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<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_agglomerative_clustering.html">Agglomerative clustering with and without structure</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_agglomerative_clustering_metrics.html">Agglomerative clustering with different metrics</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_kmeans_plusplus.html">An example of K-Means++ initialization</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_bisect_kmeans.html">Bisecting K-Means and Regular K-Means Performance Comparison</a></li>
<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 current active has-children"><a class="reference internal" href="index.html">Examples based on real world datasets</a><details open="open"><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul class="current">
<li class="toctree-l2"><a class="reference internal" href="plot_tomography_l1_reconstruction.html">Compressive sensing: tomography reconstruction with L1 prior (Lasso)</a></li>
<li class="toctree-l2"><a class="reference internal" href="plot_face_recognition.html">Faces recognition example using eigenfaces and SVMs</a></li>
<li class="toctree-l2"><a class="reference internal" href="plot_digits_denoising.html">Image denoising using kernel PCA</a></li>
<li class="toctree-l2"><a class="reference internal" href="plot_time_series_lagged_features.html">Lagged features for time series forecasting</a></li>
<li class="toctree-l2"><a class="reference internal" href="plot_model_complexity_influence.html">Model Complexity Influence</a></li>
<li class="toctree-l2"><a class="reference internal" href="plot_out_of_core_classification.html">Out-of-core classification of text documents</a></li>
<li class="toctree-l2"><a class="reference internal" href="plot_outlier_detection_wine.html">Outlier detection on a real data set</a></li>
<li class="toctree-l2"><a class="reference internal" href="plot_prediction_latency.html">Prediction Latency</a></li>
<li class="toctree-l2"><a class="reference internal" href="plot_species_distribution_modeling.html">Species distribution modeling</a></li>
<li class="toctree-l2"><a class="reference internal" href="plot_cyclical_feature_engineering.html">Time-related feature engineering</a></li>
<li class="toctree-l2"><a class="reference internal" href="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="plot_stock_market.html">Visualizing the stock market structure</a></li>
<li class="toctree-l2 current active"><a class="current reference internal" href="#">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="../frozen/index.html">Frozen 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="../frozen/plot_frozen_examples.html">Examples of Using <code class="docutils literal notranslate"><span class="pre">FrozenEstimator</span></code></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>
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<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-l1 has-children"><a class="reference internal" href="../manifold/index.html">Manifold 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="../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>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_likelihood_ratios.html">Class Likelihood Ratios to measure classification performance</a></li>
<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>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_confusion_matrix.html">Confusion matrix</a></li>
<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>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_det.html">Detection error tradeoff (DET) curve</a></li>
<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_nested_cross_validation_iris.html">Nested versus non-nested cross-validation</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_roc_crossval.html">Receiver Operating Characteristic (ROC) with cross validation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_grid_search_text_feature_extraction.html">Sample pipeline for text feature extraction and evaluation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_grid_search_stats.html">Statistical comparison of models using grid search</a></li>
<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>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_underfitting_overfitting.html">Underfitting vs. Overfitting</a></li>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_cv_indices.html">Visualizing cross-validation behavior in scikit-learn</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../multiclass/plot_multiclass_overview.html">Overview of multiclass training meta-estimators</a></li>
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<li class="toctree-l1 has-children"><a class="reference internal" href="../multioutput/index.html">Multioutput 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="../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>
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<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>
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<li class="toctree-l2"><a class="reference internal" href="../neighbors/plot_kde_1d.html">Simple 1D Kernel Density Estimation</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>
<li class="toctree-l2"><a class="reference internal" href="../neural_networks/plot_mlp_alpha.html">Varying regularization in Multi-layer Perceptron</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../compose/plot_column_transformer.html">Column Transformer with Heterogeneous Data Sources</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>
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<li class="toctree-l2"><a class="reference internal" href="../preprocessing/plot_discretization_strategies.html">Demonstrating the different strategies of KBinsDiscretizer</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../preprocessing/plot_map_data_to_normal.html">Map data to a normal distribution</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="../svm/plot_iris_svc.html">Plot different SVM classifiers in the iris dataset</a></li>
<li class="toctree-l2"><a class="reference internal" href="../svm/plot_linearsvc_support_vectors.html">Plot the support vectors in LinearSVC</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-applications-wikipedia-principal-eigenvector-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="wikipedia-principal-eigenvector">
<span id="sphx-glr-auto-examples-applications-wikipedia-principal-eigenvector-py"></span><h1>Wikipedia principal eigenvector<a class="headerlink" href="#wikipedia-principal-eigenvector" title="Link to this heading">#</a></h1>
<p>A classical way to assert the relative importance of vertices in a
graph is to compute the principal eigenvector of the adjacency matrix
so as to assign to each vertex the values of the components of the first
eigenvector as a centrality score: <a class="reference external" href="https://en.wikipedia.org/wiki/Eigenvector_centrality">https://en.wikipedia.org/wiki/Eigenvector_centrality</a>.
On the graph of webpages and links those values are called the PageRank
scores by Google.</p>
<p>The goal of this example is to analyze the graph of links inside
wikipedia articles to rank articles by relative importance according to
this eigenvector centrality.</p>
<p>The traditional way to compute the principal eigenvector is to use the
<a class="reference external" href="https://en.wikipedia.org/wiki/Power_iteration">power iteration method</a>.
Here the computation is achieved thanks to Martinsson’s Randomized SVD
algorithm implemented in scikit-learn.</p>
<p>The graph data is fetched from the DBpedia dumps. DBpedia is an extraction
of the latent structured data of the Wikipedia content.</p>
<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">os</span>
<span class="kn">from</span> <span class="nn">bz2</span> <span class="kn">import</span> <a href="https://docs.python.org/3/library/bz2.html#bz2.BZ2File" title="bz2.BZ2File" class="sphx-glr-backref-module-bz2 sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">BZ2File</span></a>
<span class="kn">from</span> <span class="nn">datetime</span> <span class="kn">import</span> <span class="n">datetime</span>
<span class="kn">from</span> <span class="nn">pprint</span> <span class="kn">import</span> <a href="https://docs.python.org/3/library/pprint.html#pprint.pprint" title="pprint.pprint" class="sphx-glr-backref-module-pprint sphx-glr-backref-type-py-function"><span class="n">pprint</span></a>
<span class="kn">from</span> <span class="nn">time</span> <span class="kn">import</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a>
<span class="kn">from</span> <span class="nn">urllib.request</span> <span class="kn">import</span> <a href="https://docs.python.org/3/library/urllib.request.html#urllib.request.urlopen" title="urllib.request.urlopen" class="sphx-glr-backref-module-urllib-request sphx-glr-backref-type-py-function"><span class="n">urlopen</span></a>

<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">scipy</span> <span class="kn">import</span> <span class="n">sparse</span>

<span class="kn">from</span> <span class="nn">sklearn.decomposition</span> <span class="kn">import</span> <span class="n">randomized_svd</span>
</pre></div>
</div>
<section id="download-data-if-not-already-on-disk">
<h2>Download data, if not already on disk<a class="headerlink" href="#download-data-if-not-already-on-disk" title="Link to this heading">#</a></h2>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="n">redirects_url</span> <span class="o">=</span> <span class="s2">&quot;http://downloads.dbpedia.org/3.5.1/en/redirects_en.nt.bz2&quot;</span>
<span class="n">redirects_filename</span> <span class="o">=</span> <span class="n">redirects_url</span><span class="o">.</span><span class="n">rsplit</span><span class="p">(</span><span class="s2">&quot;/&quot;</span><span class="p">,</span> <span class="mi">1</span><span class="p">)[</span><span class="mi">1</span><span class="p">]</span>

<span class="n">page_links_url</span> <span class="o">=</span> <span class="s2">&quot;http://downloads.dbpedia.org/3.5.1/en/page_links_en.nt.bz2&quot;</span>
<span class="n">page_links_filename</span> <span class="o">=</span> <span class="n">page_links_url</span><span class="o">.</span><span class="n">rsplit</span><span class="p">(</span><span class="s2">&quot;/&quot;</span><span class="p">,</span> <span class="mi">1</span><span class="p">)[</span><span class="mi">1</span><span class="p">]</span>

<span class="n">resources</span> <span class="o">=</span> <span class="p">[</span>
    <span class="p">(</span><span class="n">redirects_url</span><span class="p">,</span> <span class="n">redirects_filename</span><span class="p">),</span>
    <span class="p">(</span><span class="n">page_links_url</span><span class="p">,</span> <span class="n">page_links_filename</span><span class="p">),</span>
<span class="p">]</span>

<span class="k">for</span> <span class="n">url</span><span class="p">,</span> <span class="n">filename</span> <span class="ow">in</span> <span class="n">resources</span><span class="p">:</span>
    <span class="k">if</span> <span class="ow">not</span> <a href="https://docs.python.org/3/library/os.path.html#os.path.exists" title="os.path.exists" class="sphx-glr-backref-module-os-path sphx-glr-backref-type-py-function"><span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">exists</span></a><span class="p">(</span><span class="n">filename</span><span class="p">):</span>
        <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Downloading data from &#39;</span><span class="si">%s</span><span class="s2">&#39;, please wait...&quot;</span> <span class="o">%</span> <span class="n">url</span><span class="p">)</span>
        <span class="n">opener</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/urllib.request.html#urllib.request.urlopen" title="urllib.request.urlopen" class="sphx-glr-backref-module-urllib-request sphx-glr-backref-type-py-function"><span class="n">urlopen</span></a><span class="p">(</span><span class="n">url</span><span class="p">)</span>
        <span class="k">with</span> <span class="nb">open</span><span class="p">(</span><span class="n">filename</span><span class="p">,</span> <span class="s2">&quot;wb&quot;</span><span class="p">)</span> <span class="k">as</span> <span class="n">f</span><span class="p">:</span>
            <span class="n">f</span><span class="o">.</span><span class="n">write</span><span class="p">(</span><span class="n">opener</span><span class="o">.</span><span class="n">read</span><span class="p">())</span>
        <span class="nb">print</span><span class="p">()</span>
</pre></div>
</div>
</section>
<section id="loading-the-redirect-files">
<h2>Loading the redirect files<a class="headerlink" href="#loading-the-redirect-files" title="Link to this heading">#</a></h2>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">index</span><span class="p">(</span><span class="n">redirects</span><span class="p">,</span> <span class="n">index_map</span><span class="p">,</span> <span class="n">k</span><span class="p">):</span>
<span class="w">    </span><span class="sd">&quot;&quot;&quot;Find the index of an article name after redirect resolution&quot;&quot;&quot;</span>
    <span class="n">k</span> <span class="o">=</span> <span class="n">redirects</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">k</span><span class="p">,</span> <span class="n">k</span><span class="p">)</span>
    <span class="k">return</span> <span class="n">index_map</span><span class="o">.</span><span class="n">setdefault</span><span class="p">(</span><span class="n">k</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">index_map</span><span class="p">))</span>


<span class="n">DBPEDIA_RESOURCE_PREFIX_LEN</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="s2">&quot;http://dbpedia.org/resource/&quot;</span><span class="p">)</span>
<span class="n">SHORTNAME_SLICE</span> <span class="o">=</span> <span class="nb">slice</span><span class="p">(</span><span class="n">DBPEDIA_RESOURCE_PREFIX_LEN</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span>


<span class="k">def</span> <span class="nf">short_name</span><span class="p">(</span><span class="n">nt_uri</span><span class="p">):</span>
<span class="w">    </span><span class="sd">&quot;&quot;&quot;Remove the &lt; and &gt; URI markers and the common URI prefix&quot;&quot;&quot;</span>
    <span class="k">return</span> <span class="n">nt_uri</span><span class="p">[</span><span class="n">SHORTNAME_SLICE</span><span class="p">]</span>


<span class="k">def</span> <span class="nf">get_redirects</span><span class="p">(</span><span class="n">redirects_filename</span><span class="p">):</span>
<span class="w">    </span><span class="sd">&quot;&quot;&quot;Parse the redirections and build a transitively closed map out of it&quot;&quot;&quot;</span>
    <span class="n">redirects</span> <span class="o">=</span> <span class="p">{}</span>
    <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Parsing the NT redirect file&quot;</span><span class="p">)</span>
    <span class="k">for</span> <span class="n">l</span><span class="p">,</span> <span class="n">line</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><a href="https://docs.python.org/3/library/bz2.html#bz2.BZ2File" title="bz2.BZ2File" class="sphx-glr-backref-module-bz2 sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">BZ2File</span></a><span class="p">(</span><span class="n">redirects_filename</span><span class="p">)):</span>
        <span class="n">split</span> <span class="o">=</span> <span class="n">line</span><span class="o">.</span><span class="n">split</span><span class="p">()</span>
        <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">split</span><span class="p">)</span> <span class="o">!=</span> <span class="mi">4</span><span class="p">:</span>
            <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;ignoring malformed line: &quot;</span> <span class="o">+</span> <span class="n">line</span><span class="p">)</span>
            <span class="k">continue</span>
        <span class="n">redirects</span><span class="p">[</span><span class="n">short_name</span><span class="p">(</span><span class="n">split</span><span class="p">[</span><span class="mi">0</span><span class="p">])]</span> <span class="o">=</span> <span class="n">short_name</span><span class="p">(</span><span class="n">split</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span>
        <span class="k">if</span> <span class="n">l</span> <span class="o">%</span> <span class="mi">1000000</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
            <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;[</span><span class="si">%s</span><span class="s2">] line: </span><span class="si">%08d</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="p">(</span><a href="https://docs.python.org/3/library/datetime.html#datetime.datetime.now" title="datetime.datetime.now" class="sphx-glr-backref-module-datetime-datetime sphx-glr-backref-type-py-method"><span class="n">datetime</span><span class="o">.</span><span class="n">now</span></a><span class="p">()</span><span class="o">.</span><span class="n">isoformat</span><span class="p">(),</span> <span class="n">l</span><span class="p">))</span>

    <span class="c1"># compute the transitive closure</span>
    <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Computing the transitive closure of the redirect relation&quot;</span><span class="p">)</span>
    <span class="k">for</span> <span class="n">l</span><span class="p">,</span> <span class="n">source</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">redirects</span><span class="o">.</span><span class="n">keys</span><span class="p">()):</span>
        <span class="n">transitive_target</span> <span class="o">=</span> <span class="kc">None</span>
        <span class="n">target</span> <span class="o">=</span> <span class="n">redirects</span><span class="p">[</span><span class="n">source</span><span class="p">]</span>
        <span class="n">seen</span> <span class="o">=</span> <span class="p">{</span><span class="n">source</span><span class="p">}</span>
        <span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
            <span class="n">transitive_target</span> <span class="o">=</span> <span class="n">target</span>
            <span class="n">target</span> <span class="o">=</span> <span class="n">redirects</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">target</span><span class="p">)</span>
            <span class="k">if</span> <span class="n">target</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">target</span> <span class="ow">in</span> <span class="n">seen</span><span class="p">:</span>
                <span class="k">break</span>
            <span class="n">seen</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">target</span><span class="p">)</span>
        <span class="n">redirects</span><span class="p">[</span><span class="n">source</span><span class="p">]</span> <span class="o">=</span> <span class="n">transitive_target</span>
        <span class="k">if</span> <span class="n">l</span> <span class="o">%</span> <span class="mi">1000000</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
            <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;[</span><span class="si">%s</span><span class="s2">] line: </span><span class="si">%08d</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="p">(</span><a href="https://docs.python.org/3/library/datetime.html#datetime.datetime.now" title="datetime.datetime.now" class="sphx-glr-backref-module-datetime-datetime sphx-glr-backref-type-py-method"><span class="n">datetime</span><span class="o">.</span><span class="n">now</span></a><span class="p">()</span><span class="o">.</span><span class="n">isoformat</span><span class="p">(),</span> <span class="n">l</span><span class="p">))</span>

    <span class="k">return</span> <span class="n">redirects</span>
</pre></div>
</div>
</section>
<section id="computing-the-adjacency-matrix">
<h2>Computing the Adjacency matrix<a class="headerlink" href="#computing-the-adjacency-matrix" title="Link to this heading">#</a></h2>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">get_adjacency_matrix</span><span class="p">(</span><span class="n">redirects_filename</span><span class="p">,</span> <span class="n">page_links_filename</span><span class="p">,</span> <span class="n">limit</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w">    </span><span class="sd">&quot;&quot;&quot;Extract the adjacency graph as a scipy sparse matrix</span>

<span class="sd">    Redirects are resolved first.</span>

<span class="sd">    Returns X, the scipy sparse adjacency matrix, redirects as python</span>
<span class="sd">    dict from article names to article names and index_map a python dict</span>
<span class="sd">    from article names to python int (article indexes).</span>
<span class="sd">    &quot;&quot;&quot;</span>

    <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Computing the redirect map&quot;</span><span class="p">)</span>
    <span class="n">redirects</span> <span class="o">=</span> <span class="n">get_redirects</span><span class="p">(</span><span class="n">redirects_filename</span><span class="p">)</span>

    <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Computing the integer index map&quot;</span><span class="p">)</span>
    <span class="n">index_map</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
    <span class="n">links</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
    <span class="k">for</span> <span class="n">l</span><span class="p">,</span> <span class="n">line</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><a href="https://docs.python.org/3/library/bz2.html#bz2.BZ2File" title="bz2.BZ2File" class="sphx-glr-backref-module-bz2 sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">BZ2File</span></a><span class="p">(</span><span class="n">page_links_filename</span><span class="p">)):</span>
        <span class="n">split</span> <span class="o">=</span> <span class="n">line</span><span class="o">.</span><span class="n">split</span><span class="p">()</span>
        <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">split</span><span class="p">)</span> <span class="o">!=</span> <span class="mi">4</span><span class="p">:</span>
            <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;ignoring malformed line: &quot;</span> <span class="o">+</span> <span class="n">line</span><span class="p">)</span>
            <span class="k">continue</span>
        <span class="n">i</span> <span class="o">=</span> <span class="n">index</span><span class="p">(</span><span class="n">redirects</span><span class="p">,</span> <span class="n">index_map</span><span class="p">,</span> <span class="n">short_name</span><span class="p">(</span><span class="n">split</span><span class="p">[</span><span class="mi">0</span><span class="p">]))</span>
        <span class="n">j</span> <span class="o">=</span> <span class="n">index</span><span class="p">(</span><span class="n">redirects</span><span class="p">,</span> <span class="n">index_map</span><span class="p">,</span> <span class="n">short_name</span><span class="p">(</span><span class="n">split</span><span class="p">[</span><span class="mi">2</span><span class="p">]))</span>
        <span class="n">links</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">))</span>
        <span class="k">if</span> <span class="n">l</span> <span class="o">%</span> <span class="mi">1000000</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
            <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;[</span><span class="si">%s</span><span class="s2">] line: </span><span class="si">%08d</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="p">(</span><a href="https://docs.python.org/3/library/datetime.html#datetime.datetime.now" title="datetime.datetime.now" class="sphx-glr-backref-module-datetime-datetime sphx-glr-backref-type-py-method"><span class="n">datetime</span><span class="o">.</span><span class="n">now</span></a><span class="p">()</span><span class="o">.</span><span class="n">isoformat</span><span class="p">(),</span> <span class="n">l</span><span class="p">))</span>

        <span class="k">if</span> <span class="n">limit</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span> <span class="ow">and</span> <span class="n">l</span> <span class="o">&gt;=</span> <span class="n">limit</span> <span class="o">-</span> <span class="mi">1</span><span class="p">:</span>
            <span class="k">break</span>

    <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Computing the adjacency matrix&quot;</span><span class="p">)</span>
    <span class="n">X</span> <span class="o">=</span> <a href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.lil_matrix.html#scipy.sparse.lil_matrix" title="scipy.sparse.lil_matrix" class="sphx-glr-backref-module-scipy-sparse sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">sparse</span><span class="o">.</span><span class="n">lil_matrix</span></a><span class="p">((</span><span class="nb">len</span><span class="p">(</span><span class="n">index_map</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">index_map</span><span class="p">)),</span> <span class="n">dtype</span><span class="o">=</span><a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.float32" title="numpy.float32" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">np</span><span class="o">.</span><span class="n">float32</span></a><span class="p">)</span>
    <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="ow">in</span> <span class="n">links</span><span class="p">:</span>
        <span class="n">X</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="mf">1.0</span>
    <span class="k">del</span> <span class="n">links</span>
    <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Converting to CSR representation&quot;</span><span class="p">)</span>
    <span class="n">X</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">tocsr</span><span class="p">()</span>
    <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;CSR conversion done&quot;</span><span class="p">)</span>
    <span class="k">return</span> <span class="n">X</span><span class="p">,</span> <span class="n">redirects</span><span class="p">,</span> <span class="n">index_map</span>


<span class="c1"># stop after 5M links to make it possible to work in RAM</span>
<span class="n">X</span><span class="p">,</span> <span class="n">redirects</span><span class="p">,</span> <span class="n">index_map</span> <span class="o">=</span> <span class="n">get_adjacency_matrix</span><span class="p">(</span>
    <span class="n">redirects_filename</span><span class="p">,</span> <span class="n">page_links_filename</span><span class="p">,</span> <span class="n">limit</span><span class="o">=</span><span class="mi">5000000</span>
<span class="p">)</span>
<span class="n">names</span> <span class="o">=</span> <span class="p">{</span><span class="n">i</span><span class="p">:</span> <span class="n">name</span> <span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">index_map</span><span class="o">.</span><span class="n">items</span><span class="p">()}</span>
</pre></div>
</div>
</section>
<section id="computing-principal-singular-vector-using-randomized-svd">
<h2>Computing Principal Singular Vector using Randomized SVD<a class="headerlink" href="#computing-principal-singular-vector-using-randomized-svd" title="Link to this heading">#</a></h2>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Computing the principal singular vectors using randomized_svd&quot;</span><span class="p">)</span>
<span class="n">t0</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a><span class="p">()</span>
<span class="n">U</span><span class="p">,</span> <span class="n">s</span><span class="p">,</span> <span class="n">V</span> <span class="o">=</span> <span class="n">randomized_svd</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="n">n_iter</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;done in </span><span class="si">%0.3f</span><span class="s2">s&quot;</span> <span class="o">%</span> <span class="p">(</span><a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span><span class="p">))</span>

<span class="c1"># print the names of the wikipedia related strongest components of the</span>
<span class="c1"># principal singular vector which should be similar to the highest eigenvector</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Top wikipedia pages according to principal singular vectors&quot;</span><span class="p">)</span>
<a href="https://docs.python.org/3/library/pprint.html#pprint.pprint" title="pprint.pprint" class="sphx-glr-backref-module-pprint sphx-glr-backref-type-py-function"><span class="n">pprint</span></a><span class="p">([</span><span class="n">names</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">U</span><span class="o">.</span><span class="n">T</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span><span class="o">.</span><span class="n">argsort</span><span class="p">()[</span><span class="o">-</span><span class="mi">10</span><span class="p">:]])</span>
<a href="https://docs.python.org/3/library/pprint.html#pprint.pprint" title="pprint.pprint" class="sphx-glr-backref-module-pprint sphx-glr-backref-type-py-function"><span class="n">pprint</span></a><span class="p">([</span><span class="n">names</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">V</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span><span class="o">.</span><span class="n">argsort</span><span class="p">()[</span><span class="o">-</span><span class="mi">10</span><span class="p">:]])</span>
</pre></div>
</div>
</section>
<section id="computing-centrality-scores">
<h2>Computing Centrality scores<a class="headerlink" href="#computing-centrality-scores" title="Link to this heading">#</a></h2>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">centrality_scores</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.85</span><span class="p">,</span> <span class="n">max_iter</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">tol</span><span class="o">=</span><span class="mf">1e-10</span><span class="p">):</span>
<span class="w">    </span><span class="sd">&quot;&quot;&quot;Power iteration computation of the principal eigenvector</span>

<span class="sd">    This method is also known as Google PageRank and the implementation</span>
<span class="sd">    is based on the one from the NetworkX project (BSD licensed too)</span>
<span class="sd">    with copyrights by:</span>

<span class="sd">      Aric Hagberg &lt;hagberg@lanl.gov&gt;</span>
<span class="sd">      Dan Schult &lt;dschult@colgate.edu&gt;</span>
<span class="sd">      Pieter Swart &lt;swart@lanl.gov&gt;</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="n">n</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
    <span class="n">X</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
    <span class="n">incoming_counts</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.asarray.html#numpy.asarray" title="numpy.asarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">asarray</span></a><span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">ravel</span><span class="p">()</span>

    <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Normalizing the graph&quot;</span><span class="p">)</span>
    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">incoming_counts</span><span class="o">.</span><span class="n">nonzero</span><span class="p">()[</span><span class="mi">0</span><span class="p">]:</span>
        <span class="n">X</span><span class="o">.</span><span class="n">data</span><span class="p">[</span><span class="n">X</span><span class="o">.</span><span class="n">indptr</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="p">:</span> <span class="n">X</span><span class="o">.</span><span class="n">indptr</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]]</span> <span class="o">*=</span> <span class="mf">1.0</span> <span class="o">/</span> <span class="n">incoming_counts</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
    <span class="n">dangle</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.asarray.html#numpy.asarray" title="numpy.asarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">asarray</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.where.html#numpy.where" title="numpy.where" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">where</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.isclose.html#numpy.isclose" title="numpy.isclose" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">isclose</span></a><span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">),</span> <span class="mi">0</span><span class="p">),</span> <span class="mf">1.0</span> <span class="o">/</span> <span class="n">n</span><span class="p">,</span> <span class="mi">0</span><span class="p">))</span><span class="o">.</span><span class="n">ravel</span><span class="p">()</span>

    <span class="n">scores</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.full.html#numpy.full" title="numpy.full" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">full</span></a><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="mf">1.0</span> <span class="o">/</span> <span class="n">n</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.float32" title="numpy.float32" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">np</span><span class="o">.</span><span class="n">float32</span></a><span class="p">)</span>  <span class="c1"># initial guess</span>
    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">max_iter</span><span class="p">):</span>
        <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;power iteration #</span><span class="si">%d</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">i</span><span class="p">)</span>
        <span class="n">prev_scores</span> <span class="o">=</span> <span class="n">scores</span>
        <span class="n">scores</span> <span class="o">=</span> <span class="p">(</span>
            <span class="n">alpha</span> <span class="o">*</span> <span class="p">(</span><span class="n">scores</span> <span class="o">*</span> <span class="n">X</span> <span class="o">+</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.dot.html#numpy.dot" title="numpy.dot" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">dot</span></a><span class="p">(</span><span class="n">dangle</span><span class="p">,</span> <span class="n">prev_scores</span><span class="p">))</span>
            <span class="o">+</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">alpha</span><span class="p">)</span> <span class="o">*</span> <span class="n">prev_scores</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span> <span class="o">/</span> <span class="n">n</span>
        <span class="p">)</span>
        <span class="c1"># check convergence: normalized l_inf norm</span>
        <span class="n">scores_max</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">scores</span><span class="p">)</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
        <span class="k">if</span> <span class="n">scores_max</span> <span class="o">==</span> <span class="mf">0.0</span><span class="p">:</span>
            <span class="n">scores_max</span> <span class="o">=</span> <span class="mf">1.0</span>
        <span class="n">err</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">scores</span> <span class="o">-</span> <span class="n">prev_scores</span><span class="p">)</span><span class="o">.</span><span class="n">max</span><span class="p">()</span> <span class="o">/</span> <span class="n">scores_max</span>
        <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;error: </span><span class="si">%0.6f</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">err</span><span class="p">)</span>
        <span class="k">if</span> <span class="n">err</span> <span class="o">&lt;</span> <span class="n">n</span> <span class="o">*</span> <span class="n">tol</span><span class="p">:</span>
            <span class="k">return</span> <span class="n">scores</span>

    <span class="k">return</span> <span class="n">scores</span>


<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Computing principal eigenvector score using a power iteration method&quot;</span><span class="p">)</span>
<span class="n">t0</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a><span class="p">()</span>
<span class="n">scores</span> <span class="o">=</span> <span class="n">centrality_scores</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">max_iter</span><span class="o">=</span><span class="mi">100</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;done in </span><span class="si">%0.3f</span><span class="s2">s&quot;</span> <span class="o">%</span> <span class="p">(</span><a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span><span class="p">))</span>
<a href="https://docs.python.org/3/library/pprint.html#pprint.pprint" title="pprint.pprint" class="sphx-glr-backref-module-pprint sphx-glr-backref-type-py-function"><span class="n">pprint</span></a><span class="p">([</span><span class="n">names</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">scores</span><span class="p">)</span><span class="o">.</span><span class="n">argsort</span><span class="p">()[</span><span class="o">-</span><span class="mi">10</span><span class="p">:]])</span>
</pre></div>
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