) option

This attribute is documented in create above. The first version raises Not_found if the attribute is None. The _opt version returns an option.

components_

attribute components_

val components_ : t -> [`ArrayLike|`Csr_matrix|`IndexMixin|`Object] Np.Obj.t
val components_opt : t -> ([`ArrayLike|`Csr_matrix|`IndexMixin|`Object] Np.Obj.t) option

This attribute is documented in create above. The first version raises Not_found if the attribute is None. The _opt version returns an option.

density_

attribute density_

val density_ : t -> Py.Object.t
val density_opt : t -> (Py.Object.t) option

This attribute is documented in create above. The first version raises Not_found if the attribute is None. The _opt version returns an option.

to_string

method to_string

val to_string: t -> string

Print the object to a human-readable representation.

show

method show

val show: t -> string

Print the object to a human-readable representation.

pp

method pp

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

Pretty-print the object to a formatter.

abstractmethod

function abstractmethod

val abstractmethod :
  Py.Object.t ->
  Py.Object.t

A decorator indicating abstract methods.

Requires that the metaclass is ABCMeta or derived from it. A class that has a metaclass derived from ABCMeta cannot be instantiated unless all of its abstract methods are overridden. The abstract methods can be called using any of the normal 'super' call mechanisms. abstractmethod() may be used to declare abstract methods for properties and descriptors.

Usage:

class C(metaclass=ABCMeta):
    @abstractmethod
    def my_abstract_method(self, ...):
        ...

check_array

function check_array

val check_array :
  ?accept_sparse:[`S of string | `StringList of string list | `Bool of bool] ->
  ?accept_large_sparse:bool ->
  ?dtype:[`Dtypes of Np.Dtype.t list | `S of string | `Dtype of Np.Dtype.t | `None] ->
  ?order:[`F | `C] ->
  ?copy:bool ->
  ?force_all_finite:[`Allow_nan | `Bool of bool] ->
  ?ensure_2d:bool ->
  ?allow_nd:bool ->
  ?ensure_min_samples:int ->
  ?ensure_min_features:int ->
  ?estimator:[>`BaseEstimator] Np.Obj.t ->
  array:Py.Object.t ->
  unit ->
  Py.Object.t

Input validation on an array, list, sparse matrix or similar.

By default, the input is checked to be a non-empty 2D array containing only finite values. If the dtype of the array is object, attempt converting to float, raising on failure.

Parameters

• array : object Input object to check / convert.

• accept_sparse : string, boolean or list/tuple of strings (default=False) String[s] representing allowed sparse matrix formats, such as 'csc', 'csr', etc. If the input is sparse but not in the allowed format, it will be converted to the first listed format. True allows the input to be any format. False means that a sparse matrix input will raise an error.

• accept_large_sparse : bool (default=True) If a CSR, CSC, COO or BSR sparse matrix is supplied and accepted by accept_sparse, accept_large_sparse=False will cause it to be accepted only if its indices are stored with a 32-bit dtype.

  .. versionadded:: 0.20

• dtype : string, type, list of types or None (default='numeric') Data type of result. If None, the dtype of the input is preserved. If 'numeric', dtype is preserved unless array.dtype is object. If dtype is a list of types, conversion on the first type is only performed if the dtype of the input is not in the list.

• order : 'F', 'C' or None (default=None) Whether an array will be forced to be fortran or c-style. When order is None (default), then if copy=False, nothing is ensured about the memory layout of the output array; otherwise (copy=True) the memory layout of the returned array is kept as close as possible to the original array.

• copy : boolean (default=False) Whether a forced copy will be triggered. If copy=False, a copy might be triggered by a conversion.

• force_all_finite : boolean or 'allow-nan', (default=True) Whether to raise an error on np.inf, np.nan, pd.NA in array. The possibilities are:

  • True: Force all values of array to be finite.
  • False: accepts np.inf, np.nan, pd.NA in array.
  • 'allow-nan': accepts only np.nan and pd.NA values in array. Values cannot be infinite.

  .. versionadded:: 0.20 force_all_finite accepts the string 'allow-nan'.

  .. versionchanged:: 0.23 Accepts pd.NA and converts it into np.nan

• ensure_2d : boolean (default=True) Whether to raise a value error if array is not 2D.

• allow_nd : boolean (default=False) Whether to allow array.ndim > 2.

• ensure_min_samples : int (default=1) Make sure that the array has a minimum number of samples in its first axis (rows for a 2D array). Setting to 0 disables this check.

• ensure_min_features : int (default=1) Make sure that the 2D array has some minimum number of features (columns). The default value of 1 rejects empty datasets. This check is only enforced when the input data has effectively 2 dimensions or is originally 1D and ensure_2d is True. Setting to 0 disables this check.

• estimator : str or estimator instance (default=None) If passed, include the name of the estimator in warning messages.

Returns

• array_converted : object The converted and validated array.

check_is_fitted

function check_is_fitted

val check_is_fitted :
  ?attributes:[`Arr of [>`ArrayLike] Np.Obj.t | `S of string | `StringList of string list] ->
  ?msg:string ->
  ?all_or_any:[`Callable of Py.Object.t | `PyObject of Py.Object.t] ->
  estimator:[>`BaseEstimator] Np.Obj.t ->
  unit ->
  Py.Object.t

Perform is_fitted validation for estimator.

Checks if the estimator is fitted by verifying the presence of fitted attributes (ending with a trailing underscore) and otherwise raises a NotFittedError with the given message.

This utility is meant to be used internally by estimators themselves, typically in their own predict / transform methods.

Parameters

• estimator : estimator instance. estimator instance for which the check is performed.

• attributes : str, list or tuple of str, default=None Attribute name(s) given as string or a list/tuple of strings

• Eg.: ['coef_', 'estimator_', ...], 'coef_'

  If None, estimator is considered fitted if there exist an attribute that ends with a underscore and does not start with double underscore.

• msg : string The default error message is, 'This %(name)s instance is not fitted yet. Call 'fit' with appropriate arguments before using this estimator.'

  For custom messages if '%(name)s' is present in the message string, it is substituted for the estimator name.

• Eg. : 'Estimator, %(name)s, must be fitted before sparsifying'.

• all_or_any : callable, {all, any}, default all Specify whether all or any of the given attributes must exist.

Returns

None

Raises

NotFittedError If the attributes are not found.

check_random_state

function check_random_state

val check_random_state :
  [`Optional of [`I of int | `None] | `RandomState of Py.Object.t] ->
  Py.Object.t

Turn seed into a np.random.RandomState instance

Parameters

• seed : None | int | instance of RandomState If seed is None, return the RandomState singleton used by np.random. If seed is an int, return a new RandomState instance seeded with seed. If seed is already a RandomState instance, return it. Otherwise raise ValueError.

gaussian_random_matrix

function gaussian_random_matrix

val gaussian_random_matrix :
  ?random_state:int ->
  n_components:Py.Object.t ->
  n_features:Py.Object.t ->
  unit ->
  Py.Object.t

• DEPRECATED: gaussian_random_matrix is deprecated in 0.22 and will be removed in version 0.24.

johnson_lindenstrauss_min_dim

function johnson_lindenstrauss_min_dim

val johnson_lindenstrauss_min_dim :
  ?eps:[>`ArrayLike] Np.Obj.t ->
  n_samples:[`Arr of [>`ArrayLike] Np.Obj.t | `I of int] ->
  unit ->
  Py.Object.t

Find a 'safe' number of components to randomly project to

The distortion introduced by a random projection p only changes the distance between two points by a factor (1 +- eps) in an euclidean space with good probability. The projection p is an eps-embedding as defined by:

(1 - eps) ||u - v||^2 < ||p(u) - p(v)||^2 < (1 + eps) ||u - v||^2

Where u and v are any rows taken from a dataset of shape [n_samples, n_features], eps is in ]0, 1[ and p is a projection by a random Gaussian N(0, 1) matrix with shape [n_components, n_features] (or a sparse Achlioptas matrix).

The minimum number of components to guarantee the eps-embedding is given by:

n_components >= 4 log(n_samples) / (eps^2 / 2 - eps^3 / 3)

Note that the number of dimensions is independent of the original number of features but instead depends on the size of the dataset: the larger the dataset, the higher is the minimal dimensionality of an eps-embedding.

Read more in the :ref:User Guide <johnson_lindenstrauss>.

Parameters

• n_samples : int or numpy array of int greater than 0, Number of samples. If an array is given, it will compute a safe number of components array-wise.

• eps : float or numpy array of float in ]0,1[, optional (default=0.1) Maximum distortion rate as defined by the Johnson-Lindenstrauss lemma. If an array is given, it will compute a safe number of components array-wise.

Returns

• n_components : int or numpy array of int, The minimal number of components to guarantee with good probability an eps-embedding with n_samples.

Examples

>>> johnson_lindenstrauss_min_dim(1e6, eps=0.5)
663

>>> johnson_lindenstrauss_min_dim(1e6, eps=[0.5, 0.1, 0.01])
array([    663,   11841, 1112658])

>>> johnson_lindenstrauss_min_dim([1e4, 1e5, 1e6], eps=0.1)
array([ 7894,  9868, 11841])

References

.. [1] https://en.wikipedia.org/wiki/Johnson%E2%80%93Lindenstrauss_lemma

.. [2] Sanjoy Dasgupta and Anupam Gupta, 1999, 'An elementary proof of the Johnson-Lindenstrauss Lemma.'

• http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.45.3654

safe_sparse_dot

function safe_sparse_dot

val safe_sparse_dot :
  ?dense_output:Py.Object.t ->
  a:[>`ArrayLike] Np.Obj.t ->
  b:Py.Object.t ->
  unit ->
  [>`ArrayLike] Np.Obj.t

Dot product that handle the sparse matrix case correctly

Parameters

• a : array or sparse matrix

• b : array or sparse matrix

• dense_output : boolean, (default=False) When False, a and b both being sparse will yield sparse output. When True, output will always be a dense array.

Returns

• dot_product : array or sparse matrix sparse if a and b are sparse and dense_output=False.

sparse_random_matrix

function sparse_random_matrix

val sparse_random_matrix :
  ?density:Py.Object.t ->
  ?random_state:int ->
  n_components:Py.Object.t ->
  n_features:Py.Object.t ->
  unit ->
  Py.Object.t

• DEPRECATED: gaussian_random_matrix is deprecated in 0.22 and will be removed in version 0.24.