806 lines
27 KiB
Python
806 lines
27 KiB
Python
"""Random Projection transformers.
|
|
|
|
Random Projections are a simple and computationally efficient way to
|
|
reduce the dimensionality of the data by trading a controlled amount
|
|
of accuracy (as additional variance) for faster processing times and
|
|
smaller model sizes.
|
|
|
|
The dimensions and distribution of Random Projections matrices are
|
|
controlled so as to preserve the pairwise distances between any two
|
|
samples of the dataset.
|
|
|
|
The main theoretical result behind the efficiency of random projection is the
|
|
`Johnson-Lindenstrauss lemma (quoting Wikipedia)
|
|
<https://en.wikipedia.org/wiki/Johnson%E2%80%93Lindenstrauss_lemma>`_:
|
|
|
|
In mathematics, the Johnson-Lindenstrauss lemma is a result
|
|
concerning low-distortion embeddings of points from high-dimensional
|
|
into low-dimensional Euclidean space. The lemma states that a small set
|
|
of points in a high-dimensional space can be embedded into a space of
|
|
much lower dimension in such a way that distances between the points are
|
|
nearly preserved. The map used for the embedding is at least Lipschitz,
|
|
and can even be taken to be an orthogonal projection.
|
|
|
|
"""
|
|
# Authors: Olivier Grisel <olivier.grisel@ensta.org>,
|
|
# Arnaud Joly <a.joly@ulg.ac.be>
|
|
# License: BSD 3 clause
|
|
|
|
import warnings
|
|
from abc import ABCMeta, abstractmethod
|
|
from numbers import Integral, Real
|
|
|
|
import numpy as np
|
|
from scipy import linalg
|
|
import scipy.sparse as sp
|
|
|
|
from .base import BaseEstimator, TransformerMixin
|
|
from .base import ClassNamePrefixFeaturesOutMixin
|
|
|
|
from .utils import check_random_state
|
|
from .utils._param_validation import Interval, StrOptions
|
|
from .utils.extmath import safe_sparse_dot
|
|
from .utils.random import sample_without_replacement
|
|
from .utils.validation import check_array, check_is_fitted
|
|
from .exceptions import DataDimensionalityWarning
|
|
|
|
__all__ = [
|
|
"SparseRandomProjection",
|
|
"GaussianRandomProjection",
|
|
"johnson_lindenstrauss_min_dim",
|
|
]
|
|
|
|
|
|
def johnson_lindenstrauss_min_dim(n_samples, *, eps=0.1):
|
|
"""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 of 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 array-like of int
|
|
Number of samples that should be a integer greater than 0. If an array
|
|
is given, it will compute a safe number of components array-wise.
|
|
|
|
eps : float or ndarray of shape (n_components,), dtype=float, \
|
|
default=0.1
|
|
Maximum distortion rate in the range (0,1 ) 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 ndarray of int
|
|
The minimal number of components to guarantee with good probability
|
|
an eps-embedding with n_samples.
|
|
|
|
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."
|
|
<https://citeseerx.ist.psu.edu/doc_view/pid/95cd464d27c25c9c8690b378b894d337cdf021f9>`_
|
|
|
|
Examples
|
|
--------
|
|
>>> from sklearn.random_projection import johnson_lindenstrauss_min_dim
|
|
>>> 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])
|
|
"""
|
|
eps = np.asarray(eps)
|
|
n_samples = np.asarray(n_samples)
|
|
|
|
if np.any(eps <= 0.0) or np.any(eps >= 1):
|
|
raise ValueError("The JL bound is defined for eps in ]0, 1[, got %r" % eps)
|
|
|
|
if np.any(n_samples) <= 0:
|
|
raise ValueError(
|
|
"The JL bound is defined for n_samples greater than zero, got %r"
|
|
% n_samples
|
|
)
|
|
|
|
denominator = (eps**2 / 2) - (eps**3 / 3)
|
|
return (4 * np.log(n_samples) / denominator).astype(np.int64)
|
|
|
|
|
|
def _check_density(density, n_features):
|
|
"""Factorize density check according to Li et al."""
|
|
if density == "auto":
|
|
density = 1 / np.sqrt(n_features)
|
|
|
|
elif density <= 0 or density > 1:
|
|
raise ValueError("Expected density in range ]0, 1], got: %r" % density)
|
|
return density
|
|
|
|
|
|
def _check_input_size(n_components, n_features):
|
|
"""Factorize argument checking for random matrix generation."""
|
|
if n_components <= 0:
|
|
raise ValueError(
|
|
"n_components must be strictly positive, got %d" % n_components
|
|
)
|
|
if n_features <= 0:
|
|
raise ValueError("n_features must be strictly positive, got %d" % n_features)
|
|
|
|
|
|
def _gaussian_random_matrix(n_components, n_features, random_state=None):
|
|
"""Generate a dense Gaussian random matrix.
|
|
|
|
The components of the random matrix are drawn from
|
|
|
|
N(0, 1.0 / n_components).
|
|
|
|
Read more in the :ref:`User Guide <gaussian_random_matrix>`.
|
|
|
|
Parameters
|
|
----------
|
|
n_components : int,
|
|
Dimensionality of the target projection space.
|
|
|
|
n_features : int,
|
|
Dimensionality of the original source space.
|
|
|
|
random_state : int, RandomState instance or None, default=None
|
|
Controls the pseudo random number generator used to generate the matrix
|
|
at fit time.
|
|
Pass an int for reproducible output across multiple function calls.
|
|
See :term:`Glossary <random_state>`.
|
|
|
|
Returns
|
|
-------
|
|
components : ndarray of shape (n_components, n_features)
|
|
The generated Gaussian random matrix.
|
|
|
|
See Also
|
|
--------
|
|
GaussianRandomProjection
|
|
"""
|
|
_check_input_size(n_components, n_features)
|
|
rng = check_random_state(random_state)
|
|
components = rng.normal(
|
|
loc=0.0, scale=1.0 / np.sqrt(n_components), size=(n_components, n_features)
|
|
)
|
|
return components
|
|
|
|
|
|
def _sparse_random_matrix(n_components, n_features, density="auto", random_state=None):
|
|
"""Generalized Achlioptas random sparse matrix for random projection.
|
|
|
|
Setting density to 1 / 3 will yield the original matrix by Dimitris
|
|
Achlioptas while setting a lower value will yield the generalization
|
|
by Ping Li et al.
|
|
|
|
If we note :math:`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>`.
|
|
|
|
Parameters
|
|
----------
|
|
n_components : int,
|
|
Dimensionality of the target projection space.
|
|
|
|
n_features : int,
|
|
Dimensionality of the original source space.
|
|
|
|
density : float or 'auto', default='auto'
|
|
Ratio of non-zero component in the random projection matrix in the
|
|
range `(0, 1]`
|
|
|
|
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.
|
|
|
|
random_state : int, RandomState instance or None, default=None
|
|
Controls the pseudo random number generator used to generate the matrix
|
|
at fit time.
|
|
Pass an int for reproducible output across multiple function calls.
|
|
See :term:`Glossary <random_state>`.
|
|
|
|
Returns
|
|
-------
|
|
components : {ndarray, sparse matrix} of shape (n_components, n_features)
|
|
The generated Gaussian random matrix. Sparse matrix will be of CSR
|
|
format.
|
|
|
|
See Also
|
|
--------
|
|
SparseRandomProjection
|
|
|
|
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://cgi.di.uoa.gr/~optas/papers/jl.pdf
|
|
|
|
"""
|
|
_check_input_size(n_components, n_features)
|
|
density = _check_density(density, n_features)
|
|
rng = check_random_state(random_state)
|
|
|
|
if density == 1:
|
|
# skip index generation if totally dense
|
|
components = rng.binomial(1, 0.5, (n_components, n_features)) * 2 - 1
|
|
return 1 / np.sqrt(n_components) * components
|
|
|
|
else:
|
|
# Generate location of non zero elements
|
|
indices = []
|
|
offset = 0
|
|
indptr = [offset]
|
|
for _ in range(n_components):
|
|
# find the indices of the non-zero components for row i
|
|
n_nonzero_i = rng.binomial(n_features, density)
|
|
indices_i = sample_without_replacement(
|
|
n_features, n_nonzero_i, random_state=rng
|
|
)
|
|
indices.append(indices_i)
|
|
offset += n_nonzero_i
|
|
indptr.append(offset)
|
|
|
|
indices = np.concatenate(indices)
|
|
|
|
# Among non zero components the probability of the sign is 50%/50%
|
|
data = rng.binomial(1, 0.5, size=np.size(indices)) * 2 - 1
|
|
|
|
# build the CSR structure by concatenating the rows
|
|
components = sp.csr_matrix(
|
|
(data, indices, indptr), shape=(n_components, n_features)
|
|
)
|
|
|
|
return np.sqrt(1 / density) / np.sqrt(n_components) * components
|
|
|
|
|
|
class BaseRandomProjection(
|
|
TransformerMixin, BaseEstimator, ClassNamePrefixFeaturesOutMixin, metaclass=ABCMeta
|
|
):
|
|
"""Base class for random projections.
|
|
|
|
Warning: This class should not be used directly.
|
|
Use derived classes instead.
|
|
"""
|
|
|
|
_parameter_constraints: dict = {
|
|
"n_components": [
|
|
Interval(Integral, 1, None, closed="left"),
|
|
StrOptions({"auto"}),
|
|
],
|
|
"eps": [Interval(Real, 0, None, closed="neither")],
|
|
"compute_inverse_components": ["boolean"],
|
|
"random_state": ["random_state"],
|
|
}
|
|
|
|
@abstractmethod
|
|
def __init__(
|
|
self,
|
|
n_components="auto",
|
|
*,
|
|
eps=0.1,
|
|
compute_inverse_components=False,
|
|
random_state=None,
|
|
):
|
|
self.n_components = n_components
|
|
self.eps = eps
|
|
self.compute_inverse_components = compute_inverse_components
|
|
self.random_state = random_state
|
|
|
|
@abstractmethod
|
|
def _make_random_matrix(self, n_components, n_features):
|
|
"""Generate the random projection matrix.
|
|
|
|
Parameters
|
|
----------
|
|
n_components : int,
|
|
Dimensionality of the target projection space.
|
|
|
|
n_features : int,
|
|
Dimensionality of the original source space.
|
|
|
|
Returns
|
|
-------
|
|
components : {ndarray, sparse matrix} of shape (n_components, n_features)
|
|
The generated random matrix. Sparse matrix will be of CSR format.
|
|
|
|
"""
|
|
|
|
def _compute_inverse_components(self):
|
|
"""Compute the pseudo-inverse of the (densified) components."""
|
|
components = self.components_
|
|
if sp.issparse(components):
|
|
components = components.toarray()
|
|
return linalg.pinv(components, check_finite=False)
|
|
|
|
def fit(self, X, y=None):
|
|
"""Generate a sparse random projection matrix.
|
|
|
|
Parameters
|
|
----------
|
|
X : {ndarray, sparse matrix} 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
|
|
Not used, present here for API consistency by convention.
|
|
|
|
Returns
|
|
-------
|
|
self : object
|
|
BaseRandomProjection class instance.
|
|
"""
|
|
self._validate_params()
|
|
X = self._validate_data(
|
|
X, accept_sparse=["csr", "csc"], dtype=[np.float64, np.float32]
|
|
)
|
|
|
|
n_samples, n_features = X.shape
|
|
|
|
if self.n_components == "auto":
|
|
self.n_components_ = johnson_lindenstrauss_min_dim(
|
|
n_samples=n_samples, eps=self.eps
|
|
)
|
|
|
|
if self.n_components_ <= 0:
|
|
raise ValueError(
|
|
"eps=%f and n_samples=%d lead to a target dimension of "
|
|
"%d which is invalid" % (self.eps, n_samples, self.n_components_)
|
|
)
|
|
|
|
elif self.n_components_ > n_features:
|
|
raise ValueError(
|
|
"eps=%f and n_samples=%d lead to a target dimension of "
|
|
"%d which is larger than the original space with "
|
|
"n_features=%d"
|
|
% (self.eps, n_samples, self.n_components_, n_features)
|
|
)
|
|
else:
|
|
if self.n_components > n_features:
|
|
warnings.warn(
|
|
"The number of components is higher than the number of"
|
|
" features: n_features < n_components (%s < %s)."
|
|
"The dimensionality of the problem will not be reduced."
|
|
% (n_features, self.n_components),
|
|
DataDimensionalityWarning,
|
|
)
|
|
|
|
self.n_components_ = self.n_components
|
|
|
|
# Generate a projection matrix of size [n_components, n_features]
|
|
self.components_ = self._make_random_matrix(
|
|
self.n_components_, n_features
|
|
).astype(X.dtype, copy=False)
|
|
|
|
if self.compute_inverse_components:
|
|
self.inverse_components_ = self._compute_inverse_components()
|
|
|
|
return self
|
|
|
|
@property
|
|
def _n_features_out(self):
|
|
"""Number of transformed output features.
|
|
|
|
Used by ClassNamePrefixFeaturesOutMixin.get_feature_names_out.
|
|
"""
|
|
return self.n_components
|
|
|
|
def inverse_transform(self, X):
|
|
"""Project data back to its original space.
|
|
|
|
Returns an array X_original whose transform would be X. Note that even
|
|
if X is sparse, X_original is dense: this may use a lot of RAM.
|
|
|
|
If `compute_inverse_components` is False, the inverse of the components is
|
|
computed during each call to `inverse_transform` which can be costly.
|
|
|
|
Parameters
|
|
----------
|
|
X : {array-like, sparse matrix} of shape (n_samples, n_components)
|
|
Data to be transformed back.
|
|
|
|
Returns
|
|
-------
|
|
X_original : ndarray of shape (n_samples, n_features)
|
|
Reconstructed data.
|
|
"""
|
|
check_is_fitted(self)
|
|
|
|
X = check_array(X, dtype=[np.float64, np.float32], accept_sparse=("csr", "csc"))
|
|
|
|
if self.compute_inverse_components:
|
|
return X @ self.inverse_components_.T
|
|
|
|
inverse_components = self._compute_inverse_components()
|
|
return X @ inverse_components.T
|
|
|
|
def _more_tags(self):
|
|
return {
|
|
"preserves_dtype": [np.float64, np.float32],
|
|
}
|
|
|
|
|
|
class GaussianRandomProjection(BaseRandomProjection):
|
|
"""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', 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 : float, default=0.1
|
|
Parameter to control the quality of the embedding according to
|
|
the Johnson-Lindenstrauss lemma when `n_components` is set to
|
|
'auto'. The value should be strictly positive.
|
|
|
|
Smaller values lead to better embedding and higher number of
|
|
dimensions (n_components) in the target projection space.
|
|
|
|
compute_inverse_components : bool, default=False
|
|
Learn the inverse transform by computing the pseudo-inverse of the
|
|
components during fit. Note that computing the pseudo-inverse does not
|
|
scale well to large matrices.
|
|
|
|
random_state : int, RandomState instance or None, 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_ : ndarray of shape (n_components, n_features)
|
|
Random matrix used for the projection.
|
|
|
|
inverse_components_ : ndarray of shape (n_features, n_components)
|
|
Pseudo-inverse of the components, only computed if
|
|
`compute_inverse_components` is True.
|
|
|
|
.. versionadded:: 1.1
|
|
|
|
n_features_in_ : int
|
|
Number of features seen during :term:`fit`.
|
|
|
|
.. versionadded:: 0.24
|
|
|
|
feature_names_in_ : ndarray of shape (`n_features_in_`,)
|
|
Names of features seen during :term:`fit`. Defined only when `X`
|
|
has feature names that are all strings.
|
|
|
|
.. versionadded:: 1.0
|
|
|
|
See Also
|
|
--------
|
|
SparseRandomProjection : Reduce dimensionality through sparse
|
|
random projection.
|
|
|
|
Examples
|
|
--------
|
|
>>> import numpy as np
|
|
>>> from sklearn.random_projection import GaussianRandomProjection
|
|
>>> rng = np.random.RandomState(42)
|
|
>>> X = rng.rand(25, 3000)
|
|
>>> transformer = GaussianRandomProjection(random_state=rng)
|
|
>>> X_new = transformer.fit_transform(X)
|
|
>>> X_new.shape
|
|
(25, 2759)
|
|
"""
|
|
|
|
def __init__(
|
|
self,
|
|
n_components="auto",
|
|
*,
|
|
eps=0.1,
|
|
compute_inverse_components=False,
|
|
random_state=None,
|
|
):
|
|
super().__init__(
|
|
n_components=n_components,
|
|
eps=eps,
|
|
compute_inverse_components=compute_inverse_components,
|
|
random_state=random_state,
|
|
)
|
|
|
|
def _make_random_matrix(self, n_components, n_features):
|
|
"""Generate the random projection matrix.
|
|
|
|
Parameters
|
|
----------
|
|
n_components : int,
|
|
Dimensionality of the target projection space.
|
|
|
|
n_features : int,
|
|
Dimensionality of the original source space.
|
|
|
|
Returns
|
|
-------
|
|
components : ndarray of shape (n_components, n_features)
|
|
The generated random matrix.
|
|
"""
|
|
random_state = check_random_state(self.random_state)
|
|
return _gaussian_random_matrix(
|
|
n_components, n_features, random_state=random_state
|
|
)
|
|
|
|
def transform(self, X):
|
|
"""Project the data by using matrix product with the random matrix.
|
|
|
|
Parameters
|
|
----------
|
|
X : {ndarray, sparse matrix} of shape (n_samples, n_features)
|
|
The input data to project into a smaller dimensional space.
|
|
|
|
Returns
|
|
-------
|
|
X_new : ndarray of shape (n_samples, n_components)
|
|
Projected array.
|
|
"""
|
|
check_is_fitted(self)
|
|
X = self._validate_data(
|
|
X, accept_sparse=["csr", "csc"], reset=False, dtype=[np.float64, np.float32]
|
|
)
|
|
|
|
return X @ self.components_.T
|
|
|
|
|
|
class SparseRandomProjection(BaseRandomProjection):
|
|
"""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', 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 or 'auto', default='auto'
|
|
Ratio in the range (0, 1] 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 : float, default=0.1
|
|
Parameter to control the quality of the embedding according to
|
|
the Johnson-Lindenstrauss lemma when n_components is set to
|
|
'auto'. This value should be strictly positive.
|
|
|
|
Smaller values lead to better embedding and higher number of
|
|
dimensions (n_components) in the target projection space.
|
|
|
|
dense_output : bool, 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.
|
|
|
|
compute_inverse_components : bool, default=False
|
|
Learn the inverse transform by computing the pseudo-inverse of the
|
|
components during fit. Note that the pseudo-inverse is always a dense
|
|
array, even if the training data was sparse. This means that it might be
|
|
necessary to call `inverse_transform` on a small batch of samples at a
|
|
time to avoid exhausting the available memory on the host. Moreover,
|
|
computing the pseudo-inverse does not scale well to large matrices.
|
|
|
|
random_state : int, RandomState instance or None, 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_ : sparse matrix of shape (n_components, n_features)
|
|
Random matrix used for the projection. Sparse matrix will be of CSR
|
|
format.
|
|
|
|
inverse_components_ : ndarray of shape (n_features, n_components)
|
|
Pseudo-inverse of the components, only computed if
|
|
`compute_inverse_components` is True.
|
|
|
|
.. versionadded:: 1.1
|
|
|
|
density_ : float in range 0.0 - 1.0
|
|
Concrete density computed from when density = "auto".
|
|
|
|
n_features_in_ : int
|
|
Number of features seen during :term:`fit`.
|
|
|
|
.. versionadded:: 0.24
|
|
|
|
feature_names_in_ : ndarray of shape (`n_features_in_`,)
|
|
Names of features seen during :term:`fit`. Defined only when `X`
|
|
has feature names that are all strings.
|
|
|
|
.. versionadded:: 1.0
|
|
|
|
See Also
|
|
--------
|
|
GaussianRandomProjection : Reduce dimensionality through Gaussian
|
|
random projection.
|
|
|
|
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://cgi.di.uoa.gr/~optas/papers/jl.pdf
|
|
|
|
Examples
|
|
--------
|
|
>>> import numpy as np
|
|
>>> from sklearn.random_projection import SparseRandomProjection
|
|
>>> rng = np.random.RandomState(42)
|
|
>>> X = rng.rand(25, 3000)
|
|
>>> transformer = SparseRandomProjection(random_state=rng)
|
|
>>> X_new = transformer.fit_transform(X)
|
|
>>> X_new.shape
|
|
(25, 2759)
|
|
>>> # very few components are non-zero
|
|
>>> np.mean(transformer.components_ != 0)
|
|
0.0182...
|
|
"""
|
|
|
|
_parameter_constraints: dict = {
|
|
**BaseRandomProjection._parameter_constraints,
|
|
"density": [Interval(Real, 0.0, 1.0, closed="right"), StrOptions({"auto"})],
|
|
"dense_output": ["boolean"],
|
|
}
|
|
|
|
def __init__(
|
|
self,
|
|
n_components="auto",
|
|
*,
|
|
density="auto",
|
|
eps=0.1,
|
|
dense_output=False,
|
|
compute_inverse_components=False,
|
|
random_state=None,
|
|
):
|
|
super().__init__(
|
|
n_components=n_components,
|
|
eps=eps,
|
|
compute_inverse_components=compute_inverse_components,
|
|
random_state=random_state,
|
|
)
|
|
|
|
self.dense_output = dense_output
|
|
self.density = density
|
|
|
|
def _make_random_matrix(self, n_components, n_features):
|
|
"""Generate the random projection matrix
|
|
|
|
Parameters
|
|
----------
|
|
n_components : int
|
|
Dimensionality of the target projection space.
|
|
|
|
n_features : int
|
|
Dimensionality of the original source space.
|
|
|
|
Returns
|
|
-------
|
|
components : sparse matrix of shape (n_components, n_features)
|
|
The generated random matrix in CSR format.
|
|
|
|
"""
|
|
random_state = check_random_state(self.random_state)
|
|
self.density_ = _check_density(self.density, n_features)
|
|
return _sparse_random_matrix(
|
|
n_components, n_features, density=self.density_, random_state=random_state
|
|
)
|
|
|
|
def transform(self, X):
|
|
"""Project the data by using matrix product with the random matrix.
|
|
|
|
Parameters
|
|
----------
|
|
X : {ndarray, sparse matrix} of shape (n_samples, n_features)
|
|
The input data to project into a smaller dimensional space.
|
|
|
|
Returns
|
|
-------
|
|
X_new : {ndarray, sparse matrix} of shape (n_samples, n_components)
|
|
Projected array. It is a sparse matrix only when the input is sparse and
|
|
`dense_output = False`.
|
|
"""
|
|
check_is_fitted(self)
|
|
X = self._validate_data(
|
|
X, accept_sparse=["csr", "csc"], reset=False, dtype=[np.float64, np.float32]
|
|
)
|
|
|
|
return safe_sparse_dot(X, self.components_.T, dense_output=self.dense_output)
|