decomposition.TruncatedSVD

class pai4sk.decomposition.TruncatedSVD(n_components=2, algorithm='auto', n_iter=5, random_state=None, tol=0.0, use_gpu=True)

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 pai4sk.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.

If cuml is installed and if input data is cudf dataframe and if possible, then the accelerated TruncatedSVD algorithm from cuML will be used. Otherwise, scikit-learn’s TruncatedSVD algorithm will be used.

cuML in pai4sk is currently supported only | (a) with python 3.6 and | (b) without MPI. | If TruncatedSVD from cuML is run, then the return values from the APIs will be cudf dataframe and cudf Series objects instead of the return types of scikit-learn API.

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, "arpack", "randomized", "cuml", "auto", "full" or "jacobi". default = "auto".) – 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) if cuml can’t be used. “auto” will become “full” if cuml is installed and the arguments satisfy some validations. “auto” will become “randomized” if cuml is not used. algorithm should be one of “auto”, “cuml”, “full” and “jacobi”.
  • 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.
  • use_gpu (boolean, Default is True) – If True, cuML will use GPU 0. Applicable only for cuML.
Variables:
  • components (array of shape (n_components, n_features) or cudf dataframe) –
  • explained_variance (array of shape (n_components,) or cudf Series object) – The variance of the training samples transformed by a projection to each component.
  • explained_variance_ratio (array of shape (n_components,) or cudf Series object) – Percentage of variance explained by each of the selected components.
  • singular_values (array of shape (n_components,) or cudf Series object) – 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 pai4sk.decomposition import TruncatedSVD
>>> from pai4sk.random_projection import sparse_random_matrix
>>> X = 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.

fit(X, y=None)

Fit LSI model on training data X.

Parameters:
  • X ({array-like, sparse matrix} of shape (n_samples, n_features) or cudf dataframe) – Training data.
  • y (Ignored) –
Returns:

self – Returns the transformer object. If TruncatedSVD from cuML is run, then this fit method saves the computed values as cudf dataframes and cudf Series objects instead of the results’ types seen from scikit-learn’s fit method.
Return type:

object
fit_transform(X, y=None)

Fit LSI model to X and perform dimensionality reduction on X.

Parameters:
  • X ({array-like, sparse matrix} of shape (n_samples, n_features) or cudf dataframe) – Training data. If TruncatedSVD from cuML is run, then this method saves the computed values as cudf dataframes and cudf Series objects instead of the results’ types seen from scikit-learn’s API.
  • y (Ignored) –
Returns:

X_new – Reduced version of X. This will always be a dense array.
Return type:

array of shape (n_samples, n_components) or cudf dataframe
inverse_transform(X)

Transform X back to its original space.

Returns an array or cudf dataframe X_original whose transform would be X.

Parameters:X (array-like of shape (n_samples, n_components) or cudf dataframe) – New data.
Returns:X_original – Note that this is always dense. If TruncatedSVD from cuML is run, then this method returns cudf dataframe instead of the results’ types seen from scikit-learn’s transform method.
Return type:array of shape (n_samples, n_features) or cudf dataframe
transform(X)

Perform dimensionality reduction on X.

Parameters:X ({array-like, sparse matrix} of shape (n_samples, n_features) or cudf dataframe) – New data.
Returns:X_new – Reduced version of X. This will always be dense. If TruncatedSVD from cuML is run, then this method returns cudf dataframe instead of the results’ types seen from scikit-learn’s transform method.
Return type:array of shape (n_samples, n_components) or cudf dataframe