238 lines
9.1 KiB
Python
238 lines
9.1 KiB
Python
import numpy as np
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from sklearn.utils.testing import assert_array_almost_equal
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from sklearn.datasets import load_linnerud
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from sklearn import pls
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def test_pls():
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d = load_linnerud()
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X = d.data
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Y = d.target
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# 1) Canonical (symetric) PLS (PLS 2 blocks canonical mode A)
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# ===========================================================
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# Compare 2 algo.: nipals vs. svd
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# ------------------------------
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pls_bynipals = pls.PLSCanonical(n_components=X.shape[1])
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pls_bynipals.fit(X, Y)
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pls_bysvd = pls.PLSCanonical(algorithm="svd", n_components=X.shape[1])
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pls_bysvd.fit(X, Y)
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# check equalities of loading (up to the sign of the second column)
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assert_array_almost_equal(
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pls_bynipals.x_loadings_,
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np.multiply(pls_bysvd.x_loadings_, np.array([1, -1, 1])), decimal=5,
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err_msg="nipals and svd implementation lead to different x loadings")
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assert_array_almost_equal(
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pls_bynipals.y_loadings_,
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np.multiply(pls_bysvd.y_loadings_, np.array([1, -1, 1])), decimal=5,
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err_msg="nipals and svd implementation lead to different y loadings")
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# Check PLS properties (with n_components=X.shape[1])
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# ---------------------------------------------------
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plsca = pls.PLSCanonical(n_components=X.shape[1])
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plsca.fit(X, Y)
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T = plsca.x_scores_
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P = plsca.x_loadings_
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Wx = plsca.x_weights_
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U = plsca.y_scores_
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Q = plsca.y_loadings_
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Wy = plsca.y_weights_
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def check_ortho(M, err_msg):
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K = np.dot(M.T, M)
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assert_array_almost_equal(K, np.diag(np.diag(K)), err_msg=err_msg)
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# Orthogonality of weights
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# ~~~~~~~~~~~~~~~~~~~~~~~~
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check_ortho(Wx, "x weights are not orthogonal")
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check_ortho(Wy, "y weights are not orthogonal")
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# Orthogonality of latent scores
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# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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check_ortho(T, "x scores are not orthogonal")
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check_ortho(U, "y scores are not orthogonal")
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# Check X = TP' and Y = UQ' (with (p == q) components)
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# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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# center scale X, Y
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Xc, Yc, x_mean, y_mean, x_std, y_std =\
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pls._center_scale_xy(X.copy(), Y.copy(), scale=True)
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assert_array_almost_equal(Xc, np.dot(T, P.T),
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err_msg="X != TP'")
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assert_array_almost_equal(Yc, np.dot(U, Q.T),
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err_msg="Y != UQ'")
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# Check that rotations on training data lead to scores
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# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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Xr = plsca.transform(X)
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assert_array_almost_equal(Xr, plsca.x_scores_,
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err_msg="rotation on X failed")
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Xr, Yr = plsca.transform(X, Y)
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assert_array_almost_equal(Xr, plsca.x_scores_,
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err_msg="rotation on X failed")
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assert_array_almost_equal(Yr, plsca.y_scores_,
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err_msg="rotation on Y failed")
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# "Non regression test" on canonical PLS
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# --------------------------------------
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# The results were checked against the R-package plspm
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pls_ca = pls.PLSCanonical(n_components=X.shape[1])
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pls_ca.fit(X, Y)
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x_weights = np.array(
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[[-0.61330704, 0.25616119, -0.74715187],
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[-0.74697144, 0.11930791, 0.65406368],
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[-0.25668686, -0.95924297, -0.11817271]])
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assert_array_almost_equal(pls_ca.x_weights_, x_weights)
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x_rotations = np.array(
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[[-0.61330704, 0.41591889, -0.62297525],
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[-0.74697144, 0.31388326, 0.77368233],
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[-0.25668686, -0.89237972, -0.24121788]])
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assert_array_almost_equal(pls_ca.x_rotations_, x_rotations)
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y_weights = np.array(
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[[+0.58989127, 0.7890047, 0.1717553],
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[+0.77134053, -0.61351791, 0.16920272],
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[-0.23887670, -0.03267062, 0.97050016]])
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assert_array_almost_equal(pls_ca.y_weights_, y_weights)
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y_rotations = np.array(
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[[+0.58989127, 0.7168115, 0.30665872],
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[+0.77134053, -0.70791757, 0.19786539],
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[-0.23887670, -0.00343595, 0.94162826]])
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assert_array_almost_equal(pls_ca.y_rotations_, y_rotations)
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# 2) Regression PLS (PLS2): "Non regression test"
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# ===============================================
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# The results were checked against the R-packages plspm, misOmics and pls
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pls_2 = pls.PLSRegression(n_components=X.shape[1])
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pls_2.fit(X, Y)
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x_weights = np.array(
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[[-0.61330704, -0.00443647, 0.78983213],
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[-0.74697144, -0.32172099, -0.58183269],
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[-0.25668686, 0.94682413, -0.19399983]])
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assert_array_almost_equal(pls_2.x_weights_, x_weights)
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x_loadings = np.array(
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[[-0.61470416, -0.24574278, 0.78983213],
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[-0.65625755, -0.14396183, -0.58183269],
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[-0.51733059, 1.00609417, -0.19399983]])
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assert_array_almost_equal(pls_2.x_loadings_, x_loadings)
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y_weights = np.array(
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[[+0.32456184, 0.29892183, 0.20316322],
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[+0.42439636, 0.61970543, 0.19320542],
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[-0.13143144, -0.26348971, -0.17092916]])
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assert_array_almost_equal(pls_2.y_weights_, y_weights)
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y_loadings = np.array(
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[[+0.32456184, 0.29892183, 0.20316322],
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[+0.42439636, 0.61970543, 0.19320542],
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[-0.13143144, -0.26348971, -0.17092916]])
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assert_array_almost_equal(pls_2.y_loadings_, y_loadings)
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# 3) Another non-regression test of Canonical PLS on random dataset
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# =================================================================
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# The results were checked against the R-package plspm
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n = 500
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p_noise = 10
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q_noise = 5
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# 2 latents vars:
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np.random.seed(11)
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l1 = np.random.normal(size=n)
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l2 = np.random.normal(size=n)
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latents = np.array([l1, l1, l2, l2]).T
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X = latents + np.random.normal(size=4 * n).reshape((n, 4))
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Y = latents + np.random.normal(size=4 * n).reshape((n, 4))
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X = np.concatenate((X,
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np.random.normal(size=p_noise * n).reshape(n, p_noise)), axis=1)
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Y = np.concatenate((Y,
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np.random.normal(size=q_noise * n).reshape(n, q_noise)), axis=1)
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np.random.seed(None)
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pls_ca = pls.PLSCanonical(n_components=3)
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pls_ca.fit(X, Y)
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x_weights = np.array(
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[[0.65803719, 0.19197924, 0.21769083],
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[0.7009113, 0.13303969, -0.15376699],
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[0.13528197, -0.68636408, 0.13856546],
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[0.16854574, -0.66788088, -0.12485304],
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[-0.03232333, -0.04189855, 0.40690153],
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[0.1148816, -0.09643158, 0.1613305],
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[0.04792138, -0.02384992, 0.17175319],
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[-0.06781, -0.01666137, -0.18556747],
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[-0.00266945, -0.00160224, 0.11893098],
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[-0.00849528, -0.07706095, 0.1570547],
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[-0.00949471, -0.02964127, 0.34657036],
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[-0.03572177, 0.0945091, 0.3414855],
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[0.05584937, -0.02028961, -0.57682568],
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[0.05744254, -0.01482333, -0.17431274]])
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assert_array_almost_equal(pls_ca.x_weights_, x_weights)
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x_loadings = np.array(
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[[0.65649254, 0.1847647, 0.15270699],
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[0.67554234, 0.15237508, -0.09182247],
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[0.19219925, -0.67750975, 0.08673128],
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[0.2133631, -0.67034809, -0.08835483],
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[-0.03178912, -0.06668336, 0.43395268],
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[0.15684588, -0.13350241, 0.20578984],
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[0.03337736, -0.03807306, 0.09871553],
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[-0.06199844, 0.01559854, -0.1881785],
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[0.00406146, -0.00587025, 0.16413253],
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[-0.00374239, -0.05848466, 0.19140336],
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[0.00139214, -0.01033161, 0.32239136],
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[-0.05292828, 0.0953533, 0.31916881],
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[0.04031924, -0.01961045, -0.65174036],
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[0.06172484, -0.06597366, -0.1244497]])
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assert_array_almost_equal(pls_ca.x_loadings_, x_loadings)
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y_weights = np.array(
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[[0.66101097, 0.18672553, 0.22826092],
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[0.69347861, 0.18463471, -0.23995597],
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[0.14462724, -0.66504085, 0.17082434],
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[0.22247955, -0.6932605, -0.09832993],
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[0.07035859, 0.00714283, 0.67810124],
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[0.07765351, -0.0105204, -0.44108074],
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[-0.00917056, 0.04322147, 0.10062478],
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[-0.01909512, 0.06182718, 0.28830475],
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[0.01756709, 0.04797666, 0.32225745]])
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assert_array_almost_equal(pls_ca.y_weights_, y_weights)
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y_loadings = np.array(
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[[0.68568625, 0.1674376, 0.0969508],
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[0.68782064, 0.20375837, -0.1164448],
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[0.11712173, -0.68046903, 0.12001505],
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[0.17860457, -0.6798319, -0.05089681],
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[0.06265739, -0.0277703, 0.74729584],
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[0.0914178, 0.00403751, -0.5135078],
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[-0.02196918, -0.01377169, 0.09564505],
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[-0.03288952, 0.09039729, 0.31858973],
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[0.04287624, 0.05254676, 0.27836841]])
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assert_array_almost_equal(pls_ca.y_loadings_, y_loadings)
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# Orthogonality of weights
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# ~~~~~~~~~~~~~~~~~~~~~~~~
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check_ortho(pls_ca.x_weights_, "x weights are not orthogonal")
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check_ortho(pls_ca.y_weights_, "y weights are not orthogonal")
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# Orthogonality of latent scores
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# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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check_ortho(pls_ca.x_scores_, "x scores are not orthogonal")
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check_ortho(pls_ca.y_scores_, "y scores are not orthogonal")
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def test_scale():
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d = load_linnerud()
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X = d.data
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Y = d.target
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# causes X[:, -1].std() to be zero
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X[:, -1] = 1.0
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for clf in [pls.PLSCanonical(), pls.PLSRegression(),
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pls.CCA(), pls.PLSSVD()]:
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clf.set_params(scale=True)
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clf.fit(X, Y)
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