.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/decomposition/plot_sparse_coding.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_examples_decomposition_plot_sparse_coding.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_decomposition_plot_sparse_coding.py:


===========================================
使用预先计算的字典进行稀疏编码
===========================================

将信号转换为Ricker小波的稀疏组合。此示例使用
:class:`~sklearn.decomposition.SparseCoder` 估计器直观地比较了不同的稀疏编码方法。Ricker（也称为墨西哥帽或高斯的二阶导数）并不是表示这种分段常数信号的特别好的核。因此，可以看到添加不同宽度的原子有多重要，因此激励学习字典以最好地适应您的信号类型。

右侧的更丰富字典在大小上并不大，通过更重的子采样来保持在同一数量级。

.. GENERATED FROM PYTHON SOURCE LINES 12-114



.. image-sg:: /auto_examples/decomposition/images/sphx_glr_plot_sparse_coding_001.png
   :alt: Sparse coding against fixed width dictionary, Sparse coding against multiple widths dictionary
   :srcset: /auto_examples/decomposition/images/sphx_glr_plot_sparse_coding_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from sklearn.decomposition import SparseCoder


    def ricker_function(resolution, center, width):
        """离散子采样Ricker（墨西哥帽）小波"""
        x = np.linspace(0, resolution - 1, resolution)
        x = (
            (2 / (np.sqrt(3 * width) * np.pi**0.25))
            * (1 - (x - center) ** 2 / width**2)
            * np.exp(-((x - center) ** 2) / (2 * width**2))
        )
        return x


    def ricker_matrix(width, resolution, n_components):
        """里克（墨西哥帽）小波字典"""
        centers = np.linspace(0, resolution - 1, n_components)
        D = np.empty((n_components, resolution))
        for i, center in enumerate(centers):
            D[i] = ricker_function(resolution, center, width)
        D /= np.sqrt(np.sum(D**2, axis=1))[:, np.newaxis]
        return D


    resolution = 1024
    subsampling = 3  # subsampling factor
    width = 100
    n_components = resolution // subsampling

    # 计算小波字典
    D_fixed = ricker_matrix(width=width, resolution=resolution, n_components=n_components)
    D_multi = np.r_[
        tuple(
            ricker_matrix(width=w, resolution=resolution, n_components=n_components // 5)
            for w in (10, 50, 100, 500, 1000)
        )
    ]

    # 生成信号
    y = np.linspace(0, resolution - 1, resolution)
    first_quarter = y < resolution / 4
    y[first_quarter] = 3.0
    y[np.logical_not(first_quarter)] = -1.0

    # 列出以下格式的不同稀疏编码方法：
    # (标题, 变换算法, 变换alpha值, 变换非零系数数量, 颜色)
    estimators = [
        ("OMP", "omp", None, 15, "navy"),
        ("Lasso", "lasso_lars", 2, None, "turquoise"),
    ]
    lw = 2

    plt.figure(figsize=(13, 6))
    for subplot, (D, title) in enumerate(
        zip((D_fixed, D_multi), ("fixed width", "multiple widths"))
    ):
        plt.subplot(1, 2, subplot + 1)
        plt.title("Sparse coding against %s dictionary" % title)
        plt.plot(y, lw=lw, linestyle="--", label="Original signal")
        # 做一个小波近似
        for title, algo, alpha, n_nonzero, color in estimators:
            coder = SparseCoder(
                dictionary=D,
                transform_n_nonzero_coefs=n_nonzero,
                transform_alpha=alpha,
                transform_algorithm=algo,
            )
            x = coder.transform(y.reshape(1, -1))
            density = len(np.flatnonzero(x))
            x = np.ravel(np.dot(x, D))
            squared_error = np.sum((y - x) ** 2)
            plt.plot(
                x,
                color=color,
                lw=lw,
                label="%s: %s nonzero coefs,\n%.2f error" % (title, density, squared_error),
            )

        # 软阈值去偏
        coder = SparseCoder(
            dictionary=D, transform_algorithm="threshold", transform_alpha=20
        )
        x = coder.transform(y.reshape(1, -1))
        _, idx = np.where(x != 0)
        x[0, idx], _, _, _ = np.linalg.lstsq(D[idx, :].T, y, rcond=None)
        x = np.ravel(np.dot(x, D))
        squared_error = np.sum((y - x) ** 2)
        plt.plot(
            x,
            color="darkorange",
            lw=lw,
            label="Thresholding w/ debiasing:\n%d nonzero coefs, %.2f error"
            % (len(idx), squared_error),
        )
        plt.axis("tight")
        plt.legend(shadow=False, loc="best")
    plt.subplots_adjust(0.04, 0.07, 0.97, 0.90, 0.09, 0.2)
    plt.show()


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

   **Total running time of the script:** (0 minutes 0.128 seconds)


.. _sphx_glr_download_auto_examples_decomposition_plot_sparse_coding.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_sparse_coding.ipynb
        :alt: Launch binder
        :width: 150 px

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

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

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

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

    .. container:: sphx-glr-download sphx-glr-download-zip

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


.. include:: plot_sparse_coding.recommendations


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_