.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/decomposition/plot_faces_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_decomposition_plot_faces_decomposition.py: ============================ 人脸数据集分解 ============================ 本示例将 :ref:`olivetti_faces_dataset` 应用于来自模块 :mod:`sklearn.decomposition` 的不同无监督矩阵分解（降维）方法（参见文档章节 :ref:`decompositions` ）。 - 作者: Vlad Niculae, Alexandre Gramfort - 许可证: BSD 3 条款 .. GENERATED FROM PYTHON SOURCE LINES 13-17 数据集准备 ------------------- 加载和预处理 Olivetti 人脸数据集。 .. GENERATED FROM PYTHON SOURCE LINES 17-42 .. code-block:: Python import logging import matplotlib.pyplot as plt from numpy.random import RandomState from sklearn import cluster, decomposition from sklearn.datasets import fetch_olivetti_faces rng = RandomState(0) # 在标准输出上显示进度日志 logging.basicConfig(level=logging.INFO, format="%(asctime)s %(levelname)s %(message)s") faces, _ = fetch_olivetti_faces(return_X_y=True, shuffle=True, random_state=rng) n_samples, n_features = faces.shape # 全局中心化（聚焦于一个特征，对所有样本进行中心化） faces_centered = faces - faces.mean(axis=0) # 局部中心化（聚焦于一个样本，对所有特征进行中心化） faces_centered -= faces_centered.mean(axis=1).reshape(n_samples, -1) print("Dataset consists of %d faces" % n_samples) .. rst-class:: sphx-glr-script-out .. code-block:: none Dataset consists of 400 faces .. GENERATED FROM PYTHON SOURCE LINES 43-44 定义一个基础函数来绘制人脸画廊。 .. GENERATED FROM PYTHON SOURCE LINES 44-77 .. code-block:: Python n_row, n_col = 2, 3 n_components = n_row * n_col image_shape = (64, 64) def plot_gallery(title, images, n_col=n_col, n_row=n_row, cmap=plt.cm.gray): fig, axs = plt.subplots( nrows=n_row, ncols=n_col, figsize=(2.0 * n_col, 2.3 * n_row), facecolor="white", constrained_layout=True, ) fig.set_constrained_layout_pads(w_pad=0.01, h_pad=0.02, hspace=0, wspace=0) fig.set_edgecolor("black") fig.suptitle(title, size=16) for ax, vec in zip(axs.flat, images): vmax = max(vec.max(), -vec.min()) im = ax.imshow( vec.reshape(image_shape), cmap=cmap, interpolation="nearest", vmin=-vmax, vmax=vmax, ) ax.axis("off") fig.colorbar(im, ax=axs, orientation="horizontal", shrink=0.99, aspect=40, pad=0.01) plt.show() .. GENERATED FROM PYTHON SOURCE LINES 78-79 让我们来看一下我们的数据。灰色表示负值，白色表示正值。 .. GENERATED FROM PYTHON SOURCE LINES 79-83 .. code-block:: Python plot_gallery("Faces from dataset", faces_centered[:n_components]) .. image-sg:: /auto_examples/decomposition/images/sphx_glr_plot_faces_decomposition_001.png :alt: Faces from dataset :srcset: /auto_examples/decomposition/images/sphx_glr_plot_faces_decomposition_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 84-90 分解 ------------- 初始化不同的分解估计器，并将它们拟合到所有图像上，然后绘制一些结果。每个估计器提取6个分量作为向量 :math:`h \in \mathbb{R}^{4096}` 。我们只是将这些向量以64x64像素图像的形式进行人性化的可视化展示。 请参阅 :ref:`用户指南 ` 了解更多信息。 .. GENERATED FROM PYTHON SOURCE LINES 92-100 Eigenfaces - 使用随机SVD的PCA ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 使用数据的奇异值分解（SVD）进行线性降维，将其投影到低维空间。 .. note:: 通过 :py:mod:`sklearn.decomposition.PCA` 的 Eigenfaces 估计器还提供了一个标量 `noise_variance_` （像素方差的均值），该标量无法显示为图像。 .. GENERATED FROM PYTHON SOURCE LINES 102-110 .. code-block:: Python pca_estimator = decomposition.PCA( n_components=n_components, svd_solver="randomized", whiten=True ) pca_estimator.fit(faces_centered) plot_gallery( "Eigenfaces - PCA using randomized SVD", pca_estimator.components_[:n_components] ) .. image-sg:: /auto_examples/decomposition/images/sphx_glr_plot_faces_decomposition_002.png :alt: Eigenfaces - PCA using randomized SVD :srcset: /auto_examples/decomposition/images/sphx_glr_plot_faces_decomposition_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 111-115 非负分解组件 - NMF ^^^^^^^^^^^^^^^^^^^ 估计非负原始数据为两个非负矩阵的乘积。 .. GENERATED FROM PYTHON SOURCE LINES 117-121 .. code-block:: Python nmf_estimator = decomposition.NMF(n_components=n_components, tol=5e-3) nmf_estimator.fit(faces) # original non- negative dataset plot_gallery("Non-negative components - NMF", nmf_estimator.components_[:n_components]) .. image-sg:: /auto_examples/decomposition/images/sphx_glr_plot_faces_decomposition_003.png :alt: Non-negative components - NMF :srcset: /auto_examples/decomposition/images/sphx_glr_plot_faces_decomposition_003.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 122-125 独立成分 - FastICA ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 独立成分分析将多变量向量分解为相加的子成分，这些子成分是最大程度独立的。 .. GENERATED FROM PYTHON SOURCE LINES 127-135 .. code-block:: Python ica_estimator = decomposition.FastICA( n_components=n_components, max_iter=400, whiten="arbitrary-variance", tol=15e-5 ) ica_estimator.fit(faces_centered) plot_gallery( "Independent components - FastICA", ica_estimator.components_[:n_components] ) .. image-sg:: /auto_examples/decomposition/images/sphx_glr_plot_faces_decomposition_004.png :alt: Independent components - FastICA :srcset: /auto_examples/decomposition/images/sphx_glr_plot_faces_decomposition_004.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 136-140 稀疏成分 - MiniBatchSparsePCA ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 小批量稀疏PCA（:class:`~sklearn.decomposition.MiniBatchSparsePCA` ）提取最能重构数据的稀疏成分集。这个变体比类似的 :class:`~sklearn.decomposition.SparsePCA` 更快，但准确性较低。 .. GENERATED FROM PYTHON SOURCE LINES 142-151 .. code-block:: Python batch_pca_estimator = decomposition.MiniBatchSparsePCA( n_components=n_components, alpha=0.1, max_iter=100, batch_size=3, random_state=rng ) batch_pca_estimator.fit(faces_centered) plot_gallery( "Sparse components - MiniBatchSparsePCA", batch_pca_estimator.components_[:n_components], ) .. image-sg:: /auto_examples/decomposition/images/sphx_glr_plot_faces_decomposition_005.png :alt: Sparse components - MiniBatchSparsePCA :srcset: /auto_examples/decomposition/images/sphx_glr_plot_faces_decomposition_005.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 152-156 字典学习 ^^^^^^^^^^ 默认情况下，:class:`~sklearn.decomposition.MiniBatchDictionaryLearning` 将数据分成小批量，并通过对小批量进行循环以指定的迭代次数在线优化。 .. GENERATED FROM PYTHON SOURCE LINES 158-164 .. code-block:: Python batch_dict_estimator = decomposition.MiniBatchDictionaryLearning( n_components=n_components, alpha=0.1, max_iter=50, batch_size=3, random_state=rng ) batch_dict_estimator.fit(faces_centered) plot_gallery("Dictionary learning", batch_dict_estimator.components_[:n_components]) .. image-sg:: /auto_examples/decomposition/images/sphx_glr_plot_faces_decomposition_006.png :alt: Dictionary learning :srcset: /auto_examples/decomposition/images/sphx_glr_plot_faces_decomposition_006.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 165-169 聚类中心 - MiniBatchKMeans ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ :class:`sklearn.cluster.MiniBatchKMeans` 计算效率高，并通过 :meth:`~sklearn.cluster.MiniBatchKMeans.partial_fit` 方法实现在线学习。因此，将一些耗时的算法与 :class:`~sklearn.cluster.MiniBatchKMeans` 结合起来可能会有益处。 .. GENERATED FROM PYTHON SOURCE LINES 171-185 .. code-block:: Python kmeans_estimator = cluster.MiniBatchKMeans( n_clusters=n_components, tol=1e-3, batch_size=20, max_iter=50, random_state=rng, ) kmeans_estimator.fit(faces_centered) plot_gallery( "Cluster centers - MiniBatchKMeans", kmeans_estimator.cluster_centers_[:n_components], ) .. image-sg:: /auto_examples/decomposition/images/sphx_glr_plot_faces_decomposition_007.png :alt: Cluster centers - MiniBatchKMeans :srcset: /auto_examples/decomposition/images/sphx_glr_plot_faces_decomposition_007.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 186-190 因子分析成分 - FA ^^^^^^^^^^^^^^^^^^^ :class:`~sklearn.decomposition.FactorAnalysis` 类似于 :class:`~sklearn.decomposition.PCA` ，但具有独立建模输入空间每个方向方差（异方差噪声）的优势。更多内容请参阅 :ref:`用户指南 ` 。 .. GENERATED FROM PYTHON SOURCE LINES 192-212 .. code-block:: Python fa_estimator = decomposition.FactorAnalysis(n_components=n_components, max_iter=20) fa_estimator.fit(faces_centered) plot_gallery("Factor Analysis (FA)", fa_estimator.components_[:n_components]) # --- 像素级方差 plt.figure(figsize=(3.2, 3.6), facecolor="white", tight_layout=True) vec = fa_estimator.noise_variance_ vmax = max(vec.max(), -vec.min()) plt.imshow( vec.reshape(image_shape), cmap=plt.cm.gray, interpolation="nearest", vmin=-vmax, vmax=vmax, ) plt.axis("off") plt.title("Pixelwise variance from \n Factor Analysis (FA)", size=16, wrap=True) plt.colorbar(orientation="horizontal", shrink=0.8, pad=0.03) plt.show() .. rst-class:: sphx-glr-horizontal * .. image-sg:: /auto_examples/decomposition/images/sphx_glr_plot_faces_decomposition_008.png :alt: Factor Analysis (FA) :srcset: /auto_examples/decomposition/images/sphx_glr_plot_faces_decomposition_008.png :class: sphx-glr-multi-img * .. image-sg:: /auto_examples/decomposition/images/sphx_glr_plot_faces_decomposition_009.png :alt: Pixelwise variance from Factor Analysis (FA) :srcset: /auto_examples/decomposition/images/sphx_glr_plot_faces_decomposition_009.png :class: sphx-glr-multi-img .. GENERATED FROM PYTHON SOURCE LINES 213-220 分解：字典学习 ------------------ 在接下来的部分中，让我们更详细地考虑 :ref:`DictionaryLearning` 。 字典学习是一个问题，其目的是找到输入数据的稀疏表示，作为简单元素的组合。这些简单元素构成了一个字典。可以约束字典和/或编码系数为正，以匹配数据中可能存在的约束。 :class:`~sklearn.decomposition.MiniBatchDictionaryLearning` 实现了一种更快但精度较低的字典学习算法版本，更适合处理大型数据集。请在 :ref:`用户指南 ` 中阅读更多内容。 .. GENERATED FROM PYTHON SOURCE LINES 222-224 绘制数据集中相同的样本，但使用另一种颜色映射。 红色表示负值，蓝色表示正值，白色表示零。 .. GENERATED FROM PYTHON SOURCE LINES 224-227 .. code-block:: Python plot_gallery("Faces from dataset", faces_centered[:n_components], cmap=plt.cm.RdBu) .. image-sg:: /auto_examples/decomposition/images/sphx_glr_plot_faces_decomposition_010.png :alt: Faces from dataset :srcset: /auto_examples/decomposition/images/sphx_glr_plot_faces_decomposition_010.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 228-231 类似于之前的示例，我们更改参数并在所有图像上训练 :class:`~sklearn.decomposition.MiniBatchDictionaryLearning` 估计器。通常，字典学习和稀疏编码将输入数据分解为字典和编码系数矩阵。:math:`X \approx UV` ，其中 :math:`X = [x_1, . . . , x_n]` ，:math:`X \in \mathbb{R}^{m×n}` ，字典 :math:`U \in \mathbb{R}^{m×k}` ，编码系数 :math:`V \in \mathbb{R}^{k×n}` 。 此外，以下是字典和编码系数受到正约束时的结果。 .. GENERATED FROM PYTHON SOURCE LINES 233-237 字典学习 - 正字典 ^^^^^^^^^^^^^^^^^ 在以下部分中，我们在寻找字典时强制执行正值。 .. GENERATED FROM PYTHON SOURCE LINES 239-254 .. code-block:: Python dict_pos_dict_estimator = decomposition.MiniBatchDictionaryLearning( n_components=n_components, alpha=0.1, max_iter=50, batch_size=3, random_state=rng, positive_dict=True, ) dict_pos_dict_estimator.fit(faces_centered) plot_gallery( "Dictionary learning - positive dictionary", dict_pos_dict_estimator.components_[:n_components], cmap=plt.cm.RdBu, ) .. image-sg:: /auto_examples/decomposition/images/sphx_glr_plot_faces_decomposition_011.png :alt: Dictionary learning - positive dictionary :srcset: /auto_examples/decomposition/images/sphx_glr_plot_faces_decomposition_011.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 255-258 字典学习 - 正码 下面我们将编码系数限制为一个正矩阵。 .. GENERATED FROM PYTHON SOURCE LINES 260-276 .. code-block:: Python dict_pos_code_estimator = decomposition.MiniBatchDictionaryLearning( n_components=n_components, alpha=0.1, max_iter=50, batch_size=3, fit_algorithm="cd", random_state=rng, positive_code=True, ) dict_pos_code_estimator.fit(faces_centered) plot_gallery( "Dictionary learning - positive code", dict_pos_code_estimator.components_[:n_components], cmap=plt.cm.RdBu, ) .. image-sg:: /auto_examples/decomposition/images/sphx_glr_plot_faces_decomposition_012.png :alt: Dictionary learning - positive code :srcset: /auto_examples/decomposition/images/sphx_glr_plot_faces_decomposition_012.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 277-280 字典学习 - 正字典和编码 另外，如果字典值和编码系数受到正约束，结果如下。 .. GENERATED FROM PYTHON SOURCE LINES 282-298 .. code-block:: Python dict_pos_estimator = decomposition.MiniBatchDictionaryLearning( n_components=n_components, alpha=0.1, max_iter=50, batch_size=3, fit_algorithm="cd", random_state=rng, positive_dict=True, positive_code=True, ) dict_pos_estimator.fit(faces_centered) plot_gallery( "Dictionary learning - positive dictionary & code", dict_pos_estimator.components_[:n_components], cmap=plt.cm.RdBu, ) .. image-sg:: /auto_examples/decomposition/images/sphx_glr_plot_faces_decomposition_013.png :alt: Dictionary learning - positive dictionary & code :srcset: /auto_examples/decomposition/images/sphx_glr_plot_faces_decomposition_013.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 6.169 seconds) .. _sphx_glr_download_auto_examples_decomposition_plot_faces_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/decomposition/plot_faces_decomposition.ipynb :alt: Launch binder :width: 150 px .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_faces_decomposition.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_faces_decomposition.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_faces_decomposition.zip ` .. include:: plot_faces_decomposition.recommendations .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_