8000 [MRG+2] Incorrect implementation of explained_variance_ in PCA (#9105) · scikit-learn/scikit-learn@2a36ff1 · GitHub
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[MRG+2] Incorrect implementation of explained_variance_ in PCA (#9105)
* fix pca explained_variance_ * fix fit_transform * fix test_whitening * fix IncrementalPCA * uncomment the test * improve test * make CI green * revert #7843 and add what's new * fix what's new
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‎doc/whats_new.rst

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@@ -413,6 +413,12 @@ Bug fixes
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by `Joel Nothman`_ and :user:`Jon Crall <Erotemic>`.
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- Fixed the implementation of `explained_variance_`
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in :class:`decomposition.PCA`,
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:class:`decomposition.RandomizedPCA` and
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:class:`decomposition.IncrementalPCA`.
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:issue:`9105` by `Hanmin Qin <https://github.com/qinhanmin2014>`_.
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API changes summary
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-------------------
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‎sklearn/decomposition/incremental_pca.py

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@@ -251,7 +251,7 @@ def partial_fit(self, X, y=None, check_input=True):
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U, S, V = linalg.svd(X, full_matrices=False)
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U, V = svd_flip(U, V, u_based_decision=False)
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explained_variance = S ** 2 / n_total_samples
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explained_variance = S ** 2 / (n_total_samples - 1)
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explained_variance_ratio = S ** 2 / np.sum(col_var * n_total_samples)
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self.n_samples_seen_ = n_total_samples

‎sklearn/decomposition/pca.py

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@@ -285,12 +285,6 @@ class PCA(_BasePCA):
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>>> print(pca.singular_values_) # doctest: +ELLIPSIS
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[ 6.30061...]
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Notes
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-----
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PCA uses the maximum likelihood estimate of the eigenvalues, which does not
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include the Bessel correction, though in practice this should rarely make a
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difference in a machine learning context.
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See also
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--------
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KernelPCA
@@ -346,7 +340,7 @@ def fit_transform(self, X, y=None):
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if self.whiten:
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# X_new = X * V / S * sqrt(n_samples) = U * sqrt(n_samples)
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U *= sqrt(X.shape[0])
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U *= sqrt(X.shape[0] - 1)
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else:
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# X_new = X * V = U * S * V^T * V = U * S
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U *= S[:self.n_components_]
@@ -416,7 +410,7 @@ def _fit_full(self, X, n_components):
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components_ = V
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# Get variance explained by singular values
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explained_variance_ = (S ** 2) / n_samples
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explained_variance_ = (S ** 2) / (n_samples - 1)
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total_var = explained_variance_.sum()
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explained_variance_ratio_ = explained_variance_ / total_var
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singular_values_ = S.copy() # Store the singular values.
@@ -495,8 +489,8 @@ def _fit_truncated(self, X, n_components, svd_solver):
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self.n_components_ = n_components
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# Get variance explained by singular values
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self.explained_variance_ = (S ** 2) / n_samples
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total_var = np.var(X, axis=0)
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self.explained_variance_ = (S ** 2) / (n_samples - 1)
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total_var = np.var(X, ddof=1, axis=0)
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self.explained_variance_ratio_ = \
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self.explained_variance_ / total_var.sum()
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self.singular_values_ = S.copy() # Store the singular values.
@@ -714,8 +708,8 @@ def _fit(self, X):
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n_iter=self.iterated_power,
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random_state=random_state)
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self.explained_variance_ = exp_var = (S ** 2) / n_samples
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full_var = np.var(X, axis=0).sum()
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self.explained_variance_ = exp_var = (S ** 2) / (n_samples - 1)
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full_var = np.var(X, ddof=1, axis=0).sum()
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self.explained_variance_ratio_ = exp_var / full_var
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self.singular_values_ = S # Store the singular values.
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‎sklearn/decomposition/tests/test_pca.py

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@@ -174,7 +174,8 @@ def test_whitening():
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X_whitened2 = pca.transform(X_)
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assert_array_almost_equal(X_whitened, X_whitened2)
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assert_almost_equal(X_whitened.std(axis=0), np.ones(n_components),
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assert_almost_equal(X_whitened.std(ddof=1, axis=0),
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np.ones(n_components),
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decimal=6)
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assert_almost_equal(X_whitened.mean(axis=0), np.zeros(n_components))
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@@ -213,17 +214,25 @@ def test_explained_variance():
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rpca.explained_variance_ratio_, 1)
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# compare to empirical variances
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expected_result = np.linalg.eig(np.cov(X, rowvar=False))[0]
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expected_result = sorted(expected_result, reverse=True)[:2]
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X_pca = pca.transform(X)
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assert_array_almost_equal(pca.explained_variance_,
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np.var(X_pca, axis=0))
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np.var(X_pca, ddof=1, axis=0))
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assert_array_almost_equal(pca.explained_variance_, expected_result)
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X_pca = apca.transform(X)
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np.var(X_pca, axis=0))
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np.var(X_pca, ddof=1, axis=0))
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assert_array_almost_equal(apca.explained_variance_, expected_result)
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X_rpca = rpca.transform(X)
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assert_array_almost_equal(rpca.explained_variance_, np.var(X_rpca, axis=0),
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assert_array_almost_equal(rpca.explained_variance_,
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np.var(X_rpca, ddof=1, axis=0),
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decimal=1)
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assert_array_almost_equal(rpca.explained_variance_,
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expected_result, decimal=1)
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# Same with correlated data
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X = datasets.make_classification(n_samples, n_features,

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