dislib.decomposition

dislib.decomposition.qr.base.qr(a: dislib.data.array.Array, mode='full', overwrite_a=False)

QR Decomposition (blocked).

Parameters:

• a (ds-arrays) – Input ds-array.
• mode (string) – Mode of the algorithm ‘full’ - computes full Q matrix of size m x m and R of size m x n ‘economic’ - computes Q of size m x n and R of size n x n ‘r’ - computes only R of size m x n
• overwrite_a (bool) – Overwriting the input matrix as R.

Returns:

• q (ds-array) – only for modes ‘full’ and ‘economic’
• r (ds-array) – for all modes

Raises:

ValueError – If m < n for the provided matrix m x n or If blocks are not square or If top left shape is different than regular or If bottom right block is different than regular

class dislib.decomposition.pca.base.PCA(n_components=None, arity=50, method='eig', eps=1e-09)

Bases: sklearn.base.BaseEstimator

Principal component analysis (PCA).

Parameters:

• n_components (int or None, optional (default=None)) – Number of components to keep. If None, all components are kept.
• arity (int, optional (default=50)) – Arity of the reductions. Only if method=’eig’.
• method (str, optional (default=’eig’)) – Method to use in the decomposition. Can be ‘svd’ for singular value decomposition and ‘eig’ for eigendecomposition of the covariance matrix. ‘svd’ is recommended when having a large number of features. Falls back to ‘eig’ if the method is not recognized.
• eps (float, optional (default=1e-9)) – Tolerance for the convergence criterion when method=’svd’.

Variables:

• components (ds-array, shape (n_components, n_features)) –

  Principal axes in feature space, representing the directions of maximum variance in the data. The components are sorted by explained_variance_.

  Equal to the n_components eigenvectors of the covariance matrix with greater eigenvalues.

• explained_variance (ds-array, shape (1, n_components)) –

  The amount of variance explained by each of the selected components.

  Equal to the first n_components largest eigenvalues of the covariance matrix.

• mean (ds-array, shape (1, n_features)) – Per-feature empirical mean, estimated from the training set.

Examples

>>> import dislib as ds
>>> from dislib.decomposition import PCA
>>> import numpy as np
>>>
>>>
>>> if __name__ == '__main__':
>>>     x = np.array([[1, 2], [1, 4], [1, 0], [4, 2], [4, 4], [4, 0]])
>>>     bn, bm = 2, 2
>>>     data = ds.array(x=x, block_size=(bn, bm))
>>>     pca = PCA()
>>>     transformed_data = pca.fit_transform(data)
>>>     print(transformed_data)
>>>     print(pca.components_.collect())
>>>     print(pca.explained_variance_.collect())

fit(x, y=None)

Fit the model with the dataset.

Parameters:

• x (ds-array, shape (n_samples, n_features)) – Training data.
• y (ignored) – Not used, present here for API consistency by convention.

Returns:

self

Return type:

PCA

fit_transform(x)

Fit the model with the dataset and apply the dimensionality reduction to it.

Parameters:x (ds-array, shape (n_samples, n_features)) – Training data. Returns:transformed_darray Return type:ds-array, shape (n_samples, n_components)

transform(x)

Apply dimensionality reduction to ds-array.

The given dataset is projected on the first principal components previously extracted from a training ds-array.

Parameters:x (ds-array, shape (n_samples, n_features)) – New ds-array, with the same n_features as the training dataset. Returns:transformed_darray Return type:ds-array, shape (n_samples, n_components)