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<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_birch_vs_minibatchkmeans.html">Compare BIRCH and MiniBatchKMeans</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_cluster_comparison.html">Comparing different clustering algorithms on toy datasets</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_linkage_comparison.html">Comparing different hierarchical linkage methods on toy datasets</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_mini_batch_kmeans.html">Comparison of the K-Means and MiniBatchKMeans clustering algorithms</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_dbscan.html">Demo of DBSCAN clustering algorithm</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_hdbscan.html">Demo of HDBSCAN clustering algorithm</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_optics.html">Demo of OPTICS clustering algorithm</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_affinity_propagation.html">Demo of affinity propagation clustering algorithm</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_kmeans_assumptions.html">Demonstration of k-means assumptions</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_kmeans_stability_low_dim_dense.html">Empirical evaluation of the impact of k-means initialization</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_digits_agglomeration.html">Feature agglomeration</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_feature_agglomeration_vs_univariate_selection.html">Feature agglomeration vs. univariate selection</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_ward_structured_vs_unstructured.html">Hierarchical clustering: structured vs unstructured ward</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_inductive_clustering.html">Inductive Clustering</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_dict_face_patches.html">Online learning of a dictionary of parts of faces</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_agglomerative_dendrogram.html">Plot Hierarchical Clustering Dendrogram</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_coin_segmentation.html">Segmenting the picture of greek coins in regions</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_kmeans_silhouette_analysis.html">Selecting the number of clusters with silhouette analysis on KMeans clustering</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_segmentation_toy.html">Spectral clustering for image segmentation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_digits_linkage.html">Various Agglomerative Clustering on a 2D embedding of digits</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_face_compress.html">Vector Quantization Example</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../covariance/index.html">Covariance estimation</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../covariance/plot_lw_vs_oas.html">Ledoit-Wolf vs OAS estimation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../covariance/plot_mahalanobis_distances.html">Robust covariance estimation and Mahalanobis distances relevance</a></li>
<li class="toctree-l2"><a class="reference internal" href="../covariance/plot_robust_vs_empirical_covariance.html">Robust vs Empirical covariance estimate</a></li>
<li class="toctree-l2"><a class="reference internal" href="../covariance/plot_covariance_estimation.html">Shrinkage covariance estimation: LedoitWolf vs OAS and max-likelihood</a></li>
<li class="toctree-l2"><a class="reference internal" href="../covariance/plot_sparse_cov.html">Sparse inverse covariance estimation</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../cross_decomposition/index.html">Cross decomposition</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../cross_decomposition/plot_compare_cross_decomposition.html">Compare cross decomposition methods</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cross_decomposition/plot_pcr_vs_pls.html">Principal Component Regression vs Partial Least Squares Regression</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../datasets/index.html">Dataset examples</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../datasets/plot_random_multilabel_dataset.html">Plot randomly generated multilabel dataset</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../tree/index.html">Decision Trees</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../tree/plot_tree_regression.html">Decision Tree Regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../tree/plot_iris_dtc.html">Plot the decision surface of decision trees trained on the iris dataset</a></li>
<li class="toctree-l2"><a class="reference internal" href="../tree/plot_cost_complexity_pruning.html">Post pruning decision trees with cost complexity pruning</a></li>
<li class="toctree-l2"><a class="reference internal" href="../tree/plot_unveil_tree_structure.html">Understanding the decision tree structure</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../decomposition/index.html">Decomposition</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_ica_blind_source_separation.html">Blind source separation using FastICA</a></li>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_pca_vs_lda.html">Comparison of LDA and PCA 2D projection of Iris dataset</a></li>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_faces_decomposition.html">Faces dataset decompositions</a></li>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_varimax_fa.html">Factor Analysis (with rotation) to visualize patterns</a></li>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_ica_vs_pca.html">FastICA on 2D point clouds</a></li>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_image_denoising.html">Image denoising using dictionary learning</a></li>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_incremental_pca.html">Incremental PCA</a></li>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_kernel_pca.html">Kernel PCA</a></li>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_pca_vs_fa_model_selection.html">Model selection with Probabilistic PCA and Factor Analysis (FA)</a></li>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_pca_iris.html">Principal Component Analysis (PCA) on Iris Dataset</a></li>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_sparse_coding.html">Sparse coding with a precomputed dictionary</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../developing_estimators/index.html">Developing Estimators</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../developing_estimators/sklearn_is_fitted.html"><code class="docutils literal notranslate"><span class="pre">__sklearn_is_fitted__</span></code> as Developer API</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../ensemble/index.html">Ensemble methods</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_gradient_boosting_categorical.html">Categorical Feature Support in Gradient Boosting</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_stack_predictors.html">Combine predictors using stacking</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_forest_hist_grad_boosting_comparison.html">Comparing Random Forests and Histogram Gradient Boosting models</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_random_forest_regression_multioutput.html">Comparing random forests and the multi-output meta estimator</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_adaboost_regression.html">Decision Tree Regression with AdaBoost</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_gradient_boosting_early_stopping.html">Early stopping in Gradient Boosting</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_forest_importances.html">Feature importances with a forest of trees</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_feature_transformation.html">Feature transformations with ensembles of trees</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_hgbt_regression.html">Features in Histogram Gradient Boosting Trees</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_gradient_boosting_oob.html">Gradient Boosting Out-of-Bag estimates</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_gradient_boosting_regression.html">Gradient Boosting regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_gradient_boosting_regularization.html">Gradient Boosting regularization</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_random_forest_embedding.html">Hashing feature transformation using Totally Random Trees</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_isolation_forest.html">IsolationForest example</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_monotonic_constraints.html">Monotonic Constraints</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_adaboost_multiclass.html">Multi-class AdaBoosted Decision Trees</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_ensemble_oob.html">OOB Errors for Random Forests</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_voting_probas.html">Plot class probabilities calculated by the VotingClassifier</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_voting_regressor.html">Plot individual and voting regression predictions</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_voting_decision_regions.html">Plot the decision boundaries of a VotingClassifier</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_forest_iris.html">Plot the decision surfaces of ensembles of trees on the iris dataset</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_gradient_boosting_quantile.html">Prediction Intervals for Gradient Boosting Regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_bias_variance.html">Single estimator versus bagging: bias-variance decomposition</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_adaboost_twoclass.html">Two-class AdaBoost</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../applications/index.html">Examples based on real world datasets</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_tomography_l1_reconstruction.html">Compressive sensing: tomography reconstruction with L1 prior (Lasso)</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_face_recognition.html">Faces recognition example using eigenfaces and SVMs</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_digits_denoising.html">Image denoising using kernel PCA</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_time_series_lagged_features.html">Lagged features for time series forecasting</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_model_complexity_influence.html">Model Complexity Influence</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_out_of_core_classification.html">Out-of-core classification of text documents</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_outlier_detection_wine.html">Outlier detection on a real data set</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_prediction_latency.html">Prediction Latency</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_species_distribution_modeling.html">Species distribution modeling</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_cyclical_feature_engineering.html">Time-related feature engineering</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_topics_extraction_with_nmf_lda.html">Topic extraction with Non-negative Matrix Factorization and Latent Dirichlet Allocation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_stock_market.html">Visualizing the stock market structure</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/wikipedia_principal_eigenvector.html">Wikipedia principal eigenvector</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../feature_selection/index.html">Feature Selection</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../feature_selection/plot_f_test_vs_mi.html">Comparison of F-test and mutual information</a></li>
<li class="toctree-l2"><a class="reference internal" href="../feature_selection/plot_select_from_model_diabetes.html">Model-based and sequential feature selection</a></li>
<li class="toctree-l2"><a class="reference internal" href="../feature_selection/plot_feature_selection_pipeline.html">Pipeline ANOVA SVM</a></li>
<li class="toctree-l2"><a class="reference internal" href="../feature_selection/plot_rfe_digits.html">Recursive feature elimination</a></li>
<li class="toctree-l2"><a class="reference internal" href="../feature_selection/plot_rfe_with_cross_validation.html">Recursive feature elimination with cross-validation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../feature_selection/plot_feature_selection.html">Univariate Feature Selection</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../mixture/index.html">Gaussian Mixture Models</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../mixture/plot_concentration_prior.html">Concentration Prior Type Analysis of Variation Bayesian Gaussian Mixture</a></li>
<li class="toctree-l2"><a class="reference internal" href="../mixture/plot_gmm_pdf.html">Density Estimation for a Gaussian mixture</a></li>
<li class="toctree-l2"><a class="reference internal" href="../mixture/plot_gmm_init.html">GMM Initialization Methods</a></li>
<li class="toctree-l2"><a class="reference internal" href="../mixture/plot_gmm_covariances.html">GMM covariances</a></li>
<li class="toctree-l2"><a class="reference internal" href="../mixture/plot_gmm.html">Gaussian Mixture Model Ellipsoids</a></li>
<li class="toctree-l2"><a class="reference internal" href="../mixture/plot_gmm_selection.html">Gaussian Mixture Model Selection</a></li>
<li class="toctree-l2"><a class="reference internal" href="../mixture/plot_gmm_sin.html">Gaussian Mixture Model Sine Curve</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../gaussian_process/index.html">Gaussian Process for Machine Learning</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../gaussian_process/plot_gpr_noisy.html">Ability of Gaussian process regression (GPR) to estimate data noise-level</a></li>
<li class="toctree-l2"><a class="reference internal" href="../gaussian_process/plot_compare_gpr_krr.html">Comparison of kernel ridge and Gaussian process regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../gaussian_process/plot_gpr_co2.html">Forecasting of CO2 level on Mona Loa dataset using Gaussian process regression (GPR)</a></li>
<li class="toctree-l2"><a class="reference internal" href="../gaussian_process/plot_gpr_noisy_targets.html">Gaussian Processes regression: basic introductory example</a></li>
<li class="toctree-l2"><a class="reference internal" href="../gaussian_process/plot_gpc_iris.html">Gaussian process classification (GPC) on iris dataset</a></li>
<li class="toctree-l2"><a class="reference internal" href="../gaussian_process/plot_gpr_on_structured_data.html">Gaussian processes on discrete data structures</a></li>
<li class="toctree-l2"><a class="reference internal" href="../gaussian_process/plot_gpc_xor.html">Illustration of Gaussian process classification (GPC) on the XOR dataset</a></li>
<li class="toctree-l2"><a class="reference internal" href="../gaussian_process/plot_gpr_prior_posterior.html">Illustration of prior and posterior Gaussian process for different kernels</a></li>
<li class="toctree-l2"><a class="reference internal" href="../gaussian_process/plot_gpc_isoprobability.html">Iso-probability lines for Gaussian Processes classification (GPC)</a></li>
<li class="toctree-l2"><a class="reference internal" href="../gaussian_process/plot_gpc.html">Probabilistic predictions with Gaussian process classification (GPC)</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../linear_model/index.html">Generalized Linear Models</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_ard.html">Comparing Linear Bayesian Regressors</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_sgd_comparison.html">Comparing various online solvers</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_bayesian_ridge_curvefit.html">Curve Fitting with Bayesian Ridge Regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_logistic_multinomial.html">Decision Boundaries of Multinomial and One-vs-Rest Logistic Regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_sgd_early_stopping.html">Early stopping of Stochastic Gradient Descent</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_elastic_net_precomputed_gram_matrix_with_weighted_samples.html">Fitting an Elastic Net with a precomputed Gram Matrix and Weighted Samples</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_huber_vs_ridge.html">HuberRegressor vs Ridge on dataset with strong outliers</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_multi_task_lasso_support.html">Joint feature selection with multi-task Lasso</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_logistic_l1_l2_sparsity.html">L1 Penalty and Sparsity in Logistic Regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_lasso_and_elasticnet.html">L1-based models for Sparse Signals</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_lasso_lars_ic.html">Lasso model selection via information criteria</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_lasso_model_selection.html">Lasso model selection: AIC-BIC / cross-validation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_lasso_dense_vs_sparse_data.html">Lasso on dense and sparse data</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_lasso_lasso_lars_elasticnet_path.html">Lasso, Lasso-LARS, and Elastic Net paths</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_logistic.html">Logistic function</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_sparse_logistic_regression_mnist.html">MNIST classification using multinomial logistic + L1</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_sparse_logistic_regression_20newsgroups.html">Multiclass sparse logistic regression on 20newgroups</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_nnls.html">Non-negative least squares</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_sgdocsvm_vs_ocsvm.html">One-Class SVM versus One-Class SVM using Stochastic Gradient Descent</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_ols.html">Ordinary Least Squares Example</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_ols_ridge_variance.html">Ordinary Least Squares and Ridge Regression Variance</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_omp.html">Orthogonal Matching Pursuit</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_ridge_path.html">Plot Ridge coefficients as a function of the regularization</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_sgd_iris.html">Plot multi-class SGD on the iris dataset</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_poisson_regression_non_normal_loss.html">Poisson regression and non-normal loss</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_polynomial_interpolation.html">Polynomial and Spline interpolation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_quantile_regression.html">Quantile regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_logistic_path.html">Regularization path of L1- Logistic Regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_ridge_coeffs.html">Ridge coefficients as a function of the L2 Regularization</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_robust_fit.html">Robust linear estimator fitting</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_ransac.html">Robust linear model estimation using RANSAC</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_sgd_separating_hyperplane.html">SGD: Maximum margin separating hyperplane</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_sgd_penalties.html">SGD: Penalties</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_sgd_weighted_samples.html">SGD: Weighted samples</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_sgd_loss_functions.html">SGD: convex loss functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_theilsen.html">Theil-Sen Regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_tweedie_regression_insurance_claims.html">Tweedie regression on insurance claims</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../inspection/index.html">Inspection</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../inspection/plot_linear_model_coefficient_interpretation.html">Common pitfalls in the interpretation of coefficients of linear models</a></li>
<li class="toctree-l2"><a class="reference internal" href="../inspection/plot_causal_interpretation.html">Failure of Machine Learning to infer causal effects</a></li>
<li class="toctree-l2"><a class="reference internal" href="../inspection/plot_partial_dependence.html">Partial Dependence and Individual Conditional Expectation Plots</a></li>
<li class="toctree-l2"><a class="reference internal" href="../inspection/plot_permutation_importance.html">Permutation Importance vs Random Forest Feature Importance (MDI)</a></li>
<li class="toctree-l2"><a class="reference internal" href="../inspection/plot_permutation_importance_multicollinear.html">Permutation Importance with Multicollinear or Correlated Features</a></li>
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<li class="toctree-l1 has-children"><a class="reference internal" href="../kernel_approximation/index.html">Kernel Approximation</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../kernel_approximation/plot_scalable_poly_kernels.html">Scalable learning with polynomial kernel approximation</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../manifold/plot_compare_methods.html">Comparison of Manifold Learning methods</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manifold/plot_manifold_sphere.html">Manifold Learning methods on a severed sphere</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manifold/plot_lle_digits.html">Manifold learning on handwritten digits: Locally Linear Embedding, Isomap…</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manifold/plot_mds.html">Multi-dimensional scaling</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manifold/plot_swissroll.html">Swiss Roll And Swiss-Hole Reduction</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manifold/plot_t_sne_perplexity.html">t-SNE: The effect of various perplexity values on the shape</a></li>
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<li class="toctree-l1 has-children"><a class="reference internal" href="../miscellaneous/index.html">Miscellaneous</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_partial_dependence_visualization_api.html">Advanced Plotting With Partial Dependence</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_anomaly_comparison.html">Comparing anomaly detection algorithms for outlier detection on toy datasets</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_kernel_ridge_regression.html">Comparison of kernel ridge regression and SVR</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_pipeline_display.html">Displaying Pipelines</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_estimator_representation.html">Displaying estimators and complex pipelines</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_outlier_detection_bench.html">Evaluation of outlier detection estimators</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_kernel_approximation.html">Explicit feature map approximation for RBF kernels</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_multioutput_face_completion.html">Face completion with a multi-output estimators</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_set_output.html">Introducing the <code class="docutils literal notranslate"><span class="pre">set_output</span></code> API</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_isotonic_regression.html">Isotonic Regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_metadata_routing.html">Metadata Routing</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_multilabel.html">Multilabel classification</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_roc_curve_visualization_api.html">ROC Curve with Visualization API</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_johnson_lindenstrauss_bound.html">The Johnson-Lindenstrauss bound for embedding with random projections</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_display_object_visualization.html">Visualizations with Display Objects</a></li>
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<li class="toctree-l1 has-children"><a class="reference internal" href="../impute/index.html">Missing Value Imputation</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../impute/plot_missing_values.html">Imputing missing values before building an estimator</a></li>
<li class="toctree-l2"><a class="reference internal" href="../impute/plot_iterative_imputer_variants_comparison.html">Imputing missing values with variants of IterativeImputer</a></li>
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<li class="toctree-l1 has-children"><a class="reference internal" href="../model_selection/index.html">Model Selection</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_grid_search_refit_callable.html">Balance model complexity and cross-validated score</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_randomized_search.html">Comparing randomized search and grid search for hyperparameter estimation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_successive_halving_heatmap.html">Comparison between grid search and successive halving</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_grid_search_digits.html">Custom refit strategy of a grid search with cross-validation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_multi_metric_evaluation.html">Demonstration of multi-metric evaluation on cross_val_score and GridSearchCV</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_train_error_vs_test_error.html">Effect of model regularization on training and test error</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_successive_halving_iterations.html">Successive Halving Iterations</a></li>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_permutation_tests_for_classification.html">Test with permutations the significance of a classification score</a></li>
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<li class="toctree-l1 has-children"><a class="reference internal" href="../multiclass/index.html">Multiclass methods</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
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<li class="toctree-l2"><a class="reference internal" href="../multioutput/plot_classifier_chain_yeast.html">Multilabel classification using a classifier chain</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../neighbors/approximate_nearest_neighbors.html">Approximate nearest neighbors in TSNE</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neighbors/plot_caching_nearest_neighbors.html">Caching nearest neighbors</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neighbors/plot_nca_classification.html">Comparing Nearest Neighbors with and without Neighborhood Components Analysis</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neighbors/plot_nca_dim_reduction.html">Dimensionality Reduction with Neighborhood Components Analysis</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../neural_networks/plot_mlp_training_curves.html">Compare Stochastic learning strategies for MLPClassifier</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neural_networks/plot_rbm_logistic_classification.html">Restricted Boltzmann Machine features for digit classification</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../compose/plot_feature_union.html">Concatenating multiple feature extraction methods</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../compose/plot_digits_pipe.html">Pipelining: chaining a PCA and a logistic regression</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../preprocessing/plot_all_scaling.html">Compare the effect of different scalers on data with outliers</a></li>
<li class="toctree-l2"><a class="reference internal" href="../preprocessing/plot_target_encoder.html">Comparing Target Encoder with Other Encoders</a></li>
<li class="toctree-l2"><a class="reference internal" href="../preprocessing/plot_discretization_strategies.html">Demonstrating the different strategies of KBinsDiscretizer</a></li>
<li class="toctree-l2"><a class="reference internal" href="../preprocessing/plot_discretization_classification.html">Feature discretization</a></li>
<li class="toctree-l2"><a class="reference internal" href="../preprocessing/plot_scaling_importance.html">Importance of Feature Scaling</a></li>
<li class="toctree-l2"><a class="reference internal" href="../preprocessing/plot_map_data_to_normal.html">Map data to a normal distribution</a></li>
<li class="toctree-l2"><a class="reference internal" href="../preprocessing/plot_target_encoder_cross_val.html">Target Encoder’s Internal Cross fitting</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../semi_supervised/plot_semi_supervised_versus_svm_iris.html">Decision boundary of semi-supervised classifiers versus SVM on the Iris dataset</a></li>
<li class="toctree-l2"><a class="reference internal" href="../semi_supervised/plot_self_training_varying_threshold.html">Effect of varying threshold for self-training</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../semi_supervised/plot_label_propagation_digits.html">Label Propagation digits: Demonstrating performance</a></li>
<li class="toctree-l2"><a class="reference internal" href="../semi_supervised/plot_label_propagation_structure.html">Label Propagation learning a complex structure</a></li>
<li class="toctree-l2"><a class="reference internal" href="../semi_supervised/plot_semi_supervised_newsgroups.html">Semi-supervised Classification on a Text Dataset</a></li>
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<li class="toctree-l2"><a class="reference internal" href="plot_oneclass.html">One-class SVM with non-linear kernel (RBF)</a></li>
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<li class="toctree-l2 current active"><a class="current reference internal" href="#">Plot different SVM classifiers in the iris dataset</a></li>
<li class="toctree-l2"><a class="reference internal" href="plot_linearsvc_support_vectors.html">Plot the support vectors in LinearSVC</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../exercises/plot_iris_exercise.html">SVM Exercise</a></li>
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<div class="sphx-glr-download-link-note admonition note">
<p class="admonition-title">Note</p>
<p><a class="reference internal" href="#sphx-glr-download-auto-examples-svm-plot-iris-svc-py"><span class="std std-ref">Go to the end</span></a>
to download the full example code. or to run this example in your browser via JupyterLite or Binder</p>
</div>
<section class="sphx-glr-example-title" id="plot-different-svm-classifiers-in-the-iris-dataset">
<span id="sphx-glr-auto-examples-svm-plot-iris-svc-py"></span><h1>Plot different SVM classifiers in the iris dataset<a class="headerlink" href="#plot-different-svm-classifiers-in-the-iris-dataset" title="Link to this heading">#</a></h1>
<p>Comparison of different linear SVM classifiers on a 2D projection of the iris
dataset. We only consider the first 2 features of this dataset:</p>
<ul class="simple">
<li><p>Sepal length</p></li>
<li><p>Sepal width</p></li>
</ul>
<p>This example shows how to plot the decision surface for four SVM classifiers
with different kernels.</p>
<p>The linear models <code class="docutils literal notranslate"><span class="pre">LinearSVC()</span></code> and <code class="docutils literal notranslate"><span class="pre">SVC(kernel='linear')</span></code> yield slightly
different decision boundaries. This can be a consequence of the following
differences:</p>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">LinearSVC</span></code> minimizes the squared hinge loss while <code class="docutils literal notranslate"><span class="pre">SVC</span></code> minimizes the
regular hinge loss.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">LinearSVC</span></code> uses the One-vs-All (also known as One-vs-Rest) multiclass
reduction while <code class="docutils literal notranslate"><span class="pre">SVC</span></code> uses the One-vs-One multiclass reduction.</p></li>
</ul>
<p>Both linear models have linear decision boundaries (intersecting hyperplanes)
while the non-linear kernel models (polynomial or Gaussian RBF) have more
flexible non-linear decision boundaries with shapes that depend on the kind of
kernel and its parameters.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>while plotting the decision function of classifiers for toy 2D
datasets can help get an intuitive understanding of their respective
expressive power, be aware that those intuitions don’t always generalize to
more realistic high-dimensional problems.</p>
</div>
<img src="../../_images/sphx_glr_plot_iris_svc_001.png" srcset="../../_images/sphx_glr_plot_iris_svc_001.png" alt="SVC with linear kernel, LinearSVC (linear kernel), SVC with RBF kernel, SVC with polynomial (degree 3) kernel" class = "sphx-glr-single-img"/><div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Authors: The scikit-learn developers</span>
<span class="c1"># SPDX-License-Identifier: BSD-3-Clause</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">datasets</span><span class="p">,</span> <span class="n">svm</span>
<span class="kn">from</span> <span class="nn">sklearn.inspection</span> <span class="kn">import</span> <span class="n">DecisionBoundaryDisplay</span>
<span class="c1"># import some data to play with</span>
<span class="n">iris</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.datasets.load_iris.html#sklearn.datasets.load_iris" title="sklearn.datasets.load_iris" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">datasets</span><span class="o">.</span><span class="n">load_iris</span></a><span class="p">()</span>
<span class="c1"># Take the first two features. We could avoid this by using a two-dim dataset</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">iris</span><span class="o">.</span><span class="n">data</span><span class="p">[:,</span> <span class="p">:</span><span class="mi">2</span><span class="p">]</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">iris</span><span class="o">.</span><span class="n">target</span>
<span class="c1"># we create an instance of SVM and fit out data. We do not scale our</span>
<span class="c1"># data since we want to plot the support vectors</span>
<span class="n">C</span> <span class="o">=</span> <span class="mf">1.0</span> <span class="c1"># SVM regularization parameter</span>
<span class="n">models</span> <span class="o">=</span> <span class="p">(</span>
<a href="../../modules/generated/sklearn.svm.SVC.html#sklearn.svm.SVC" title="sklearn.svm.SVC" class="sphx-glr-backref-module-sklearn-svm sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">svm</span><span class="o">.</span><span class="n">SVC</span></a><span class="p">(</span><span class="n">kernel</span><span class="o">=</span><span class="s2">"linear"</span><span class="p">,</span> <span class="n">C</span><span class="o">=</span><span class="n">C</span><span class="p">),</span>
<a href="../../modules/generated/sklearn.svm.LinearSVC.html#sklearn.svm.LinearSVC" title="sklearn.svm.LinearSVC" class="sphx-glr-backref-module-sklearn-svm sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">svm</span><span class="o">.</span><span class="n">LinearSVC</span></a><span class="p">(</span><span class="n">C</span><span class="o">=</span><span class="n">C</span><span class="p">,</span> <span class="n">max_iter</span><span class="o">=</span><span class="mi">10000</span><span class="p">),</span>
<a href="../../modules/generated/sklearn.svm.SVC.html#sklearn.svm.SVC" title="sklearn.svm.SVC" class="sphx-glr-backref-module-sklearn-svm sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">svm</span><span class="o">.</span><span class="n">SVC</span></a><span class="p">(</span><span class="n">kernel</span><span class="o">=</span><span class="s2">"rbf"</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=</span><span class="mf">0.7</span><span class="p">,</span> <span class="n">C</span><span class="o">=</span><span class="n">C</span><span class="p">),</span>
<a href="../../modules/generated/sklearn.svm.SVC.html#sklearn.svm.SVC" title="sklearn.svm.SVC" class="sphx-glr-backref-module-sklearn-svm sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">svm</span><span class="o">.</span><span class="n">SVC</span></a><span class="p">(</span><span class="n">kernel</span><span class="o">=</span><span class="s2">"poly"</span><span class="p">,</span> <span class="n">degree</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=</span><span class="s2">"auto"</span><span class="p">,</span> <span class="n">C</span><span class="o">=</span><span class="n">C</span><span class="p">),</span>
<span class="p">)</span>
<span class="n">models</span> <span class="o">=</span> <span class="p">(</span><span class="n">clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span> <span class="k">for</span> <span class="n">clf</span> <span class="ow">in</span> <span class="n">models</span><span class="p">)</span>
<span class="c1"># title for the plots</span>
<span class="n">titles</span> <span class="o">=</span> <span class="p">(</span>
<span class="s2">"SVC with linear kernel"</span><span class="p">,</span>
<span class="s2">"LinearSVC (linear kernel)"</span><span class="p">,</span>
<span class="s2">"SVC with RBF kernel"</span><span class="p">,</span>
<span class="s2">"SVC with polynomial (degree 3) kernel"</span><span class="p">,</span>
<span class="p">)</span>
<span class="c1"># Set-up 2x2 grid for plotting.</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">sub</span> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplots.html#matplotlib.pyplot.subplots" title="matplotlib.pyplot.subplots" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span></a><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplots_adjust.html#matplotlib.pyplot.subplots_adjust" title="matplotlib.pyplot.subplots_adjust" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplots_adjust</span></a><span class="p">(</span><span class="n">wspace</span><span class="o">=</span><span class="mf">0.4</span><span class="p">,</span> <span class="n">hspace</span><span class="o">=</span><span class="mf">0.4</span><span class="p">)</span>
<span class="n">X0</span><span class="p">,</span> <span class="n">X1</span> <span class="o">=</span> <span class="n">X</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">X</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span>
<span class="k">for</span> <span class="n">clf</span><span class="p">,</span> <span class="n">title</span><span class="p">,</span> <span class="n">ax</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">models</span><span class="p">,</span> <span class="n">titles</span><span class="p">,</span> <span class="n">sub</span><span class="o">.</span><span class="n">flatten</span><span class="p">()):</span>
<span class="n">disp</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.inspection.DecisionBoundaryDisplay.html#sklearn.inspection.DecisionBoundaryDisplay.from_estimator" title="sklearn.inspection.DecisionBoundaryDisplay.from_estimator" class="sphx-glr-backref-module-sklearn-inspection-DecisionBoundaryDisplay sphx-glr-backref-type-py-method"><span class="n">DecisionBoundaryDisplay</span><span class="o">.</span><span class="n">from_estimator</span></a><span class="p">(</span>
<span class="n">clf</span><span class="p">,</span>
<span class="n">X</span><span class="p">,</span>
<span class="n">response_method</span><span class="o">=</span><span class="s2">"predict"</span><span class="p">,</span>
<span class="n">cmap</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">coolwarm</span><span class="p">,</span>
<span class="n">alpha</span><span class="o">=</span><span class="mf">0.8</span><span class="p">,</span>
<span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">,</span>
<span class="n">xlabel</span><span class="o">=</span><span class="n">iris</span><span class="o">.</span><span class="n">feature_names</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span>
<span class="n">ylabel</span><span class="o">=</span><span class="n">iris</span><span class="o">.</span><span class="n">feature_names</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span>
<span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">X0</span><span class="p">,</span> <span class="n">X1</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="n">y</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">coolwarm</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">edgecolors</span><span class="o">=</span><span class="s2">"k"</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xticks</span><span class="p">(())</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_yticks</span><span class="p">(())</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="n">title</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
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