def test_pls_errors():
d = load_linnerud()
X = d.data
Y = d.target
for clf in [pls_.PLSCanonical(), pls_.PLSRegression(), pls_.PLSSVD()]:
clf.n_components = 4
assert_raise_message(ValueError, "Invalid number of components",
clf.fit, X, Y)
def test_univariate_pls_regression():
# Ensure 1d Y is correctly interpreted
d = load_linnerud()
X = d.data
Y = d.target
clf = pls_.PLSRegression()
# Compare 1d to column vector
model1 = clf.fit(X, Y[:, 0]).coef_
model2 = clf.fit(X, Y[:, :1]).coef_
assert_array_almost_equal(model1, model2)
def test_scale_and_stability():
# We test scale=True parameter
# This allows to check numerical stability over platforms as well
d = load_linnerud()
X1 = d.data
Y1 = d.target
# causes X[:, -1].std() to be zero
X1[:, -1] = 1.0
# From bug #2821
# Test with X2, T2 s.t. clf.x_score[:, 1] == 0, clf.y_score[:, 1] == 0
# This test robustness of algorithm when dealing with value close to 0
X2 = np.array([[0., 0., 1.], [1., 0., 0.], [2., 2., 2.], [3., 5., 4.]])
Y2 = np.array([[0.1, -0.2], [0.9, 1.1], [6.2, 5.9], [11.9, 12.3]])
for (X, Y) in [(X1, Y1), (X2, Y2)]:
X_std = X.std(axis=0, ddof=1)
X_std[X_std == 0] = 1
Y_std = Y.std(axis=0, ddof=1)
Y_std[Y_std == 0] = 1
X_s = (X - X.mean(axis=0)) / X_std
Y_s = (Y - Y.mean(axis=0)) / Y_std
for clf in [
CCA(),
pls_.PLSCanonical(),
pls_.PLSRegression(),
pls_.PLSSVD()
]:
clf.set_params(scale=True)
X_score, Y_score = clf.fit_transform(X, Y)
clf.set_params(scale=False)
X_s_score, Y_s_score = clf.fit_transform(X_s, Y_s)
assert_array_almost_equal(X_s_score, X_score)
assert_array_almost_equal(Y_s_score, Y_score)
# Scaling should be idempotent
clf.set_params(scale=True)
X_score, Y_score = clf.fit_transform(X_s, Y_s)
assert_array_almost_equal(X_s_score, X_score)
assert_array_almost_equal(Y_s_score, Y_score)
def test_pls_scaling():
# sanity check for scale=True
n_samples = 1000
n_targets = 5
n_features = 10
rng = check_random_state(0)
Q = rng.randn(n_targets, n_features)
Y = rng.randn(n_samples, n_targets)
X = np.dot(Y, Q) + 2 * rng.randn(n_samples, n_features) + 1
X *= 1000
X_scaled = StandardScaler().fit_transform(X)
pls = pls_.PLSRegression(n_components=5, scale=True)
pls.fit(X, Y)
score = pls.score(X, Y)
pls.fit(X_scaled, Y)
score_scaled = pls.score(X_scaled, Y)
assert_approx_equal(score, score_scaled)
def test_pls():
d = load_linnerud()
X = d.data
Y = d.target
# 1) Canonical (symmetric) 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_,
pls_bysvd.x_loadings_,
decimal=5,
err_msg="nipals and svd implementations lead to different x loadings")
assert_array_almost_equal(
pls_bynipals.y_loadings_,
pls_bysvd.y_loadings_,
decimal=5,
err_msg="nipals and svd implementations 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")
# Check that inverse_transform works
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Xreconstructed = plsca.inverse_transform(Xr)
assert_array_almost_equal(Xreconstructed,
X,
err_msg="inverse_transform failed")
# "Non regression test" on canonical PLS
# --------------------------------------
# The results were checked against the R-package plspm
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]])
# x_weights_sign_flip holds columns of 1 or -1, depending on sign flip
# between R and python
x_weights_sign_flip = 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]])
x_rotations_sign_flip = 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]])
y_weights_sign_flip = 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]])
y_rotations_sign_flip = pls_ca.y_rotations_ / y_rotations
# x_weights = X.dot(x_rotation)
# Hence R/python sign flip should be the same in x_weight and x_rotation
assert_array_almost_equal(x_rotations_sign_flip, x_weights_sign_flip)
# This test that R / python give the same result up to column
# sign indeterminacy
assert_array_almost_equal(np.abs(x_rotations_sign_flip), 1, 4)
assert_array_almost_equal(np.abs(x_weights_sign_flip), 1, 4)
assert_array_almost_equal(y_rotations_sign_flip, y_weights_sign_flip)
assert_array_almost_equal(np.abs(y_rotations_sign_flip), 1, 4)
assert_array_almost_equal(np.abs(y_weights_sign_flip), 1, 4)
# 2) Regression PLS (PLS2): "Non regression test"
# ===============================================
# The results were checked against the R-packages plspm, misOmics and pls
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]])
x_weights_sign_flip = 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]])
x_loadings_sign_flip = 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]])
y_weights_sign_flip = 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]])
y_loadings_sign_flip = pls_2.y_loadings_ / y_loadings
# x_loadings[:, i] = Xi.dot(x_weights[:, i]) \forall i
assert_array_almost_equal(x_loadings_sign_flip, x_weights_sign_flip, 4)
assert_array_almost_equal(np.abs(x_loadings_sign_flip), 1, 4)
assert_array_almost_equal(np.abs(x_weights_sign_flip), 1, 4)
assert_array_almost_equal(y_loadings_sign_flip, y_weights_sign_flip, 4)
assert_array_almost_equal(np.abs(y_loadings_sign_flip), 1, 4)
assert_array_almost_equal(np.abs(y_weights_sign_flip), 1, 4)
# 3) Another non-regression test of Canonical PLS on random dataset
# =================================================================
# The results were checked against the R-package plspm
n = 500
p_noise = 10
q_noise = 5
# 2 latents vars:
rng = check_random_state(11)
l1 = rng.normal(size=n)
l2 = rng.normal(size=n)
latents = np.array([l1, l1, l2, l2]).T
X = latents + rng.normal(size=4 * n).reshape((n, 4))
Y = latents + rng.normal(size=4 * n).reshape((n, 4))
X = np.concatenate((X, rng.normal(size=p_noise * n).reshape(n, p_noise)),
axis=1)
Y = np.concatenate((Y, rng.normal(size=q_noise * n).reshape(n, q_noise)),
axis=1)
pls_ca = pls_.PLSCanonical(n_components=3)
pls_ca.fit(X, Y)
x_weights = np.array([[0.65803719, 0.19197924, 0.21769083],
[0.7009113, 0.13303969, -0.15376699],
[0.13528197, -0.68636408, 0.13856546],
[0.16854574, -0.66788088, -0.12485304],
[-0.03232333, -0.04189855, 0.40690153],
[0.1148816, -0.09643158, 0.1613305],
[0.04792138, -0.02384992, 0.17175319],
[-0.06781, -0.01666137, -0.18556747],
[-0.00266945, -0.00160224, 0.11893098],
[-0.00849528, -0.07706095, 0.1570547],
[-0.00949471, -0.02964127, 0.34657036],
[-0.03572177, 0.0945091, 0.3414855],
[0.05584937, -0.02028961, -0.57682568],
[0.05744254, -0.01482333, -0.17431274]])
x_weights_sign_flip = pls_ca.x_weights_ / x_weights
x_loadings = np.array([[0.65649254, 0.1847647, 0.15270699],
[0.67554234, 0.15237508, -0.09182247],
[0.19219925, -0.67750975, 0.08673128],
[0.2133631, -0.67034809, -0.08835483],
[-0.03178912, -0.06668336, 0.43395268],
[0.15684588, -0.13350241, 0.20578984],
[0.03337736, -0.03807306, 0.09871553],
[-0.06199844, 0.01559854, -0.1881785],
[0.00406146, -0.00587025, 0.16413253],
[-0.00374239, -0.05848466, 0.19140336],
[0.00139214, -0.01033161, 0.32239136],
[-0.05292828, 0.0953533, 0.31916881],
[0.04031924, -0.01961045, -0.65174036],
[0.06172484, -0.06597366, -0.1244497]])
x_loadings_sign_flip = pls_ca.x_loadings_ / x_loadings
y_weights = np.array([[0.66101097, 0.18672553, 0.22826092],
[0.69347861, 0.18463471, -0.23995597],
[0.14462724, -0.66504085, 0.17082434],
[0.22247955, -0.6932605, -0.09832993],
[0.07035859, 0.00714283, 0.67810124],
[0.07765351, -0.0105204, -0.44108074],
[-0.00917056, 0.04322147, 0.10062478],
[-0.01909512, 0.06182718, 0.28830475],
[0.01756709, 0.04797666, 0.32225745]])
y_weights_sign_flip = pls_ca.y_weights_ / y_weights
y_loadings = np.array([[0.68568625, 0.1674376, 0.0969508],
[0.68782064, 0.20375837, -0.1164448],
[0.11712173, -0.68046903, 0.12001505],
[0.17860457, -0.6798319, -0.05089681],
[0.06265739, -0.0277703, 0.74729584],
[0.0914178, 0.00403751, -0.5135078],
[-0.02196918, -0.01377169, 0.09564505],
[-0.03288952, 0.09039729, 0.31858973],
[0.04287624, 0.05254676, 0.27836841]])
y_loadings_sign_flip = pls_ca.y_loadings_ / y_loadings
assert_array_almost_equal(x_loadings_sign_flip, x_weights_sign_flip, 4)
assert_array_almost_equal(np.abs(x_weights_sign_flip), 1, 4)
assert_array_almost_equal(np.abs(x_loadings_sign_flip), 1, 4)
assert_array_almost_equal(y_loadings_sign_flip, y_weights_sign_flip, 4)
assert_array_almost_equal(np.abs(y_weights_sign_flip), 1, 4)
assert_array_almost_equal(np.abs(y_loadings_sign_flip), 1, 4)
# Orthogonality of weights
# ~~~~~~~~~~~~~~~~~~~~~~~~
check_ortho(pls_ca.x_weights_, "x weights are not orthogonal")
check_ortho(pls_ca.y_weights_, "y weights are not orthogonal")
# Orthogonality of latent scores
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
check_ortho(pls_ca.x_scores_, "x scores are not orthogonal")
check_ortho(pls_ca.y_scores_, "y scores are not orthogonal")
# 4) Another "Non regression test" of PLS Regression (PLS2):
# Checking behavior when the first column of Y is constant
# ===============================================
# The results were compared against a modified version of plsreg2
# from the R-package plsdepot
X = d.data
Y = d.target
Y[:, 0] = 1
pls_2 = pls_.PLSRegression(n_components=X.shape[1])
pls_2.fit(X, Y)
x_weights = np.array([[-0.6273573, 0.007081799, 0.7786994],
[-0.7493417, -0.277612681, -0.6011807],
[-0.2119194, 0.960666981, -0.1794690]])
x_weights_sign_flip = pls_2.x_weights_ / x_weights
x_loadings = np.array([[-0.6273512, -0.22464538, 0.7786994],
[-0.6643156, -0.09871193, -0.6011807],
[-0.5125877, 1.01407380, -0.1794690]])
x_loadings_sign_flip = pls_2.x_loadings_ / x_loadings
y_loadings = np.array([[0.0000000, 0.0000000, 0.0000000],
[0.4357300, 0.5828479, 0.2174802],
[-0.1353739, -0.2486423, -0.1810386]])
# R/python sign flip should be the same in x_weight and x_rotation
assert_array_almost_equal(x_loadings_sign_flip, x_weights_sign_flip, 4)
# This test that R / python give the same result up to column
# sign indeterminacy
assert_array_almost_equal(np.abs(x_loadings_sign_flip), 1, 4)
assert_array_almost_equal(np.abs(x_weights_sign_flip), 1, 4)
# For the PLSRegression with default parameters, it holds that
# y_loadings==y_weights. In this case we only test that R/python
# give the same result for the y_loadings irrespective of the sign
assert_array_almost_equal(np.abs(pls_2.y_loadings_), np.abs(y_loadings), 4)