# mars.learn.decomposition.TruncatedSVD¶

class mars.learn.decomposition.TruncatedSVD(n_components=2, algorithm='randomized', n_iter=5, random_state=None, tol=0.0)[source]

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 User Guide.

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.

components_
Type

array, shape (n_components, n_features)

explained_variance_

The variance of the training samples transformed by a projection to each component.

Type

array, shape (n_components,)

explained_variance_ratio_

Percentage of variance explained by each of the selected components.

Type

array, shape (n_components,)

singular_values_

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.

Type

array, shape (n_components,)

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)
TruncatedSVD(algorithm='randomized', n_components=5, n_iter=7,
random_state=42, tol=0.0)
>>> print(svd.explained_variance_ratio_)
[0.0606... 0.0584... 0.0497... 0.0434... 0.0372...]
>>> print(svd.explained_variance_ratio_.sum())
0.249...
>>> print(svd.singular_values_)
[2.5841... 2.5245... 2.3201... 2.1753... 2.0443...]


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.

__init__(n_components=2, algorithm='randomized', n_iter=5, random_state=None, tol=0.0)[source]

Initialize self. See help(type(self)) for accurate signature.

Methods

 __init__([n_components, algorithm, n_iter, …]) Initialize self. fit(X[, y, session]) Fit LSI model on training data X. fit_transform(X[, y, session]) Fit LSI model to X and perform dimensionality reduction on X. get_params([deep]) Get parameters for this estimator. inverse_transform(X[, session]) Transform X back to its original space. set_params(**params) Set the parameters of this estimator. transform(X[, session]) Perform dimensionality reduction on X.