.. _example_linear_model_plot_logistic_l1_l2_sparsity.py: ============================================== L1 Penalty and Sparsity in Logistic Regression ============================================== Comparison of the sparsity (percentage of zero coefficients) of solutions when L1 and L2 penalty are used for different values of C. We can see that large values of C give more freedom to the model. Conversely, smaller values of C constrain the model more. In the L1 penalty case, this leads to sparser solutions. We classify 8x8 images of digits into two classes: 0-4 against 5-9. The visualization shows coefficients of the models for varying C. .. image:: images/plot_logistic_l1_l2_sparsity_001.png :align: center **Script output**:: C=100.00 Sparsity with L1 penalty: 6.25% score with L1 penalty: 0.9115 Sparsity with L2 penalty: 4.69% score with L2 penalty: 0.9098 C=1.00 Sparsity with L1 penalty: 9.38% score with L1 penalty: 0.9098 Sparsity with L2 penalty: 4.69% score with L2 penalty: 0.9093 C=0.01 Sparsity with L1 penalty: 85.94% score with L1 penalty: 0.8620 Sparsity with L2 penalty: 4.69% score with L2 penalty: 0.8915 **Python source code:** :download:`plot_logistic_l1_l2_sparsity.py ` .. literalinclude:: plot_logistic_l1_l2_sparsity.py :lines: 15- **Total running time of the example:** 0.44 seconds ( 0 minutes 0.44 seconds)