File Content: plot_sgd_penalties.py """ ============== SGD: Penalties ============== Plot the contours of the three penalties. All of the above are supported by :class:`sklearn.linear_model.stochastic_gradient`. """ from __future__ import division print(__doc__) import numpy as np import matplotlib.pyplot as plt def l1(xs): return np.array([np.sqrt((1 - np.sqrt(x ** 2.0)) ** 2.0) for x in xs]) def l2(xs): return np.array([np.sqrt(1.0 - x ** 2.0) for x in xs]) def el(xs, z): return np.array([(2 - 2 * x - 2 * z + 4 * x * z - (4 * z ** 2 - 8 * x * z ** 2 + 8 * x ** 2 * z ** 2 - 16 * x ** 2 * z ** 3 + 8 * x * z ** 3 + 4 * x ** 2 * z ** 4) ** (1. / 2) - 2 * x * z ** 2) / (2 - 4 * z) for x in xs]) def cross(ext): plt.plot([-ext, ext], [0, 0], "k-") plt.plot([0, 0], [-ext, ext], "k-") xs = np.linspace(0, 1, 100) alpha = 0.501 # 0.5 division throuh zero cross(1.2) l1_color = "navy" l2_color = "c" elastic_net_color = "darkorange" lw = 2 plt.plot(xs, l1(xs), color=l1_color, label="L1", lw=lw) plt.plot(xs, -1.0 * l1(xs), color=l1_color, lw=lw) plt.plot(-1 * xs, l1(xs), color=l1_color, lw=lw) plt.plot(-1 * xs, -1.0 * l1(xs), color=l1_color, lw=lw) plt.plot(xs, l2(xs), color=l2_color, label="L2", lw=lw) plt.plot(xs, -1.0 * l2(xs), color=l2_color, lw=lw) plt.plot(-1 * xs, l2(xs), color=l2_color, lw=lw) plt.plot(-1 * xs, -1.0 * l2(xs), color=l2_color, lw=lw) plt.plot(xs, el(xs, alpha), color=elastic_net_color, label="Elastic Net", lw=lw) plt.plot(xs, -1.0 * el(xs, alpha), color=elastic_net_color, lw=lw) plt.plot(-1 * xs, el(xs, alpha), color=elastic_net_color, lw=lw) plt.plot(-1 * xs, -1.0 * el(xs, alpha), color=elastic_net_color, lw=lw) plt.xlabel(r"$w_0$") plt.ylabel(r"$w_1$") plt.legend() plt.axis("equal") plt.show() Submit