.. 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 ` 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: =========================================== Sparse coding with a precomputed dictionary =========================================== Transform a signal as a sparse combination of Ricker wavelets. This example visually compares different sparse coding methods using the :class:`~sklearn.decomposition.SparseCoder` estimator. The Ricker (also known as Mexican hat or the second derivative of a Gaussian) is not a particularly good kernel to represent piecewise constant signals like this one. It can therefore be seen how much adding different widths of atoms matters and it therefore motivates learning the dictionary to best fit your type of signals. The richer dictionary on the right is not larger in size, heavier subsampling is performed in order to stay on the same order of magnitude. .. GENERATED FROM PYTHON SOURCE LINES 18-124 .. 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 # Authors: The scikit-learn developers # SPDX-License-Identifier: BSD-3-Clause import matplotlib.pyplot as plt import numpy as np from sklearn.decomposition import SparseCoder def ricker_function(resolution, center, width): """Discrete sub-sampled Ricker (Mexican hat) wavelet""" 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): """Dictionary of Ricker (Mexican hat) wavelets""" 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 # Compute a wavelet dictionary 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) ) ] # Generate a signal 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 # List the different sparse coding methods in the following format: # (title, transform_algorithm, transform_alpha, # transform_n_nozero_coefs, color) 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") # Do a wavelet approximation 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), ) # Soft thresholding debiasing 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 0.273 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 ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_sparse_coding.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_sparse_coding.zip ` .. include:: plot_sparse_coding.recommendations .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_