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.. "auto_examples/cross_decomposition/plot_compare_cross_decomposition.py"
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.. only:: html
.. note::
:class: sphx-glr-download-link-note
:ref:`Go to the end <sphx_glr_download_auto_examples_cross_decomposition_plot_compare_cross_decomposition.py>`
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.. rst-class:: sphx-glr-example-title
.. _sphx_glr_auto_examples_cross_decomposition_plot_compare_cross_decomposition.py:
===================================
Compare cross decomposition methods
===================================
Simple usage of various cross decomposition algorithms:
- PLSCanonical
- PLSRegression, with multivariate response, a.k.a. PLS2
- PLSRegression, with univariate response, a.k.a. PLS1
- CCA
Given 2 multivariate covarying two-dimensional datasets, X, and Y,
PLS extracts the 'directions of covariance', i.e. the components of each
datasets that explain the most shared variance between both datasets.
This is apparent on the **scatterplot matrix** display: components 1 in
dataset X and dataset Y are maximally correlated (points lie around the
first diagonal). This is also true for components 2 in both dataset,
however, the correlation across datasets for different components is
weak: the point cloud is very spherical.
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Dataset based latent variables model
------------------------------------
.. GENERATED FROM PYTHON SOURCE LINES 27-49
.. code-block:: Python
import numpy as np
n = 500
# 2 latents vars:
l1 = np.random.normal(size=n)
l2 = np.random.normal(size=n)
latents = np.array([l1, l1, l2, l2]).T
X = latents + np.random.normal(size=4 * n).reshape((n, 4))
Y = latents + np.random.normal(size=4 * n).reshape((n, 4))
X_train = X[: n // 2]
Y_train = Y[: n // 2]
X_test = X[n // 2 :]
Y_test = Y[n // 2 :]
print("Corr(X)")
print(np.round(np.corrcoef(X.T), 2))
print("Corr(Y)")
print(np.round(np.corrcoef(Y.T), 2))
.. rst-class:: sphx-glr-script-out
.. code-block:: none
Corr(X)
[[ 1. 0.45 0.02 0.06]
[ 0.45 1. -0.1 -0.01]
[ 0.02 -0.1 1. 0.47]
[ 0.06 -0.01 0.47 1. ]]
Corr(Y)
[[ 1. 0.5 -0.06 -0.04]
[ 0.5 1. 0. -0.07]
[-0.06 0. 1. 0.51]
[-0.04 -0.07 0.51 1. ]]
.. GENERATED FROM PYTHON SOURCE LINES 50-55
Canonical (symmetric) PLS
-------------------------
Transform data
~~~~~~~~~~~~~~
.. GENERATED FROM PYTHON SOURCE LINES 55-63
.. code-block:: Python
from sklearn.cross_decomposition import PLSCanonical
plsca = PLSCanonical(n_components=2)
plsca.fit(X_train, Y_train)
X_train_r, Y_train_r = plsca.transform(X_train, Y_train)
X_test_r, Y_test_r = plsca.transform(X_test, Y_test)
.. GENERATED FROM PYTHON SOURCE LINES 64-66
Scatter plot of scores
~~~~~~~~~~~~~~~~~~~~~~
.. GENERATED FROM PYTHON SOURCE LINES 66-125
.. code-block:: Python
import matplotlib.pyplot as plt
# On diagonal plot X vs Y scores on each components
plt.figure(figsize=(12, 8))
plt.subplot(221)
plt.scatter(X_train_r[:, 0], Y_train_r[:, 0], label="train", marker="o", s=25)
plt.scatter(X_test_r[:, 0], Y_test_r[:, 0], label="test", marker="o", s=25)
plt.xlabel("x scores")
plt.ylabel("y scores")
plt.title(
"Comp. 1: X vs Y (test corr = %.2f)"
% np.corrcoef(X_test_r[:, 0], Y_test_r[:, 0])[0, 1]
)
plt.xticks(())
plt.yticks(())
plt.legend(loc="best")
plt.subplot(224)
plt.scatter(X_train_r[:, 1], Y_train_r[:, 1], label="train", marker="o", s=25)
plt.scatter(X_test_r[:, 1], Y_test_r[:, 1], label="test", marker="o", s=25)
plt.xlabel("x scores")
plt.ylabel("y scores")
plt.title(
"Comp. 2: X vs Y (test corr = %.2f)"
% np.corrcoef(X_test_r[:, 1], Y_test_r[:, 1])[0, 1]
)
plt.xticks(())
plt.yticks(())
plt.legend(loc="best")
# Off diagonal plot components 1 vs 2 for X and Y
plt.subplot(222)
plt.scatter(X_train_r[:, 0], X_train_r[:, 1], label="train", marker="*", s=50)
plt.scatter(X_test_r[:, 0], X_test_r[:, 1], label="test", marker="*", s=50)
plt.xlabel("X comp. 1")
plt.ylabel("X comp. 2")
plt.title(
"X comp. 1 vs X comp. 2 (test corr = %.2f)"
% np.corrcoef(X_test_r[:, 0], X_test_r[:, 1])[0, 1]
)
plt.legend(loc="best")
plt.xticks(())
plt.yticks(())
plt.subplot(223)
plt.scatter(Y_train_r[:, 0], Y_train_r[:, 1], label="train", marker="*", s=50)
plt.scatter(Y_test_r[:, 0], Y_test_r[:, 1], label="test", marker="*", s=50)
plt.xlabel("Y comp. 1")
plt.ylabel("Y comp. 2")
plt.title(
"Y comp. 1 vs Y comp. 2 , (test corr = %.2f)"
% np.corrcoef(Y_test_r[:, 0], Y_test_r[:, 1])[0, 1]
)
plt.legend(loc="best")
plt.xticks(())
plt.yticks(())
plt.show()
.. image-sg:: /auto_examples/cross_decomposition/images/sphx_glr_plot_compare_cross_decomposition_001.png
:alt: Comp. 1: X vs Y (test corr = 0.65), Comp. 2: X vs Y (test corr = 0.68), X comp. 1 vs X comp. 2 (test corr = -0.06), Y comp. 1 vs Y comp. 2 , (test corr = -0.06)
:srcset: /auto_examples/cross_decomposition/images/sphx_glr_plot_compare_cross_decomposition_001.png
:class: sphx-glr-single-img
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PLS regression, with multivariate response, a.k.a. PLS2
-------------------------------------------------------
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.. code-block:: Python
from sklearn.cross_decomposition import PLSRegression
n = 1000
q = 3
p = 10
X = np.random.normal(size=n * p).reshape((n, p))
B = np.array([[1, 2] + [0] * (p - 2)] * q).T
# each Yj = 1*X1 + 2*X2 + noize
Y = np.dot(X, B) + np.random.normal(size=n * q).reshape((n, q)) + 5
pls2 = PLSRegression(n_components=3)
pls2.fit(X, Y)
print("True B (such that: Y = XB + Err)")
print(B)
# compare pls2.coef_ with B
print("Estimated B")
print(np.round(pls2.coef_, 1))
pls2.predict(X)
.. rst-class:: sphx-glr-script-out
.. code-block:: none
True B (such that: Y = XB + Err)
[[1 1 1]
[2 2 2]
[0 0 0]
[0 0 0]
[0 0 0]
[0 0 0]
[0 0 0]
[0 0 0]
[0 0 0]
[0 0 0]]
Estimated B
[[ 1. 2. 0. 0. 0. -0. 0. 0. 0.1 -0. ]
[ 1.1 2. -0. 0. 0. 0. 0. 0. 0. 0. ]
[ 1. 2. 0. 0. 0. 0. 0. 0. 0. -0. ]]
array([[4.95213778, 5.10988205, 5.08029173],
[3.80414253, 3.81422502, 3.83199463],
[3.92896897, 3.76438188, 3.8798454 ],
...,
[5.47804127, 5.59007842, 5.58442585],
[4.73908648, 4.87282488, 4.85481267],
[1.16714557, 0.99951652, 1.09671339]])
.. GENERATED FROM PYTHON SOURCE LINES 149-151
PLS regression, with univariate response, a.k.a. PLS1
-----------------------------------------------------
.. GENERATED FROM PYTHON SOURCE LINES 151-162
.. code-block:: Python
n = 1000
p = 10
X = np.random.normal(size=n * p).reshape((n, p))
y = X[:, 0] + 2 * X[:, 1] + np.random.normal(size=n * 1) + 5
pls1 = PLSRegression(n_components=3)
pls1.fit(X, y)
# note that the number of components exceeds 1 (the dimension of y)
print("Estimated betas")
print(np.round(pls1.coef_, 1))
.. rst-class:: sphx-glr-script-out
.. code-block:: none
Estimated betas
[[ 1. 2. 0.1 -0. -0. -0. -0. 0. -0. 0. ]]
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CCA (PLS mode B with symmetric deflation)
-----------------------------------------
.. GENERATED FROM PYTHON SOURCE LINES 165-172
.. code-block:: Python
from sklearn.cross_decomposition import CCA
cca = CCA(n_components=2)
cca.fit(X_train, Y_train)
X_train_r, Y_train_r = cca.transform(X_train, Y_train)
X_test_r, Y_test_r = cca.transform(X_test, Y_test)
.. rst-class:: sphx-glr-timing
**Total running time of the script:** (0 minutes 0.220 seconds)
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.. rst-class:: sphx-glr-signature
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