# Copyright 1999-2021 Alibaba Group Holding Ltd.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
import numpy as np
from sklearn.base import BaseEstimator, TransformerMixin
from ... import tensor as mt
from ...tensor.linalg import randomized_svd
from ...tensor.utils import check_random_state
from ...core import ExecutableTuple
from ..utils import check_array
__all__ = ["TruncatedSVD"]
[docs]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). Contrary to PCA, this
estimator does not center the data before computing the singular value
decomposition. 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 algorithms: 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 (default 5)
Number of iterations for randomized SVD solver. Not used by ARPACK.
The default is larger than the default in `randomized_svd` to handle
sparse matrices that may have large slowly decaying spectrum.
random_state : int, RandomState instance or None, optional, default = None
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`.
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_ : array, shape (n_components,)
The variance of the training samples transformed by a projection to
each component.
explained_variance_ratio_ : array, shape (n_components,)
Percentage of variance explained by each of the selected components.
singular_values_ : array, shape (n_components,)
The singular values corresponding to each of the selected components.
The singular values are equal to the 2-norms of the ``n_components``
variables in the lower-dimensional space.
Examples
--------
>>> from mars.learn.decomposition import TruncatedSVD
>>> import mars.tensor as mt
>>> from sklearn.random_projection import sparse_random_matrix
>>> X = mt.tensor(sparse_random_matrix(100, 100, density=0.01, random_state=42))
>>> svd = TruncatedSVD(n_components=5, n_iter=7, random_state=42)
>>> svd.fit(X) # doctest: +NORMALIZE_WHITESPACE
TruncatedSVD(algorithm='randomized', n_components=5, n_iter=7,
random_state=42, tol=0.0)
>>> print(svd.explained_variance_ratio_) # doctest: +ELLIPSIS
[0.0606... 0.0584... 0.0497... 0.0434... 0.0372...]
>>> print(svd.explained_variance_ratio_.sum()) # doctest: +ELLIPSIS
0.249...
>>> print(svd.singular_values_) # doctest: +ELLIPSIS
[2.5841... 2.5245... 2.3201... 2.1753... 2.0443...]
See also
--------
PCA
References
----------
Finding structure with randomness: Stochastic algorithms for constructing
approximate matrix decompositions
Halko, et al., 2009 (arXiv:909) https://arxiv.org/pdf/0909.4061.pdf
Notes
-----
SVD suffers from a problem called "sign indeterminacy", 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.
"""
[docs] def __init__(
self,
n_components=2,
algorithm="randomized",
n_iter=5,
random_state=None,
tol=0.0,
):
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, session=None):
"""Fit LSI model on training data X.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Training data.
session : session to run
y : Ignored
Returns
-------
self : object
Returns the transformer object.
"""
self.fit_transform(X, session=session)
return self
def fit_transform(self, X, y=None, session=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.
session : session to run
y : Ignored
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", "csc"], ensure_min_features=2)
random_state = check_random_state(self.random_state)
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])
raise NotImplementedError("Does not support arpack for truncated_svd")
elif self.algorithm == "randomized":
k = self.n_components
n_features = X.shape[1]
if k >= n_features:
raise ValueError(
f"n_components must be < n_features; got {k} >= {n_features}"
)
U, Sigma, VT = randomized_svd(
X, self.n_components, n_iter=self.n_iter, random_state=random_state
)
else:
raise ValueError(f"unknown algorithm {self.algorithm!r}")
self.components_ = VT
# Calculate explained variance & explained variance ratio
X_transformed = U * Sigma
self.explained_variance_ = exp_var = np.var(X_transformed, axis=0)
full_var = mt.var(X, axis=0).sum()
self.explained_variance_ratio_ = exp_var / full_var
self.singular_values_ = Sigma # Store the singular values.
to_run_tensors = [
X_transformed,
self.components_,
self.explained_variance_,
self.explained_variance_ratio_,
self.singular_values_,
]
ExecutableTuple(to_run_tensors).execute(session=session)
return X_transformed
def transform(self, X, session=None):
"""Perform dimensionality reduction on X.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
New data.
session : session to run
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")
ret = mt.dot(X, self.components_.T)
ret.execute(session=session)
return ret
def inverse_transform(self, X, session=None):
"""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.
session : session to run
Returns
-------
X_original : array, shape (n_samples, n_features)
Note that this is always a dense array.
"""
X = check_array(X)
ret = mt.dot(X, self.components_)
ret.execute(session=session)
return ret