User Guide

• 1. Supervised learning
  • 1.1. Generalized Linear Models
    • 1.1.1. Ordinary Least Squares
      • 1.1.1.1. Ordinary Least Squares Complexity
    • 1.1.2. Ridge Regression
      • 1.1.2.1. Ridge Complexity
      • 1.1.2.2. Setting the regularization parameter: generalized Cross-Validation
    • 1.1.3. Lasso
      • 1.1.3.1. Setting regularization parameter
        • 1.1.3.1.1. Using cross-validation
        • 1.1.3.1.2. Information-criteria based model selection
        • 1.1.3.1.3. Comparison with the regularization parameter of SVM
    • 1.1.4. Multi-task Lasso
    • 1.1.5. Elastic-Net
    • 1.1.6. Multi-task Elastic-Net
    • 1.1.7. Least Angle Regression
    • 1.1.8. LARS Lasso
      • 1.1.8.1. Mathematical formulation
    • 1.1.9. Orthogonal Matching Pursuit (OMP)
    • 1.1.10. Bayesian Regression
      • 1.1.10.1. Bayesian Ridge Regression
      • 1.1.10.2. Automatic Relevance Determination - ARD
    • 1.1.11. Logistic regression
    • 1.1.12. Stochastic Gradient Descent - SGD
    • 1.1.13. Perceptron
    • 1.1.14. Passive Aggressive Algorithms
    • 1.1.15. Robustness regression: outliers and modeling errors
      • 1.1.15.1. Different scenario and useful concepts
      • 1.1.15.2. RANSAC: RANdom SAmple Consensus
        • 1.1.15.2.1. Details of the algorithm
      • 1.1.15.3. Theil-Sen estimator: generalized-median-based estimator
        • 1.1.15.3.1. Theoretical considerations
      • 1.1.15.4. Huber Regression
      • 1.1.15.5. Notes
    • 1.1.16. Polynomial regression: extending linear models with basis functions
  • 1.2. Linear and Quadratic Discriminant Analysis
    • 1.2.1. Dimensionality reduction using Linear Discriminant Analysis
    • 1.2.2. Mathematical formulation of the LDA and QDA classifiers
    • 1.2.3. Mathematical formulation of LDA dimensionality reduction
    • 1.2.4. Shrinkage
    • 1.2.5. Estimation algorithms
  • 1.3. Kernel ridge regression
  • 1.4. Support Vector Machines
    • 1.4.1. Classification
      • 1.4.1.1. Multi-class classification
      • 1.4.1.2. Scores and probabilities
      • 1.4.1.3. Unbalanced problems
    • 1.4.2. Regression
    • 1.4.3. Density estimation, novelty detection
    • 1.4.4. Complexity
    • 1.4.5. Tips on Practical Use
    • 1.4.6. Kernel functions
      • 1.4.6.1. Custom Kernels
        • 1.4.6.1.1. Using Python functions as kernels
        • 1.4.6.1.2. Using the Gram matrix
        • 1.4.6.1.3. Parameters of the RBF Kernel
    • 1.4.7. Mathematical formulation
      • 1.4.7.1. SVC
      • 1.4.7.2. NuSVC
      • 1.4.7.3. SVR
    • 1.4.8. Implementation details
  • 1.5. Stochastic Gradient Descent
    • 1.5.1. Classification
    • 1.5.2. Regression
    • 1.5.3. Stochastic Gradient Descent for sparse data
    • 1.5.4. Complexity
    • 1.5.5. Stopping criterion
    • 1.5.6. Tips on Practical Use
    • 1.5.7. Mathematical formulation
      • 1.5.7.1. SGD
    • 1.5.8. Implementation details
  • 1.6. Nearest Neighbors
    • 1.6.1. Unsupervised Nearest Neighbors
      • 1.6.1.1. Finding the Nearest Neighbors
      • 1.6.1.2. KDTree and BallTree Classes
    • 1.6.2. Nearest Neighbors Classification
    • 1.6.3. Nearest Neighbors Regression
    • 1.6.4. Nearest Neighbor Algorithms
      • 1.6.4.1. Brute Force
      • 1.6.4.2. K-D Tree
      • 1.6.4.3. Ball Tree
      • 1.6.4.4. Choice of Nearest Neighbors Algorithm
      • 1.6.4.5. Effect of leaf_size
    • 1.6.5. Nearest Centroid Classifier
      • 1.6.5.1. Nearest Shrunken Centroid
    • 1.6.6. Neighborhood Components Analysis
      • 1.6.6.1. Classification
      • 1.6.6.2. Dimensionality reduction
      • 1.6.6.3. Mathematical formulation
        • 1.6.6.3.1. Mahalanobis distance
      • 1.6.6.4. Implementation
      • 1.6.6.5. Complexity
        • 1.6.6.5.1. Training
        • 1.6.6.5.2. Transform
  • 1.7. Gaussian Processes
    • 1.7.1. Gaussian Process Regression (GPR)
    • 1.7.2. GPR examples
      • 1.7.2.1. GPR with noise-level estimation
      • 1.7.2.2. Comparison of GPR and Kernel Ridge Regression
      • 1.7.2.3. GPR on Mauna Loa CO2 data
    • 1.7.3. Gaussian Process Classification (GPC)
    • 1.7.4. GPC examples
      • 1.7.4.1. Probabilistic predictions with GPC
      • 1.7.4.2. Illustration of GPC on the XOR dataset
      • 1.7.4.3. Gaussian process classification (GPC) on iris dataset
    • 1.7.5. Kernels for Gaussian Processes
      • 1.7.5.1. Gaussian Process Kernel API
      • 1.7.5.2. Basic kernels
      • 1.7.5.3. Kernel operators
      • 1.7.5.4. Radial-basis function (RBF) kernel
      • 1.7.5.5. Matérn kernel
      • 1.7.5.6. Rational quadratic kernel
      • 1.7.5.7. Exp-Sine-Squared kernel
      • 1.7.5.8. Dot-Product kernel
      • 1.7.5.9. References
  • 1.8. Cross decomposition
  • 1.9. Naive Bayes
    • 1.9.1. Gaussian Naive Bayes
    • 1.9.2. Multinomial Naive Bayes
    • 1.9.3. Complement Naive Bayes
    • 1.9.4. Bernoulli Naive Bayes
    • 1.9.5. Out-of-core naive Bayes model fitting
  • 1.10. Decision Trees
    • 1.10.1. Classification
    • 1.10.2. Regression
    • 1.10.3. Multi-output problems
    • 1.10.4. Complexity
    • 1.10.5. Tips on practical use
    • 1.10.6. Tree algorithms: ID3, C4.5, C5.0 and CART
    • 1.10.7. Mathematical formulation
      • 1.10.7.1. Classification criteria
      • 1.10.7.2. Regression criteria
  • 1.11. Ensemble methods
    • 1.11.1. Bagging meta-estimator
    • 1.11.2. Forests of randomized trees
      • 1.11.2.1. Random Forests
      • 1.11.2.2. Extremely Randomized Trees
      • 1.11.2.3. Parameters
      • 1.11.2.4. Parallelization
      • 1.11.2.5. Feature importance evaluation
      • 1.11.2.6. Totally Random Trees Embedding
    • 1.11.3. AdaBoost
      • 1.11.3.1. Usage
    • 1.11.4. Gradient Tree Boosting
      • 1.11.4.1. Classification
      • 1.11.4.2. Regression
      • 1.11.4.3. Fitting additional weak-learners
      • 1.11.4.4. Controlling the tree size
      • 1.11.4.5. Mathematical formulation
        • 1.11.4.5.1. Loss Functions
      • 1.11.4.6. Regularization
        • 1.11.4.6.1. Shrinkage
        • 1.11.4.6.2. Subsampling
      • 1.11.4.7. Interpretation
        • 1.11.4.7.1. Feature importance
    • 1.11.5. Voting Classifier
      • 1.11.5.1. Majority Class Labels (Majority/Hard Voting)
        • 1.11.5.1.1. Usage
      • 1.11.5.2. Weighted Average Probabilities (Soft Voting)
      • 1.11.5.3. Using the VotingClassifier with GridSearchCV
        • 1.11.5.3.1. Usage
    • 1.11.6. Voting Regressor
  • 1.12. Multiclass and multilabel algorithms
    • 1.12.1. Multilabel classification format
    • 1.12.2. One-Vs-The-Rest
      • 1.12.2.1. Multiclass learning
      • 1.12.2.2. Multilabel learning
    • 1.12.3. One-Vs-One
      • 1.12.3.1. Multiclass learning
    • 1.12.4. Error-Correcting Output-Codes
      • 1.12.4.1. Multiclass learning
    • 1.12.5. Multioutput regression
    • 1.12.6. Multioutput classification
    • 1.12.7. Classifier Chain
    • 1.12.8. Regressor Chain
  • 1.13. Feature selection
    • 1.13.1. Removing features with low variance
    • 1.13.2. Univariate feature selection
    • 1.13.3. Recursive feature elimination
    • 1.13.4. Feature selection using SelectFromModel
      • 1.13.4.1. L1-based feature selection
      • 1.13.4.2. Tree-based feature selection
    • 1.13.5. Feature selection as part of a pipeline
  • 1.14. Semi-Supervised
    • 1.14.1. Label Propagation
  • 1.15. Isotonic regression
  • 1.16. Probability calibration
  • 1.17. Neural network models (supervised)
    • 1.17.1. Multi-layer Perceptron
    • 1.17.2. Classification
    • 1.17.3. Regression
    • 1.17.4. Regularization
    • 1.17.5. Algorithms
    • 1.17.6. Complexity
    • 1.17.7. Mathematical formulation
    • 1.17.8. Tips on Practical Use
    • 1.17.9. More control with warm_start
• 2. Unsupervised learning
  • 2.1. Gaussian mixture models
    • 2.1.1. Gaussian Mixture
      • 2.1.1.1. Pros and cons of class GaussianMixture
        • 2.1.1.1.1. Pros
        • 2.1.1.1.2. Cons
      • 2.1.1.2. Selecting the number of components in a classical Gaussian Mixture Model
      • 2.1.1.3. Estimation algorithm Expectation-maximization
    • 2.1.2. Variational Bayesian Gaussian Mixture
      • 2.1.2.1. Estimation algorithm: variational inference
      • 2.1.2.2. Pros and cons of variational inference with BayesianGaussianMixture
        • 2.1.2.2.1. Pros
        • 2.1.2.2.2. Cons
      • 2.1.2.3. The Dirichlet Process
  • 2.2. Manifold learning
    • 2.2.1. Introduction
    • 2.2.2. Isomap
      • 2.2.2.1. Complexity
    • 2.2.3. Locally Linear Embedding
      • 2.2.3.1. Complexity
    • 2.2.4. Modified Locally Linear Embedding
      • 2.2.4.1. Complexity
    • 2.2.5. Hessian Eigenmapping
      • 2.2.5.1. Complexity
    • 2.2.6. Spectral Embedding
      • 2.2.6.1. Complexity
    • 2.2.7. Local Tangent Space Alignment
      • 2.2.7.1. Complexity
    • 2.2.8. Multi-dimensional Scaling (MDS)
      • 2.2.8.1. Metric MDS
      • 2.2.8.2. Nonmetric MDS
    • 2.2.9. t-distributed Stochastic Neighbor Embedding (t-SNE)
      • 2.2.9.1. Optimizing t-SNE
      • 2.2.9.2. Barnes-Hut t-SNE
    • 2.2.10. Tips on practical use
  • 2.3. Clustering
    • 2.3.1. Overview of clustering methods
    • 2.3.2. K-means
      • 2.3.2.1. Mini Batch K-Means
    • 2.3.3. Affinity Propagation
    • 2.3.4. Mean Shift
    • 2.3.5. Spectral clustering
      • 2.3.5.1. Different label assignment strategies
      • 2.3.5.2. Spectral Clustering Graphs
    • 2.3.6. Hierarchical clustering
      • 2.3.6.1. Different linkage type: Ward, complete, average, and single linkage
      • 2.3.6.2. Adding connectivity constraints
      • 2.3.6.3. Varying the metric
    • 2.3.7. DBSCAN
    • 2.3.8. OPTICS
    • 2.3.9. Birch
    • 2.3.10. Clustering performance evaluation
      • 2.3.10.1. Adjusted Rand index
        • 2.3.10.1.1. Advantages
        • 2.3.10.1.2. Drawbacks
        • 2.3.10.1.3. Mathematical formulation
      • 2.3.10.2. Mutual Information based scores
        • 2.3.10.2.1. Advantages
        • 2.3.10.2.2. Drawbacks
        • 2.3.10.2.3. Mathematical formulation
      • 2.3.10.3. Homogeneity, completeness and V-measure
        • 2.3.10.3.1. Advantages
        • 2.3.10.3.2. Drawbacks
        • 2.3.10.3.3. Mathematical formulation
      • 2.3.10.4. Fowlkes-Mallows scores
        • 2.3.10.4.1. Advantages
        • 2.3.10.4.2. Drawbacks
      • 2.3.10.5. Silhouette Coefficient
        • 2.3.10.5.1. Advantages
        • 2.3.10.5.2. Drawbacks
      • 2.3.10.6. Calinski-Harabasz Index
        • 2.3.10.6.1. Advantages
        • 2.3.10.6.2. Drawbacks
      • 2.3.10.7. Davies-Bouldin Index
        • 2.3.10.7.1. Advantages
        • 2.3.10.7.2. Drawbacks
      • 2.3.10.8. Contingency Matrix
        • 2.3.10.8.1. Advantages
        • 2.3.10.8.2. Drawbacks
  • 2.4. Biclustering
    • 2.4.1. Spectral Co-Clustering
      • 2.4.1.1. Mathematical formulation
    • 2.4.2. Spectral Biclustering
      • 2.4.2.1. Mathematical formulation
    • 2.4.3. Biclustering evaluation
  • 2.5. Decomposing signals in components (matrix factorization problems)
    • 2.5.1. Principal component analysis (PCA)
      • 2.5.1.1. Exact PCA and probabilistic interpretation
      • 2.5.1.2. Incremental PCA
      • 2.5.1.3. PCA using randomized SVD
      • 2.5.1.4. Kernel PCA
      • 2.5.1.5. Sparse principal components analysis (SparsePCA and MiniBatchSparsePCA)
    • 2.5.2. Truncated singular value decomposition and latent semantic analysis
    • 2.5.3. Dictionary Learning
      • 2.5.3.1. Sparse coding with a precomputed dictionary
      • 2.5.3.2. Generic dictionary learning
      • 2.5.3.3. Mini-batch dictionary learning
    • 2.5.4. Factor Analysis
    • 2.5.5. Independent component analysis (ICA)
    • 2.5.6. Non-negative matrix factorization (NMF or NNMF)
      • 2.5.6.1. NMF with the Frobenius norm
      • 2.5.6.2. NMF with a beta-divergence
    • 2.5.7. Latent Dirichlet Allocation (LDA)
  • 2.6. Covariance estimation
    • 2.6.1. Empirical covariance
    • 2.6.2. Shrunk Covariance
      • 2.6.2.1. Basic shrinkage
      • 2.6.2.2. Ledoit-Wolf shrinkage
      • 2.6.2.3. Oracle Approximating Shrinkage
    • 2.6.3. Sparse inverse covariance
    • 2.6.4. Robust Covariance Estimation
      • 2.6.4.1. Minimum Covariance Determinant
  • 2.7. Novelty and Outlier Detection
    • 2.7.1. Overview of outlier detection methods
    • 2.7.2. Novelty Detection
    • 2.7.3. Outlier Detection
      • 2.7.3.1. Fitting an elliptic envelope
      • 2.7.3.2. Isolation Forest
      • 2.7.3.3. Local Outlier Factor
    • 2.7.4. Novelty detection with Local Outlier Factor
  • 2.8. Density Estimation
    • 2.8.1. Density Estimation: Histograms
    • 2.8.2. Kernel Density Estimation
  • 2.9. Neural network models (unsupervised)
    • 2.9.1. Restricted Boltzmann machines
      • 2.9.1.1. Graphical model and parametrization
      • 2.9.1.2. Bernoulli Restricted Boltzmann machines
      • 2.9.1.3. Stochastic Maximum Likelihood learning
• 3. Model selection and evaluation
  • 3.1. Cross-validation: evaluating estimator performance
    • 3.1.1. Computing cross-validated metrics
      • 3.1.1.1. The cross_validate function and multiple metric evaluation
      • 3.1.1.2. Obtaining predictions by cross-validation
    • 3.1.2. Cross validation iterators
      • 3.1.2.1. Cross-validation iterators for i.i.d. data
        • 3.1.2.1.1. K-fold
        • 3.1.2.1.2. Repeated K-Fold
        • 3.1.2.1.3. Leave One Out (LOO)
        • 3.1.2.1.4. Leave P Out (LPO)
        • 3.1.2.1.5. Random permutations cross-validation a.k.a. Shuffle & Split
      • 3.1.2.2. Cross-validation iterators with stratification based on class labels.
        • 3.1.2.2.1. Stratified k-fold
        • 3.1.2.2.2. Stratified Shuffle Split
      • 3.1.2.3. Cross-validation iterators for grouped data.
        • 3.1.2.3.1. Group k-fold
        • 3.1.2.3.2. Leave One Group Out
        • 3.1.2.3.3. Leave P Groups Out
        • 3.1.2.3.4. Group Shuffle Split
      • 3.1.2.4. Predefined Fold-Splits / Validation-Sets
      • 3.1.2.5. Cross validation of time series data
        • 3.1.2.5.1. Time Series Split
    • 3.1.3. A note on shuffling
    • 3.1.4. Cross validation and model selection
  • 3.2. Tuning the hyper-parameters of an estimator
    • 3.2.1. Exhaustive Grid Search
    • 3.2.2. Randomized Parameter Optimization
    • 3.2.3. Tips for parameter search
      • 3.2.3.1. Specifying an objective metric
      • 3.2.3.2. Specifying multiple metrics for evaluation
      • 3.2.3.3. Composite estimators and parameter spaces
      • 3.2.3.4. Model selection: development and evaluation
      • 3.2.3.5. Parallelism
      • 3.2.3.6. Robustness to failure
    • 3.2.4. Alternatives to brute force parameter search
      • 3.2.4.1. Model specific cross-validation
        • 3.2.4.1.1. sklearn.linear_model.ElasticNetCV
        • 3.2.4.1.2. sklearn.linear_model.LarsCV
        • 3.2.4.1.3. sklearn.linear_model.LassoCV
          • 3.2.4.1.3.1. Examples using sklearn.linear_model.LassoCV
        • 3.2.4.1.4. sklearn.linear_model.LassoLarsCV
          • 3.2.4.1.4.1. Examples using sklearn.linear_model.LassoLarsCV
        • 3.2.4.1.5. sklearn.linear_model.LogisticRegressionCV
        • 3.2.4.1.6. sklearn.linear_model.MultiTaskElasticNetCV
        • 3.2.4.1.7. sklearn.linear_model.MultiTaskLassoCV
        • 3.2.4.1.8. sklearn.linear_model.OrthogonalMatchingPursuitCV
          • 3.2.4.1.8.1. Examples using sklearn.linear_model.OrthogonalMatchingPursuitCV
        • 3.2.4.1.9. sklearn.linear_model.RidgeCV
          • 3.2.4.1.9.1. Examples using sklearn.linear_model.RidgeCV
        • 3.2.4.1.10. sklearn.linear_model.RidgeClassifierCV
      • 3.2.4.2. Information Criterion
        • 3.2.4.2.1. sklearn.linear_model.LassoLarsIC
          • 3.2.4.2.1.1. Examples using sklearn.linear_model.LassoLarsIC
      • 3.2.4.3. Out of Bag Estimates
        • 3.2.4.3.1. sklearn.ensemble.RandomForestClassifier
          • 3.2.4.3.1.1. Examples using sklearn.ensemble.RandomForestClassifier
        • 3.2.4.3.2. sklearn.ensemble.RandomForestRegressor
          • 3.2.4.3.2.1. Examples using sklearn.ensemble.RandomForestRegressor
        • 3.2.4.3.3. sklearn.ensemble.ExtraTreesClassifier
          • 3.2.4.3.3.1. Examples using sklearn.ensemble.ExtraTreesClassifier
        • 3.2.4.3.4. sklearn.ensemble.ExtraTreesRegressor
          • 3.2.4.3.4.1. Examples using sklearn.ensemble.ExtraTreesRegressor
        • 3.2.4.3.5. sklearn.ensemble.GradientBoostingClassifier
          • 3.2.4.3.5.1. Examples using sklearn.ensemble.GradientBoostingClassifier
        • 3.2.4.3.6. sklearn.ensemble.GradientBoostingRegressor
          • 3.2.4.3.6.1. Examples using sklearn.ensemble.GradientBoostingRegressor
  • 3.3. Model evaluation: quantifying the quality of predictions
    • 3.3.1. The scoring parameter: defining model evaluation rules
      • 3.3.1.1. Common cases: predefined values
      • 3.3.1.2. Defining your scoring strategy from metric functions
      • 3.3.1.3. Implementing your own scoring object
      • 3.3.1.4. Using multiple metric evaluation
    • 3.3.2. Classification metrics
      • 3.3.2.1. From binary to multiclass and multilabel
      • 3.3.2.2. Accuracy score
      • 3.3.2.3. Balanced accuracy score
      • 3.3.2.4. Cohen’s kappa
      • 3.3.2.5. Confusion matrix
      • 3.3.2.6. Classification report
      • 3.3.2.7. Hamming loss
      • 3.3.2.8. Precision, recall and F-measures
        • 3.3.2.8.1. Binary classification
        • 3.3.2.8.2. Multiclass and multilabel classification
      • 3.3.2.9. Jaccard similarity coefficient score
      • 3.3.2.10. Hinge loss
      • 3.3.2.11. Log loss
      • 3.3.2.12. Matthews correlation coefficient
      • 3.3.2.13. Multi-label confusion matrix
      • 3.3.2.14. Receiver operating characteristic (ROC)
      • 3.3.2.15. Zero one loss
      • 3.3.2.16. Brier score loss
    • 3.3.3. Multilabel ranking metrics
      • 3.3.3.1. Coverage error
      • 3.3.3.2. Label ranking average precision
      • 3.3.3.3. Ranking loss
    • 3.3.4. Regression metrics
      • 3.3.4.1. Explained variance score
      • 3.3.4.2. Max error
      • 3.3.4.3. Mean absolute error
      • 3.3.4.4. Mean squared error
      • 3.3.4.5. Mean squared logarithmic error
      • 3.3.4.6. Median absolute error
      • 3.3.4.7. R² score, the coefficient of determination
    • 3.3.5. Clustering metrics
    • 3.3.6. Dummy estimators
  • 3.4. Model persistence
    • 3.4.1. Persistence example
    • 3.4.2. Security & maintainability limitations
  • 3.5. Validation curves: plotting scores to evaluate models
    • 3.5.1. Validation curve
    • 3.5.2. Learning curve
• 4. Inspection
  • 4.1. Partial dependence plots
• 5. Dataset transformations
  • 5.1. Pipelines and composite estimators
    • 5.1.1. Pipeline: chaining estimators
      • 5.1.1.1. Usage
        • 5.1.1.1.1. Construction
        • 5.1.1.1.2. Accessing steps
        • 5.1.1.1.3. Nested parameters
      • 5.1.1.2. Notes
      • 5.1.1.3. Caching transformers: avoid repeated computation
    • 5.1.2. Transforming target in regression
    • 5.1.3. FeatureUnion: composite feature spaces
      • 5.1.3.1. Usage
    • 5.1.4. ColumnTransformer for heterogeneous data
  • 5.2. Feature extraction
    • 5.2.1. Loading features from dicts
    • 5.2.2. Feature hashing
      • 5.2.2.1. Implementation details
    • 5.2.3. Text feature extraction
      • 5.2.3.1. The Bag of Words representation
      • 5.2.3.2. Sparsity
      • 5.2.3.3. Common Vectorizer usage
        • 5.2.3.3.1. Using stop words
      • 5.2.3.4. Tf–idf term weighting
      • 5.2.3.5. Decoding text files
      • 5.2.3.6. Applications and examples
      • 5.2.3.7. Limitations of the Bag of Words representation
      • 5.2.3.8. Vectorizing a large text corpus with the hashing trick
      • 5.2.3.9. Performing out-of-core scaling with HashingVectorizer
      • 5.2.3.10. Customizing the vectorizer classes
    • 5.2.4. Image feature extraction
      • 5.2.4.1. Patch extraction
      • 5.2.4.2. Connectivity graph of an image
  • 5.3. Preprocessing data
    • 5.3.1. Standardization, or mean removal and variance scaling
      • 5.3.1.1. Scaling features to a range
      • 5.3.1.2. Scaling sparse data
      • 5.3.1.3. Scaling data with outliers
      • 5.3.1.4. Centering kernel matrices
    • 5.3.2. Non-linear transformation
      • 5.3.2.1. Mapping to a Uniform distribution
      • 5.3.2.2. Mapping to a Gaussian distribution
    • 5.3.3. Normalization
    • 5.3.4. Encoding categorical features
    • 5.3.5. Discretization
      • 5.3.5.1. K-bins discretization
      • 5.3.5.2. Feature binarization
    • 5.3.6. Imputation of missing values
    • 5.3.7. Generating polynomial features
    • 5.3.8. Custom transformers
  • 5.4. Imputation of missing values
    • 5.4.1. Univariate vs. Multivariate Imputation
    • 5.4.2. Univariate feature imputation
    • 5.4.3. Multivariate feature imputation
      • 5.4.3.1. Flexibility of IterativeImputer
      • 5.4.3.2. Multiple vs. Single Imputation
    • 5.4.4. References
    • 5.4.5. Marking imputed values
  • 5.5. Unsupervised dimensionality reduction
    • 5.5.1. PCA: principal component analysis
    • 5.5.2. Random projections
    • 5.5.3. Feature agglomeration
  • 5.6. Random Projection
    • 5.6.1. The Johnson-Lindenstrauss lemma
    • 5.6.2. Gaussian random projection
    • 5.6.3. Sparse random projection
  • 5.7. Kernel Approximation
    • 5.7.1. Nystroem Method for Kernel Approximation
    • 5.7.2. Radial Basis Function Kernel
    • 5.7.3. Additive Chi Squared Kernel
    • 5.7.4. Skewed Chi Squared Kernel
    • 5.7.5. Mathematical Details
  • 5.8. Pairwise metrics, Affinities and Kernels
    • 5.8.1. Cosine similarity
    • 5.8.2. Linear kernel
    • 5.8.3. Polynomial kernel
    • 5.8.4. Sigmoid kernel
    • 5.8.5. RBF kernel
    • 5.8.6. Laplacian kernel
    • 5.8.7. Chi-squared kernel
  • 5.9. Transforming the prediction target (y)
    • 5.9.1. Label binarization
    • 5.9.2. Label encoding
• 6. Dataset loading utilities
  • 6.1. General dataset API
  • 6.2. Toy datasets
    • 6.2.1. Boston house prices dataset
    • 6.2.2. Iris plants dataset
    • 6.2.3. Diabetes dataset
    • 6.2.4. Optical recognition of handwritten digits dataset
    • 6.2.5. Linnerrud dataset
    • 6.2.6. Wine recognition dataset
    • 6.2.7. Breast cancer wisconsin (diagnostic) dataset
  • 6.3. Real world datasets
    • 6.3.1. The Olivetti faces dataset
    • 6.3.2. The 20 newsgroups text dataset
      • 6.3.2.1. Usage
      • 6.3.2.2. Converting text to vectors
      • 6.3.2.3. Filtering text for more realistic training
    • 6.3.3. The Labeled Faces in the Wild face recognition dataset
      • 6.3.3.1. Usage
      • 6.3.3.2. Examples
    • 6.3.4. Forest covertypes
    • 6.3.5. RCV1 dataset
    • 6.3.6. Kddcup 99 dataset
    • 6.3.7. California Housing dataset
  • 6.4. Generated datasets
    • 6.4.1. Generators for classification and clustering
      • 6.4.1.1. Single label
      • 6.4.1.2. Multilabel
      • 6.4.1.3. Biclustering
    • 6.4.2. Generators for regression
    • 6.4.3. Generators for manifold learning
    • 6.4.4. Generators for decomposition
  • 6.5. Loading other datasets
    • 6.5.1. Sample images
    • 6.5.2. Datasets in svmlight / libsvm format
    • 6.5.3. Downloading datasets from the openml.org repository
      • 6.5.3.1. Dataset Versions
    • 6.5.4. Loading from external datasets
• 7. Computing with scikit-learn
  • 7.1. Strategies to scale computationally: bigger data
    • 7.1.1. Scaling with instances using out-of-core learning
      • 7.1.1.1. Streaming instances
      • 7.1.1.2. Extracting features
      • 7.1.1.3. Incremental learning
      • 7.1.1.4. Examples
      • 7.1.1.5. Notes
  • 7.2. Computational Performance
    • 7.2.1. Prediction Latency
      • 7.2.1.1. Bulk versus Atomic mode
      • 7.2.1.2. Configuring Scikit-learn for reduced validation overhead
      • 7.2.1.3. Influence of the Number of Features
      • 7.2.1.4. Influence of the Input Data Representation
      • 7.2.1.5. Influence of the Model Complexity
      • 7.2.1.6. Feature Extraction Latency
    • 7.2.2. Prediction Throughput
    • 7.2.3. Tips and Tricks
      • 7.2.3.1. Linear algebra libraries
      • 7.2.3.2. Limiting Working Memory
      • 7.2.3.3. Model Compression
      • 7.2.3.4. Model Reshaping
      • 7.2.3.5. Links
  • 7.3. Parallelism, resource management, and configuration
    • 7.3.1. Parallel and distributed computing
    • 7.3.2. Configuration switches
      • 7.3.2.1. Python runtime
      • 7.3.2.2. Environment variables