TruncatedSVD

class ibex.sklearn.decomposition.TruncatedSVD(n_components=2, algorithm='randomized', n_iter=5, random_state=None, tol=0.0)

Bases: sklearn.decomposition.truncated_svd.TruncatedSVD, ibex._base.FrameMixin

Note

The documentation following is of the class wrapped by this class. There are some changes, in particular:

Note

The documentation following is of the original class wrapped by this class. This class wraps the attribute components_.

Example:

>>> import pandas as pd
>>> import numpy as np
>>> from ibex.sklearn import datasets
>>> from ibex.sklearn.decomposition import PCA as PdPCA

>>> iris = datasets.load_iris()
>>> features = iris['feature_names']
>>> iris = pd.DataFrame(
...     np.c_[iris['data'], iris['target']],
...     columns=features+['class'])

>>> iris[features]
sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)
0                5.1               3.5                1.4               0.2
1                4.9               3.0                1.4               0.2
2                4.7               3.2                1.3               0.2
3                4.6               3.1                1.5               0.2
4                5.0               3.6                1.4               0.2
...

>>> PdPCA(n_components=2).fit(iris[features], iris['class']).transform(iris[features])
    comp_0    comp_1
0   -2.684207 ...0.326607
1   -2.715391 ...0.169557
2   -2.889820 ...0.137346
3   -2.746437 ...0.311124
4   -2.728593 ...0.333925
...

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.

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_ : 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.
>>> from sklearn.decomposition import TruncatedSVD
>>> from sklearn.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)  
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...]

PCA RandomizedPCA

Finding structure with randomness: Stochastic algorithms for constructing approximate matrix decompositions Halko, et al., 2009 (arXiv:909) http://arxiv.org/pdf/0909.4061

SVD suffers from a problem called “sign indeterminancy”, 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)[source]

Note

The documentation following is of the class wrapped by this class. There are some changes, in particular:

Fit LSI model on training data X.

X : {array-like, sparse matrix}, shape (n_samples, n_features)
Training data.

y : Ignored.

self : object
Returns the transformer object.
fit_transform(X, y=None)[source]

Note

The documentation following is of the class wrapped by this class. There are some changes, in particular:

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

X : {array-like, sparse matrix}, shape (n_samples, n_features)
Training data.

y : Ignored.

X_new : array, shape (n_samples, n_components)
Reduced version of X. This will always be a dense array.
inverse_transform(X)[source]

Note

The documentation following is of the class wrapped by this class. There are some changes, in particular:

Transform X back to its original space.

Returns an array X_original whose transform would be X.

X : array-like, shape (n_samples, n_components)
New data.
X_original : array, shape (n_samples, n_features)
Note that this is always a dense array.
transform(X)[source]

Note

The documentation following is of the class wrapped by this class. There are some changes, in particular:

Perform dimensionality reduction on X.

X : {array-like, sparse matrix}, shape (n_samples, n_features)
New data.
X_new : array, shape (n_samples, n_components)
Reduced version of X. This will always be a dense array.