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 sparse matrices efficiently.
In particular, truncated SVD works on term count/tf-idf matrices as returned by the vectorizers in :mod:`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 :func:`~sklearn.utils.extmath.randomized_svd` to handle sparse matrices that may have large slowly decaying spectrum.
random_state : int, RandomState instance, default=None Used during randomized svd. Pass an int for reproducible results across multiple function calls. See :term:`Glossary <random_state>`.
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 sklearn.decomposition import TruncatedSVD >>> from scipy.sparse import random as sparse_random >>> from sklearn.random_projection import sparse_random_matrix >>> X = sparse_random(100, 100, density=0.01, format='csr', ... random_state=42) >>> svd = TruncatedSVD(n_components=5, n_iter=7, random_state=42) >>> svd.fit(X) TruncatedSVD(n_components=5, n_iter=7, random_state=42) >>> print(svd.explained_variance_ratio_) 0.0646... 0.0633... 0.0639... 0.0535... 0.0406...
>>> print(svd.explained_variance_ratio_.sum()) 0.286... >>> print(svd.singular_values_) 1.553... 1.512... 1.510... 1.370... 1.199...
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.