Reduce dimensionality through sparse random projection
Sparse random matrix is an alternative to dense random projection matrix that guarantees similar embedding quality while being much more memory efficient and allowing faster computation of the projected data.
If we note `s = 1 / density` the components of the random matrix are drawn from:
- -sqrt(s) / sqrt(n_components) with probability 1 / 2s
- 0 with probability 1 - 1 / s
- +sqrt(s) / sqrt(n_components) with probability 1 / 2s
Read more in the :ref:`User Guide <sparse_random_matrix>`.
.. versionadded:: 0.13
Parameters ---------- n_components : int or 'auto', optional (default = 'auto') Dimensionality of the target projection space.
n_components can be automatically adjusted according to the number of samples in the dataset and the bound given by the Johnson-Lindenstrauss lemma. In that case the quality of the embedding is controlled by the ``eps`` parameter.
It should be noted that Johnson-Lindenstrauss lemma can yield very conservative estimated of the required number of components as it makes no assumption on the structure of the dataset.
density : float in range ]0, 1], optional (default='auto') Ratio of non-zero component in the random projection matrix.
If density = 'auto', the value is set to the minimum density as recommended by Ping Li et al.: 1 / sqrt(n_features).
Use density = 1 / 3.0 if you want to reproduce the results from Achlioptas, 2001.
eps : strictly positive float, optional, (default=0.1) Parameter to control the quality of the embedding according to the Johnson-Lindenstrauss lemma when n_components is set to 'auto'.
Smaller values lead to better embedding and higher number of dimensions (n_components) in the target projection space.
dense_output : boolean, optional (default=False) If True, ensure that the output of the random projection is a dense numpy array even if the input and random projection matrix are both sparse. In practice, if the number of components is small the number of zero components in the projected data will be very small and it will be more CPU and memory efficient to use a dense representation.
If False, the projected data uses a sparse representation if the input is sparse.
random_state : int, RandomState instance or None, optional (default=None) Controls the pseudo random number generator used to generate the projection matrix at fit time. Pass an int for reproducible output across multiple function calls. See :term:`Glossary <random_state>`.
Attributes ---------- n_components_ : int Concrete number of components computed when n_components='auto'.
components_ : CSR matrix with shape n_components, n_features
Random matrix used for the projection.
density_ : float in range 0.0 - 1.0 Concrete density computed from when density = 'auto'.
Examples -------- >>> import numpy as np >>> from sklearn.random_projection import SparseRandomProjection >>> rng = np.random.RandomState(42) >>> X = rng.rand(100, 10000) >>> transformer = SparseRandomProjection(random_state=rng) >>> X_new = transformer.fit_transform(X) >>> X_new.shape (100, 3947) >>> # very few components are non-zero >>> np.mean(transformer.components_ != 0) 0.0100...
See Also -------- GaussianRandomProjection
References ----------
.. 1
Ping Li, T. Hastie and K. W. Church, 2006, 'Very Sparse Random Projections'. https://web.stanford.edu/~hastie/Papers/Ping/KDD06_rp.pdf
.. 2
D. Achlioptas, 2001, 'Database-friendly random projections', https://users.soe.ucsc.edu/~optas/papers/jl.pdf