NMF
¶
-
class
ibex.sklearn.decomposition.
NMF
(n_components=None, init=None, solver='cd', beta_loss='frobenius', tol=0.0001, max_iter=200, random_state=None, alpha=0.0, l1_ratio=0.0, verbose=0, shuffle=False)¶ Bases:
sklearn.decomposition.nmf.NMF
,ibex._base.FrameMixin
Note
The documentation following is of the class wrapped by this class. There are some changes, in particular:
- A parameter
X
denotes apandas.DataFrame
. - A parameter
y
denotes apandas.Series
.
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 ...
Non-Negative Matrix Factorization (NMF)
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.
- n_components : int or None
- Number of components, if n_components is not set all features are kept.
- init : ‘random’ | ‘nndsvd’ | ‘nndsvda’ | ‘nndsvdar’ | ‘custom’
Method used to initialize the procedure. Default: ‘nndsvd’ if n_components < n_features, otherwise random. Valid options:
- ‘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.
- 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 dataWH
from the fitted model. - n_iter_ : int
- Actual number of iterations.
>>> 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_
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).
-
fit
(X, y=None, **params)[source]¶ Note
The documentation following is of the class wrapped by this class. There are some changes, in particular:
- A parameter
X
denotes apandas.DataFrame
. - A parameter
y
denotes apandas.Series
.
Learn a NMF model for the data X.
- X : {array-like, sparse matrix}, shape (n_samples, n_features)
- Data matrix to be decomposed
y : Ignored.
self
- A parameter
-
fit_transform
(X, y=None, W=None, H=None)[source]¶ Note
The documentation following is of the class wrapped by this class. There are some changes, in particular:
- A parameter
X
denotes apandas.DataFrame
. - A parameter
y
denotes apandas.Series
.
Learn a NMF model for the data X and returns the transformed data.
This is more efficient than calling fit followed by transform.
- X : {array-like, sparse matrix}, shape (n_samples, n_features)
- Data matrix to be decomposed
y : Ignored.
- W : array-like, shape (n_samples, n_components)
- If init=’custom’, it is used as initial guess for the solution.
- H : array-like, shape (n_components, n_features)
- If init=’custom’, it is used as initial guess for the solution.
- W : array, shape (n_samples, n_components)
- Transformed data.
- A parameter
-
inverse_transform
(W)[source]¶ Note
The documentation following is of the class wrapped by this class. There are some changes, in particular:
- A parameter
X
denotes apandas.DataFrame
. - A parameter
y
denotes apandas.Series
.
Transform data back to its original space.
- W : {array-like, sparse matrix}, shape (n_samples, n_components)
- Transformed data matrix
- X : {array-like, sparse matrix}, shape (n_samples, n_features)
- Data matrix of original shape
New in version 0.18.
- A parameter
-
transform
(X)[source]¶ Note
The documentation following is of the class wrapped by this class. There are some changes, in particular:
- A parameter
X
denotes apandas.DataFrame
. - A parameter
y
denotes apandas.Series
.
Transform the data X according to the fitted NMF model
- X : {array-like, sparse matrix}, shape (n_samples, n_features)
- Data matrix to be transformed by the model
- W : array, shape (n_samples, n_components)
- Transformed data
- A parameter
- A parameter