.. _sphx_glr_auto_examples_linear_model_plot_sgd_loss_functions.py: ========================== SGD: convex loss functions ========================== A plot that compares the various convex loss functions supported by :class:`sklearn.linear_model.SGDClassifier` . .. image:: /auto_examples/linear_model/images/sphx_glr_plot_sgd_loss_functions_001.png :align: center .. code-block:: python print(__doc__) import numpy as np import matplotlib.pyplot as plt def modified_huber_loss(y_true, y_pred): z = y_pred * y_true loss = -4 * z loss[z >= -1] = (1 - z[z >= -1]) ** 2 loss[z >= 1.] = 0 return loss xmin, xmax = -4, 4 xx = np.linspace(xmin, xmax, 100) lw = 2 plt.plot([xmin, 0, 0, xmax], [1, 1, 0, 0], color='gold', lw=lw, label="Zero-one loss") plt.plot(xx, np.where(xx < 1, 1 - xx, 0), color='teal', lw=lw, label="Hinge loss") plt.plot(xx, -np.minimum(xx, 0), color='yellowgreen', lw=lw, label="Perceptron loss") plt.plot(xx, np.log2(1 + np.exp(-xx)), color='cornflowerblue', lw=lw, label="Log loss") plt.plot(xx, np.where(xx < 1, 1 - xx, 0) ** 2, color='orange', lw=lw, label="Squared hinge loss") plt.plot(xx, modified_huber_loss(xx, 1), color='darkorchid', lw=lw, linestyle='--', label="Modified Huber loss") plt.ylim((0, 8)) plt.legend(loc="upper right") plt.xlabel(r"Decision function $f(x)$") plt.ylabel("$L(y, f(x))$") plt.show() **Total running time of the script:** (0 minutes 0.068 seconds) .. container:: sphx-glr-download **Download Python source code:** :download:`plot_sgd_loss_functions.py ` .. container:: sphx-glr-download **Download IPython notebook:** :download:`plot_sgd_loss_functions.ipynb `