skoot.decomposition.SelectiveNMF

class skoot.decomposition.SelectiveNMF(cols=None, as_df=True, trans_col_name=None, **kwargs)[source][source]

Non-Negative Matrix Factorization (NMF) (applied to selected columns).

Find two non-negative matrices (W, H) whose product approximates the non- negative matrix X. This factorization can be used for example for dimensionality reduction, source separation or topic extraction.

The objective function is:

0.5 * ||X - WH||_Fro^2
+ alpha * l1_ratio * ||vec(W)||_1
+ alpha * l1_ratio * ||vec(H)||_1
+ 0.5 * alpha * (1 - l1_ratio) * ||W||_Fro^2
+ 0.5 * alpha * (1 - l1_ratio) * ||H||_Fro^2

Where:

||A||_Fro^2 = \sum_{i,j} A_{ij}^2 (Frobenius norm)
||vec(A)||_1 = \sum_{i,j} abs(A_{ij}) (Elementwise L1 norm)

For multiplicative-update (‘mu’) solver, the Frobenius norm (0.5 * ||X - WH||_Fro^2) can be changed into another beta-divergence loss, by changing the beta_loss parameter.

The objective function is minimized with an alternating minimization of W and H.

Read more in the User Guide.

This class wraps scikit-learn’s NMF. When a pd.DataFrame is passed to the fit method, the transformation is applied to the selected columns, which are subsequently dropped from the frame. All remaining columns are left alone.

Parameters:

cols : array-like, shape=(n_features,), optional (default=None)

The names of the columns on which to apply the transformation. If no column names are provided, the transformer will be fit on the entire frame. Note that the transformation will also only apply to the specified columns, and any other non-specified columns will still be present after the transformation.

as_df : bool, optional (default=True)

Whether to return a Pandas DataFrame in the transform method. If False, will return a Numpy ndarray instead. Since most skoot transformers depend on explicitly-named DataFrame features, the as_df parameter is True by default.

trans_col_name : str, unicode or iterable, optional

The name or list of names to apply to the transformed column(s). If a string is provided, it is used as a prefix for new columns. If an iterable is provided, its dimensions must match the number of produced columns. If None (default), will use the estimator class name as the prefix.

n_components : int or None

Number of components, if n_components is not set all features are kept.

init : None | ‘random’ | ‘nndsvd’ | ‘nndsvda’ | ‘nndsvdar’ | ‘custom’

Method used to initialize the procedure. Default: None. Valid options:

  • None: ‘nndsvd’ if n_components <= min(n_samples, n_features),
    otherwise random.
  • ‘random’: non-negative random matrices, scaled with:
    sqrt(X.mean() / n_components)
  • ‘nndsvd’: Nonnegative Double Singular Value Decomposition (NNDSVD)
    initialization (better for sparseness)
  • ‘nndsvda’: NNDSVD with zeros filled with the average of X
    (better when sparsity is not desired)
  • ‘nndsvdar’: NNDSVD with zeros filled with small random values
    (generally faster, less accurate alternative to NNDSVDa for when sparsity is not desired)
  • ‘custom’: use custom matrices W and H

solver : ‘cd’ | ‘mu’

Numerical solver to use: ‘cd’ is a Coordinate Descent solver. ‘mu’ is a Multiplicative Update solver.

New in version 0.17: Coordinate Descent solver.

New in version 0.19: Multiplicative Update solver.

beta_loss : float or string, default ‘frobenius’

String must be in {‘frobenius’, ‘kullback-leibler’, ‘itakura-saito’}. Beta divergence to be minimized, measuring the distance between X and the dot product WH. Note that values different from ‘frobenius’ (or 2) and ‘kullback-leibler’ (or 1) lead to significantly slower fits. Note that for beta_loss <= 0 (or ‘itakura-saito’), the input matrix X cannot contain zeros. Used only in ‘mu’ solver.

New in version 0.19.

tol : float, default: 1e-4

Tolerance of the stopping condition.

max_iter : integer, default: 200

Maximum number of iterations before timing out.

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.

alpha : double, default: 0.

Constant that multiplies the regularization terms. Set it to zero to have no regularization.

New in version 0.17: alpha used in the Coordinate Descent solver.

l1_ratio : double, default: 0.

The regularization mixing parameter, with 0 <= l1_ratio <= 1. For l1_ratio = 0 the penalty is an elementwise L2 penalty (aka Frobenius Norm). For l1_ratio = 1 it is an elementwise L1 penalty. For 0 < l1_ratio < 1, the penalty is a combination of L1 and L2.

New in version 0.17: Regularization parameter l1_ratio used in the Coordinate Descent solver.

verbose : bool, default=False

Whether to be verbose.

shuffle : boolean, default: False

If true, randomize the order of coordinates in the CD solver.

New in version 0.17: shuffle parameter used in the Coordinate Descent solver.

Attributes

components_ (array, [n_components, n_features]) Factorization matrix, sometimes called ‘dictionary’.
reconstruction_err_ (number) Frobenius norm of the matrix difference, or beta-divergence, between the training data X and the reconstructed data WH from the fitted model.
n_iter_ (int) Actual number of iterations.

See also

SelectiveIncrementalPCA, SelectiveKernalPCA, SelectivePCA, SelectiveTruncatedSVD

References

Cichocki, Andrzej, and P. H. A. N. Anh-Huy. “Fast local algorithms for large scale nonnegative matrix and tensor factorizations.” IEICE transactions on fundamentals of electronics, communications and computer sciences 92.3: 708-721, 2009.

Fevotte, C., & Idier, J. (2011). Algorithms for nonnegative matrix factorization with the beta-divergence. Neural Computation, 23(9).

Examples

>>> import numpy as np
>>> X = np.array([[1, 1], [2, 1], [3, 1.2], [4, 1], [5, 0.8], [6, 1]])
>>> from sklearn.decomposition import NMF
>>> model = NMF(n_components=2, init='random', random_state=0)
>>> W = model.fit_transform(X)
>>> H = model.components_

Methods

fit(X[, y]) Fit the wrapped transformer.
fit_transform(X[, y]) Fit to data, then transform it.
get_params([deep]) Get parameters for this estimator.
set_params(**params) Set the parameters of this estimator.
transform(X) Transform a test dataframe.
__init__(cols=None, as_df=True, trans_col_name=None, **kwargs)[source]

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

fit(X, y=None, **fit_kwargs)[source]

Fit the wrapped transformer.

This method will fit the wrapped sklearn transformer on the selected columns, leaving other columns alone.

Parameters:

X : pd.DataFrame, shape=(n_samples, n_features)

The Pandas frame to fit. The frame will only be fit on the prescribed cols (see __init__) or all of them if cols is None. Furthermore, X will not be altered in the process of the fit.

y : array-like or None, shape=(n_samples,), optional (default=None)

Pass-through for sklearn.pipeline.Pipeline. Even if explicitly set, will not change behavior of fit.
fit_transform(X, y=None, **fit_params)[source]

Fit to data, then transform it.

Fits transformer to X and y with optional parameters fit_params and returns a transformed version of X.

Parameters:

X : numpy array of shape [n_samples, n_features]

Training set.

y : numpy array of shape [n_samples]

Target values.
Returns:

X_new : numpy array of shape [n_samples, n_features_new]

Transformed array.
get_params(deep=True)[source]

Get parameters for this estimator.

Parameters:

deep : boolean, optional

If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns:

params : mapping of string to any

Parameter names mapped to their values.
set_params(**params)[source]

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Returns:self
transform(X)[source]

Transform a test dataframe.

Parameters:

X : pd.DataFrame, shape=(n_samples, n_features)

The Pandas frame to transform. The operation will be applied to a copy of the input data, and the result will be returned.
Returns:

X : pd.DataFrame, shape=(n_samples, n_features)

The operation is applied to a copy of X, and the result set is returned.