Precision errors in KernelPCA #5970
Description
The following triggers an error. The random state is set, but there are still some precision errors.
>>> from sklearn.datasets import make_circles
>>> from sklearn.decomposition import KernelPCA
>>> from sklearn.utils.testing import assert_array_almost_equal
>>>
>>> X_circle, y_circle = make_circles(400, random_state=0, factor=0.3, noise=0.15)
>>> kpca = KernelPCA(random_state=0).fit(X_circle)
>>> kpca2 = KernelPCA(n_components=53, random_state=0).fit(X_circle)
>>>
>>> assert_array_almost_equal(kpca.lambdas_[:50], kpca2.lambdas_[:50])
>>> assert_array_almost_equal(kpca.alphas_[:2, :10], kpca2.alphas_[:2, :10])
AssertionError:
Arrays are not almost equal to 6 decimals
(mismatch 80.0%)
x: array([[ 4.52347019e-02, -7.41626885e-02, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
9.93712254e-01, 0.00000000e+00, 0.00000000e+00,...
y: array([[ 0.0452347 , -0.07416269, -0.0008139 , -0.00213575, 0.00693525,
-0.02749284, 0.05635691, 0.09004436, 0.00364872, 0.01541384],
[ 0.00916891, 0.00235399, -0.04403946, 0.02472058, 0.07725798,
-0.1409346 , 0.38463443, 0.22568812, 0.01437247, 0.1645341 ]])
Old version of issue, without using random state.
The following is raising an error below, but I don't think it should be:
>>> from sklearn.datasets import make_circles
>>> X_circle, y_circle = make_circles(400, random_state=0, factor=0.3, noise=0.15)
>>> from sklearn.decomposition import KernelPCA
>>> kpca = KernelPCA().fit(X_circle)
>>> kpca2 = KernelPCA(n_components=53).fit(X_circle)
>>>
>>> from sklearn.utils.testing import assert_array_almost_equal
>>> assert_array_almost_equal(kpca.lambdas_[:50], kpca2.lambdas_[:50])
>>> assert_array_almost_equal(kpca.alphas_[:2, :10], kpca2.alphas_[:2, :10])
AssertionError:
Arrays are not almost equal to 6 decimals
(mismatch 90.0%)
x: array([[-0.045235, -0.074163, 0. , 0. , 0. , -0.157852,
0. , 0. , 0. , 0. ],
[-0.009169, 0.002354, -0.07098 , 0.003515, -0.015677, -0.354438,
-0.18636 , 0.056072, 0.017528, -0.178867]])
y: array([[ 0.045235, -0.074163, -0.005973, 0.005636, -0.000913, -0.031506,
0.006255, 0.047652, -0.015241, -0.018319],
[ 0.009169, 0.002354, -0.175217, -0.019426, 0.011081, -0.130316,
-0.056403, -0.004699, -0.175928, -0.041456]])
You could see some signs are flipped, some numbers rounded off, etc. Unless I'm confused about the theory of Kernel PCAs, this shouldn't be raising an error, right?
@mblondel, what do you think?