Source code for mars.learn.decomposition._truncated_svd

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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) >>> # 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) 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 =, 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 =, self.components_) ret.execute(session=session) return ret