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import numpy as np
from numpy.testing import assert_array_almost_equal
from sklearn.datasets import load_linnerud
from sklearn import pls
d = load_linnerud()
X = d.data
Y = d.target
def test_pls():
# 1) Canonical (symetric) PLS (PLS 2 blocks canonical mode A)
# ===========================================================
# Compare 2 algo.: nipals vs. svd
# ------------------------------
pls_bynipals = pls.PLSCanonical(n_components=X.shape[1])
pls_bynipals.fit(X, Y)
pls_bysvd = pls.PLSCanonical(algorithm="svd", n_components=X.shape[1])
pls_bysvd.fit(X, Y)
# check equalities of loading (up to the sign of the second column)
assert_array_almost_equal(
pls_bynipals.x_loadings_,
np.multiply(pls_bysvd.x_loadings_, np.array([1, -1, 1])), decimal=5,
err_msg="nipals and svd implementation lead to different x loadings")
assert_array_almost_equal(
pls_bynipals.y_loadings_,
np.multiply(pls_bysvd.y_loadings_, np.array([1, -1, 1])), decimal=5,
err_msg="nipals and svd implementation lead to different y loadings")
# Check PLS properties (with n_components=X.shape[1])
# ---------------------------------------------------
plsca = pls.PLSCanonical(n_components=X.shape[1])
plsca.fit(X, Y)
T = plsca.x_scores_
P = plsca.x_loadings_
Wx = plsca.x_weights_
U = plsca.y_scores_
Q = plsca.y_loadings_
Wy = plsca.y_weights_
def check_ortho(M, err_msg):
K = np.dot(M.T, M)
assert_array_almost_equal(K, np.diag(np.diag(K)), err_msg=err_msg)
# Orthogonality of weights
# ~~~~~~~~~~~~~~~~~~~~~~~~
check_ortho(Wx, "x weights are not orthogonal")
check_ortho(Wy, "y weights are not orthogonal")
# Orthogonality of latent scores
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
check_ortho(T, "x scores are not orthogonal")
check_ortho(U, "y scores are not orthogonal")
# Check X = TP' and Y = UQ' (with (p == q) components)
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# center scale X, Y
Xc, Yc, x_mean, y_mean, x_std, y_std =\
pls._center_scale_xy(X.copy(), Y.copy(), scale=True)
assert_array_almost_equal(Xc, np.dot(T, P.T),
err_msg="X != TP'")
assert_array_almost_equal(Yc, np.dot(U, Q.T),
err_msg="Y != UQ'")
# Check that rotations on training data lead to scores
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Xr = plsca.transform(X)
assert_array_almost_equal(Xr, plsca.x_scores_,
err_msg="rotation on X failed")
Xr, Yr = plsca.transform(X, Y)
assert_array_almost_equal(Xr, plsca.x_scores_,
err_msg="rotation on X failed")
assert_array_almost_equal(Yr, plsca.y_scores_,
err_msg="rotation on Y failed")
# "Non regression test" on canonical PLS
# --------------------------------------
pls_ca = pls.PLSCanonical(n_components=X.shape[1])
pls_ca.fit(X, Y)
x_weights = np.array(
[[-0.61330704, 0.25616119, -0.74715187],
[-0.74697144, 0.11930791, 0.65406368],
[-0.25668686, -0.95924297, -0.11817271]])
assert_array_almost_equal(pls_ca.x_weights_, x_weights)
x_rotations = np.array(
[[-0.61330704, 0.41591889, -0.62297525],
[-0.74697144, 0.31388326, 0.77368233],
[-0.25668686, -0.89237972, -0.24121788]])
assert_array_almost_equal(pls_ca.x_rotations_, x_rotations)
y_weights = np.array(
[[+0.58989127, 0.7890047, 0.1717553],
[+0.77134053, -0.61351791, 0.16920272],
[-0.23887670, -0.03267062, 0.97050016]])
assert_array_almost_equal(pls_ca.y_weights_, y_weights)
y_rotations = np.array(
[[+0.58989127, 0.7168115, 0.30665872],
[+0.77134053, -0.70791757, 0.19786539],
[-0.23887670, -0.00343595, 0.94162826]])
assert_array_almost_equal(pls_ca.y_rotations_, y_rotations)
# 2) Regression PLS (PLS2): "Non regression test"
# ===============================================
pls_2 = pls.PLSRegression(n_components=X.shape[1])
pls_2.fit(X, Y)
x_weights = np.array(
[[-0.61330704, -0.00443647, 0.78983213],
[-0.74697144, -0.32172099, -0.58183269],
[-0.25668686, 0.94682413, -0.19399983]])
assert_array_almost_equal(pls_2.x_weights_, x_weights)
x_loadings = np.array(
[[-0.61470416, -0.24574278, 0.78983213],
[-0.65625755, -0.14396183, -0.58183269],
[-0.51733059, 1.00609417, -0.19399983]])
assert_array_almost_equal(pls_2.x_loadings_, x_loadings)
y_weights = np.array(
[[+0.32456184, 0.29892183, 0.20316322],
[+0.42439636, 0.61970543, 0.19320542],
[-0.13143144, -0.26348971, -0.17092916]])
assert_array_almost_equal(pls_2.y_weights_, y_weights)
y_loadings = np.array(
[[+0.32456184, 0.29892183, 0.20316322],
[+0.42439636, 0.61970543, 0.19320542],
[-0.13143144, -0.26348971, -0.17092916]])
assert_array_almost_equal(pls_2.y_loadings_, y_loadings)
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