/usr/lib/python3/dist-packages/sklearn/decomposition/truncated_svd.py is in python3-sklearn 0.17.0-4.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 | """Truncated SVD for sparse matrices, aka latent semantic analysis (LSA).
"""
# Author: Lars Buitinck <L.J.Buitinck@uva.nl>
# Olivier Grisel <olivier.grisel@ensta.org>
# Michael Becker <mike@beckerfuffle.com>
# License: 3-clause BSD.
import numpy as np
import scipy.sparse as sp
try:
from scipy.sparse.linalg import svds
except ImportError:
from ..utils.arpack import svds
from ..base import BaseEstimator, TransformerMixin
from ..utils import check_array, as_float_array, check_random_state
from ..utils.extmath import randomized_svd, safe_sparse_dot, svd_flip
from ..utils.sparsefuncs import mean_variance_axis
__all__ = ["TruncatedSVD"]
class TruncatedSVD(BaseEstimator, TransformerMixin):
"""Dimensionality reduction using truncated SVD (aka LSA).
This transformer performs linear dimensionality reduction by means of
truncated singular value decomposition (SVD). It is very similar to PCA,
but operates on sample vectors directly, instead of on a covariance matrix.
This means it can work with scipy.sparse matrices efficiently.
In particular, truncated SVD works on term count/tf-idf matrices as
returned by the vectorizers in sklearn.feature_extraction.text. In that
context, it is known as latent semantic analysis (LSA).
This estimator supports two algorithm: a fast randomized SVD solver, and
a "naive" algorithm that uses ARPACK as an eigensolver on (X * X.T) or
(X.T * X), whichever is more efficient.
Read more in the :ref:`User Guide <LSA>`.
Parameters
----------
n_components : int, default = 2
Desired dimensionality of output data.
Must be strictly less than the number of features.
The default value is useful for visualisation. For LSA, a value of
100 is recommended.
algorithm : string, default = "randomized"
SVD solver to use. Either "arpack" for the ARPACK wrapper in SciPy
(scipy.sparse.linalg.svds), or "randomized" for the randomized
algorithm due to Halko (2009).
n_iter : int, optional
Number of iterations for randomized SVD solver. Not used by ARPACK.
random_state : int or RandomState, optional
(Seed for) pseudo-random number generator. If not given, the
numpy.random singleton is used.
tol : float, optional
Tolerance for ARPACK. 0 means machine precision. Ignored by randomized
SVD solver.
Attributes
----------
components_ : array, shape (n_components, n_features)
explained_variance_ratio_ : array, [n_components]
Percentage of variance explained by each of the selected components.
explained_variance_ : array, [n_components]
The variance of the training samples transformed by a projection to
each component.
Examples
--------
>>> from sklearn.decomposition import TruncatedSVD
>>> from sklearn.random_projection import sparse_random_matrix
>>> X = sparse_random_matrix(100, 100, density=0.01, random_state=42)
>>> svd = TruncatedSVD(n_components=5, random_state=42)
>>> svd.fit(X) # doctest: +NORMALIZE_WHITESPACE
TruncatedSVD(algorithm='randomized', n_components=5, n_iter=5,
random_state=42, tol=0.0)
>>> print(svd.explained_variance_ratio_) # doctest: +ELLIPSIS
[ 0.0782... 0.0552... 0.0544... 0.0499... 0.0413...]
>>> print(svd.explained_variance_ratio_.sum()) # doctest: +ELLIPSIS
0.279...
See also
--------
PCA
RandomizedPCA
References
----------
Finding structure with randomness: Stochastic algorithms for constructing
approximate matrix decompositions
Halko, et al., 2009 (arXiv:909) http://arxiv.org/pdf/0909.4061
Notes
-----
SVD suffers from a problem called "sign indeterminancy", which means the
sign of the ``components_`` and the output from transform depend on the
algorithm and random state. To work around this, fit instances of this
class to data once, then keep the instance around to do transformations.
"""
def __init__(self, n_components=2, algorithm="randomized", n_iter=5,
random_state=None, tol=0.):
self.algorithm = algorithm
self.n_components = n_components
self.n_iter = n_iter
self.random_state = random_state
self.tol = tol
def fit(self, X, y=None):
"""Fit LSI model on training data X.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Training data.
Returns
-------
self : object
Returns the transformer object.
"""
self.fit_transform(X)
return self
def fit_transform(self, X, y=None):
"""Fit LSI model to X and perform dimensionality reduction on X.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Training data.
Returns
-------
X_new : array, shape (n_samples, n_components)
Reduced version of X. This will always be a dense array.
"""
X = as_float_array(X, copy=False)
random_state = check_random_state(self.random_state)
# If sparse and not csr or csc, convert to csr
if sp.issparse(X) and X.getformat() not in ["csr", "csc"]:
X = X.tocsr()
if self.algorithm == "arpack":
U, Sigma, VT = svds(X, k=self.n_components, tol=self.tol)
# svds doesn't abide by scipy.linalg.svd/randomized_svd
# conventions, so reverse its outputs.
Sigma = Sigma[::-1]
U, VT = svd_flip(U[:, ::-1], VT[::-1])
elif self.algorithm == "randomized":
k = self.n_components
n_features = X.shape[1]
if k >= n_features:
raise ValueError("n_components must be < n_features;"
" got %d >= %d" % (k, n_features))
U, Sigma, VT = randomized_svd(X, self.n_components,
n_iter=self.n_iter,
random_state=random_state)
else:
raise ValueError("unknown algorithm %r" % self.algorithm)
self.components_ = VT
# Calculate explained variance & explained variance ratio
X_transformed = np.dot(U, np.diag(Sigma))
self.explained_variance_ = exp_var = np.var(X_transformed, axis=0)
if sp.issparse(X):
_, full_var = mean_variance_axis(X, axis=0)
full_var = full_var.sum()
else:
full_var = np.var(X, axis=0).sum()
self.explained_variance_ratio_ = exp_var / full_var
return X_transformed
def transform(self, X):
"""Perform dimensionality reduction on X.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
New data.
Returns
-------
X_new : array, shape (n_samples, n_components)
Reduced version of X. This will always be a dense array.
"""
X = check_array(X, accept_sparse='csr')
return safe_sparse_dot(X, self.components_.T)
def inverse_transform(self, X):
"""Transform X back to its original space.
Returns an array X_original whose transform would be X.
Parameters
----------
X : array-like, shape (n_samples, n_components)
New data.
Returns
-------
X_original : array, shape (n_samples, n_features)
Note that this is always a dense array.
"""
X = check_array(X)
return np.dot(X, self.components_)
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