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.. "auto_examples/neighbors/plot_nca_dim_reduction.py"
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.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_neighbors_plot_nca_dim_reduction.py>`
        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_neighbors_plot_nca_dim_reduction.py:


==============================================================
使用邻域成分分析进行降维
==============================================================

使用邻域成分分析进行降维的示例。

本示例比较了不同的（线性）降维方法在数字数据集上的应用。该数据集包含从0到9的数字图像，每个类别大约有180个样本。每张图像的维度为8x8 = 64，并被降维到二维数据点。

主成分分析（PCA）应用于此数据集，识别出在数据中占最大方差的属性组合（主成分，或特征空间中的方向）。在这里，我们将不同的样本绘制在前两个主成分上。

线性判别分析（LDA）试图识别在*类别之间*占最大方差的属性。特别地，LDA与PCA不同，是一种有监督的方法，使用已知的类别标签。

邻域成分分析（NCA）试图找到一个特征空间，使得随机最近邻算法能够提供最佳的准确性。与LDA一样，它也是一种有监督的方法。

可以看到，尽管维度大幅度降低，NCA仍然强制数据进行视觉上有意义的聚类。

.. GENERATED FROM PYTHON SOURCE LINES 19-88



.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /auto_examples/neighbors/images/sphx_glr_plot_nca_dim_reduction_001.png
         :alt: PCA, KNN (k=3) Test accuracy = 0.52
         :srcset: /auto_examples/neighbors/images/sphx_glr_plot_nca_dim_reduction_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/neighbors/images/sphx_glr_plot_nca_dim_reduction_002.png
         :alt: LDA, KNN (k=3) Test accuracy = 0.66
         :srcset: /auto_examples/neighbors/images/sphx_glr_plot_nca_dim_reduction_002.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/neighbors/images/sphx_glr_plot_nca_dim_reduction_003.png
         :alt: NCA, KNN (k=3) Test accuracy = 0.70
         :srcset: /auto_examples/neighbors/images/sphx_glr_plot_nca_dim_reduction_003.png
         :class: sphx-glr-multi-img





.. code-block:: Python


    # SPDX-License-Identifier: BSD-3-Clause

    import matplotlib.pyplot as plt
    import numpy as np

    from sklearn import datasets
    from sklearn.decomposition import PCA
    from sklearn.discriminant_analysis import LinearDiscriminantAnalysis
    from sklearn.model_selection import train_test_split
    from sklearn.neighbors import KNeighborsClassifier, NeighborhoodComponentsAnalysis
    from sklearn.pipeline import make_pipeline
    from sklearn.preprocessing import StandardScaler

    n_neighbors = 3
    random_state = 0

    # 加载数字数据集
    X, y = datasets.load_digits(return_X_y=True)

    # 划分为训练集/测试集
    X_train, X_test, y_train, y_test = train_test_split(
        X, y, test_size=0.5, stratify=y, random_state=random_state
    )

    dim = len(X[0])
    n_classes = len(np.unique(y))

    # 使用PCA将维度减少到2
    pca = make_pipeline(StandardScaler(), PCA(n_components=2, random_state=random_state))

    # 使用线性判别分析将维度减少到2
    lda = make_pipeline(StandardScaler(), LinearDiscriminantAnalysis(n_components=2))

    # 使用邻域成分分析将维度减少到2
    nca = make_pipeline(
        StandardScaler(),
        NeighborhoodComponentsAnalysis(n_components=2, random_state=random_state),
    )

    # 使用最近邻分类器来评估这些方法
    knn = KNeighborsClassifier(n_neighbors=n_neighbors)

    # 列出要比较的方法
    dim_reduction_methods = [("PCA", pca), ("LDA", lda), ("NCA", nca)]

    # plt.figure()
    for i, (name, model) in enumerate(dim_reduction_methods):
        plt.figure()
        # plt.subplot(1, 3, i + 1, aspect=1)

        # 拟合该方法的模型
        model.fit(X_train, y_train)

        # 在嵌入的训练集上拟合一个最近邻分类器
        knn.fit(model.transform(X_train), y_train)

        # 计算嵌入测试集上的最近邻准确率
        acc_knn = knn.score(model.transform(X_test), y_test)

        # 使用拟合模型将数据集嵌入到二维空间中
        X_embedded = model.transform(X)

        # 绘制投影点并显示评估分数
        plt.scatter(X_embedded[:, 0], X_embedded[:, 1], c=y, s=30, cmap="Set1")
        plt.title(
            "{}, KNN (k={})\nTest accuracy = {:.2f}".format(name, n_neighbors, acc_knn)
        )
    plt.show()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.967 seconds)


.. _sphx_glr_download_auto_examples_neighbors_plot_nca_dim_reduction.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/neighbors/plot_nca_dim_reduction.ipynb
        :alt: Launch binder
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_nca_dim_reduction.ipynb <plot_nca_dim_reduction.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_nca_dim_reduction.py <plot_nca_dim_reduction.py>`

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      :download:`Download zipped: plot_nca_dim_reduction.zip <plot_nca_dim_reduction.zip>`


.. include:: plot_nca_dim_reduction.recommendations


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