.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/cross_decomposition/plot_compare_cross_decomposition.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. or to run this example in your browser via Binder .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_cross_decomposition_plot_compare_cross_decomposition.py: =================================== 比较交叉分解方法 =================================== 各种交叉分解算法的简单用法： - PLSCanonical - PLS回归，具有多变量响应，又称PLS2 - PLS回归，具有单变量响应，又称PLS1 - CCA 给定两个多变量协变的二维数据集X和Y，PLS提取“协方差方向”，即解释两个数据集之间最大共享方差的各个成分。这在**散点矩阵图**显示中很明显：数据集X和数据集Y中的成分1是最大相关的（点位于第一对角线附近）。对于两个数据集中的成分2也是如此，然而，不同成分之间跨数据集的相关性较弱：点云非常球形。 .. GENERATED FROM PYTHON SOURCE LINES 18-20 基于数据集的潜在变量模型 ------------------------------------ .. GENERATED FROM PYTHON SOURCE LINES 20-42 .. 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. 0.49 -0.05 -0.04] [ 0.49 1. -0.01 -0.01] [-0.05 -0.01 1. 0.48] [-0.04 -0.01 0.48 1. ]] Corr(Y) [[ 1. 0.53 0.03 -0.02] [ 0.53 1. 0. -0.03] [ 0.03 0. 1. 0.5 ] [-0.02 -0.03 0.5 1. ]] .. GENERATED FROM PYTHON SOURCE LINES 43-48 规范（对称）PLS ----------------- 转换数据 ~~~~~~~~~~~~~~ .. GENERATED FROM PYTHON SOURCE LINES 48-56 .. 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 57-59 分数的散点图 ~~~~~~~~~~~~~~ .. GENERATED FROM PYTHON SOURCE LINES 59-119 .. code-block:: Python import matplotlib.pyplot as plt # 在对角线上绘制每个成分的X与Y得分 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") # 非对角线图组件 1 对 2 的 X 和 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 = 0.72), Comp. 2: X vs Y (test corr = 0.63), X comp. 1 vs X comp. 2 (test corr = 0.16), Y comp. 1 vs Y comp. 2 , (test corr = -0.01) :srcset: /auto_examples/cross_decomposition/images/sphx_glr_plot_compare_cross_decomposition_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 120-122 PLS 回归，多变量响应，又称 PLS2 ------------------------------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 122-143 .. 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 # 每个 Yj = 1*X1 + 2*X2 + 噪声 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) # 比较 pls2.coef_ 和 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. -0.1 -0. -0. -0. -0. -0.1 0. -0. ] [ 1. 1.9 -0. -0. 0. 0.1 -0. 0. -0. -0. ] [ 1. 1.9 -0. -0. -0. 0. -0. -0. -0. -0. ]] array([[4.46260781, 4.3792903 , 4.36836896], [5.22294138, 5.07398425, 5.06453542], [3.2416229 , 3.5337111 , 3.43197656], ..., [8.8168107 , 8.67329602, 8.61637485], [9.55912109, 9.37260612, 9.3419536 ], [6.80361268, 6.99998367, 6.88026638]]) .. GENERATED FROM PYTHON SOURCE LINES 144-146 PLS 回归，具有单变量响应，又称 PLS1 ----------------------------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 146-157 .. 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) # 请注意，组件的数量超过了1（y的维度） print("Estimated betas") print(np.round(pls1.coef_, 1)) .. rst-class:: sphx-glr-script-out .. code-block:: none Estimated betas [[ 0.9 2. -0. -0. -0. -0.1 0. -0. 0. -0. ]] .. GENERATED FROM PYTHON SOURCE LINES 158-160 CCA（对称消减的PLS模式B） ----------------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 160-168 .. 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 0.103 seconds) .. _sphx_glr_download_auto_examples_cross_decomposition_plot_compare_cross_decomposition.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: binder-badge .. image:: images/binder_badge_logo.svg :target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/main?urlpath=lab/tree/notebooks/auto_examples/cross_decomposition/plot_compare_cross_decomposition.ipynb :alt: Launch binder :width: 150 px .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_compare_cross_decomposition.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_compare_cross_decomposition.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_compare_cross_decomposition.zip ` .. include:: plot_compare_cross_decomposition.recommendations .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_