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Add URL to reference of Minka paper used in PCA #19207

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Jan 26, 2021
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Add URL to reference of Minka paper used in PCA #19207

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Add URL to reference of Minka paper used in PCA
hamogu Jan 19, 2021
e4361fa
Added ULRs for all references in the PCA docstring
hamogu Jan 20, 2021
53728ee
Update reference to link to exanded version directly
hamogu Jan 22, 2021
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30 changes: 18 additions & 12 deletions 30 sklearn/decomposition/_pca.py
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Expand Up @@ -32,7 +32,8 @@ def _assess_dimension(spectrum, rank, n_samples):
"""Compute the log-likelihood of a rank ``rank`` dataset.

The dataset is assumed to be embedded in gaussian noise of shape(n,
dimf) having spectrum ``spectrum``.
dimf) having spectrum ``spectrum``. This implements the method of
T. P. Minka.

Parameters
----------
Expand All @@ -50,10 +51,11 @@ def _assess_dimension(spectrum, rank, n_samples):
ll : float
The log-likelihood.

Notes
-----
References
----------
This implements the method of `Thomas P. Minka:
Automatic Choice of Dimensionality for PCA. NIPS 2000: 598-604`
Automatic Choice of Dimensionality for PCA. NIPS 2000: 598-604
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<https://proceedings.neurips.cc/paper/2000/file/7503cfacd12053d309b6bed5c89de212-Paper.pdf>`_
"""

n_features = spectrum.shape[0]
Expand Down Expand Up @@ -271,26 +273,30 @@ class PCA(_BasePCA):

References
----------
For n_components == 'mle', this class uses the method of *Minka, T. P.
"Automatic choice of dimensionality for PCA". In NIPS, pp. 598-604*
For n_components == 'mle', this class uses the method from:
`Minka, T. P.. "Automatic choice of dimensionality for PCA".
In NIPS, pp. 598-604 <https://tminka.github.io/papers/pca/minka-pca.pdf>`_

Implements the probabilistic PCA model from:
Tipping, M. E., and Bishop, C. M. (1999). "Probabilistic principal
`Tipping, M. E., and Bishop, C. M. (1999). "Probabilistic principal
component analysis". Journal of the Royal Statistical Society:
Series B (Statistical Methodology), 61(3), 611-622.
<http://www.miketipping.com/papers/met-mppca.pdf>`_
via the score and score_samples methods.
See http://www.miketipping.com/papers/met-mppca.pdf

For svd_solver == 'arpack', refer to `scipy.sparse.linalg.svds`.

For svd_solver == 'randomized', see:
*Halko, N., Martinsson, P. G., and Tropp, J. A. (2011).
`Halko, N., Martinsson, P. G., and Tropp, J. A. (2011).
"Finding structure with randomness: Probabilistic algorithms for
constructing approximate matrix decompositions".
SIAM review, 53(2), 217-288.* and also
*Martinsson, P. G., Rokhlin, V., and Tygert, M. (2011).
SIAM review, 53(2), 217-288.
<https://doi.org/10.1137/090771806>`_
and also
`Martinsson, P. G., Rokhlin, V., and Tygert, M. (2011).
"A randomized algorithm for the decomposition of matrices".
Applied and Computational Harmonic Analysis, 30(1), 47-68.*
Applied and Computational Harmonic Analysis, 30(1), 47-68
<https://doi.org/10.1016/j.acha.2010.02.003>`_.

Examples
--------
Expand Down
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