@@ -32,7 +32,8 @@ def _assess_dimension(spectrum, rank, n_samples):
3232 """Compute the log-likelihood of a rank ``rank`` dataset.
3333
3434 The dataset is assumed to be embedded in gaussian noise of shape(n,
35- dimf) having spectrum ``spectrum``.
35+ dimf) having spectrum ``spectrum``. This implements the method of
36+ T. P. Minka.
3637
3738 Parameters
3839 ----------
@@ -50,10 +51,11 @@ def _assess_dimension(spectrum, rank, n_samples):
5051 ll : float
5152 The log-likelihood.
5253
53- Notes
54- -----
54+ References
55+ ----------
5556 This implements the method of `Thomas P. Minka:
56- Automatic Choice of Dimensionality for PCA. NIPS 2000: 598-604`
57+ Automatic Choice of Dimensionality for PCA. NIPS 2000: 598-604
58+ <https://proceedings.neurips.cc/paper/2000/file/7503cfacd12053d309b6bed5c89de212-Paper.pdf>`_
5759 """
5860
5961 n_features = spectrum .shape [0 ]
@@ -271,26 +273,30 @@ class PCA(_BasePCA):
271273
272274 References
273275 ----------
274- For n_components == 'mle', this class uses the method of *Minka, T. P.
275- "Automatic choice of dimensionality for PCA". In NIPS, pp. 598-604*
276+ For n_components == 'mle', this class uses the method from:
277+ `Minka, T. P.. "Automatic choice of dimensionality for PCA".
278+ In NIPS, pp. 598-604 <https://tminka.github.io/papers/pca/minka-pca.pdf>`_
276279
277280 Implements the probabilistic PCA model from:
278- Tipping, M. E., and Bishop, C. M. (1999). "Probabilistic principal
281+ ` Tipping, M. E., and Bishop, C. M. (1999). "Probabilistic principal
279282 component analysis". Journal of the Royal Statistical Society:
280283 Series B (Statistical Methodology), 61(3), 611-622.
284+ <http://www.miketipping.com/papers/met-mppca.pdf>`_
281285 via the score and score_samples methods.
282- See http://www.miketipping.com/papers/met-mppca.pdf
283286
284287 For svd_solver == 'arpack', refer to `scipy.sparse.linalg.svds`.
285288
286289 For svd_solver == 'randomized', see:
287- * Halko, N., Martinsson, P. G., and Tropp, J. A. (2011).
290+ ` Halko, N., Martinsson, P. G., and Tropp, J. A. (2011).
288291 "Finding structure with randomness: Probabilistic algorithms for
289292 constructing approximate matrix decompositions".
290- SIAM review, 53(2), 217-288.* and also
291- *Martinsson, P. G., Rokhlin, V., and Tygert, M. (2011).
293+ SIAM review, 53(2), 217-288.
294+ <https://doi.org/10.1137/090771806>`_
295+ and also
296+ `Martinsson, P. G., Rokhlin, V., and Tygert, M. (2011).
292297 "A randomized algorithm for the decomposition of matrices".
293- Applied and Computational Harmonic Analysis, 30(1), 47-68.*
298+ Applied and Computational Harmonic Analysis, 30(1), 47-68
299+ <https://doi.org/10.1016/j.acha.2010.02.003>`_.
294300
295301 Examples
296302 --------
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