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</style><table class="sidebar sidebar-collapse nomobile nowraplinks"><tbody><tr><td class="sidebar-pretitle">Part of a series on</td></tr><tr><th class="sidebar-title-with-pretitle"><a href="Machine_learning" title="Machine learning">Machine learning</a><br>and <a href="Data_mining" title="Data mining">data mining</a></th></tr><tr><td class="sidebar-content">
<div class="sidebar-list mw-collapsible mw-collapsed machine-learning-list-title"><div class="sidebar-list-title" style="border-top:1px solid #aaa; text-align:center;;color: var(--color-base)">Paradigms</div><div class="sidebar-list-content mw-collapsible-content hlist">
<ul><li><a href="Supervised_learning" title="Supervised learning">Supervised learning</a></li>
<li><a href="Unsupervised_learning" title="Unsupervised learning">Unsupervised learning</a></li>
<li><a href="Semi-supervised_learning" class="mw-redirect" title="Semi-supervised learning">Semi-supervised learning</a></li>
<li><a href="Self-supervised_learning" title="Self-supervised learning">Self-supervised learning</a></li>
<li><a href="Reinforcement_learning" title="Reinforcement learning">Reinforcement learning</a></li>
<li><a href="Meta-learning_(computer_science)" title="Meta-learning (computer science)">Meta-learning</a></li>
<li><a href="Online_machine_learning" title="Online machine learning">Online learning</a></li>
<li><a href="Batch_learning" class="mw-redirect" title="Batch learning">Batch learning</a></li>
<li><a href="Curriculum_learning" title="Curriculum learning">Curriculum learning</a></li>
<li><a href="Rule-based_machine_learning" title="Rule-based machine learning">Rule-based learning</a></li>
<li><a href="Neuro-symbolic_AI" title="Neuro-symbolic AI">Neuro-symbolic AI</a></li>
<li><a href="Neuromorphic_engineering" class="mw-redirect" title="Neuromorphic engineering">Neuromorphic engineering</a></li>
<li><a href="Quantum_machine_learning" title="Quantum machine learning">Quantum machine learning</a></li></ul></div></div></td>
</tr><tr><td class="sidebar-content">
<div class="sidebar-list mw-collapsible machine-learning-list-title"><div class="sidebar-list-title" style="border-top:1px solid #aaa; text-align:center;;color: var(--color-base)">Problems</div><div class="sidebar-list-content mw-collapsible-content hlist">
<ul><li><a href="Statistical_classification" title="Statistical classification">Classification</a></li>
<li><a href="Generative_model" title="Generative model">Generative modeling</a></li>
<li><a href="Regression_analysis" title="Regression analysis">Regression</a></li>
<li><a href="Cluster_analysis" title="Cluster analysis">Clustering</a></li>
<li><a href="Dimensionality_reduction" title="Dimensionality reduction">Dimensionality reduction</a></li>
<li><a href="Density_estimation" title="Density estimation">Density estimation</a></li>
<li><a href="Anomaly_detection" title="Anomaly detection">Anomaly detection</a></li>
<li><a href="Data_cleaning" class="mw-redirect" title="Data cleaning">Data cleaning</a></li>
<li><a href="Automated_machine_learning" title="Automated machine learning">AutoML</a></li>
<li><a href="Association_rule_learning" title="Association rule learning">Association rules</a></li>
<li><a href="Semantic_analysis_(machine_learning)" title="Semantic analysis (machine learning)">Semantic analysis</a></li>
<li><a href="Structured_prediction" title="Structured prediction">Structured prediction</a></li>

<li><a href="Feature_learning" title="Feature learning">Feature learning</a></li>
<li><a href="Learning_to_rank" title="Learning to rank">Learning to rank</a></li>
<li><a href="Grammar_induction" title="Grammar induction">Grammar induction</a></li>
<li><a href="Ontology_learning" title="Ontology learning">Ontology learning</a></li>
<li><a href="Multimodal_learning" title="Multimodal learning">Multimodal learning</a></li></ul></div></div></td>
</tr><tr><td class="sidebar-content">
<div class="sidebar-list mw-collapsible mw-collapsed machine-learning-list-title"><div class="sidebar-list-title" style="border-top:1px solid #aaa; text-align:center;;color: var(--color-base)"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="Supervised_learning" title="Supervised learning">Supervised learning</a><br><span class="nobold"><span style="font-size: 85%;">(<b><a href="Statistical_classification" title="Statistical classification">classification</a></b>&nbsp;• <b><a href="Regression_analysis" title="Regression analysis">regression</a></b>)</span></span> </div></div><div class="sidebar-list-content mw-collapsible-content hlist">
<ul><li><a href="Apprenticeship_learning" title="Apprenticeship learning">Apprenticeship learning</a></li>
<li><a href="Decision_tree_learning" title="Decision tree learning">Decision trees</a></li>
<li><a href="Ensemble_learning" title="Ensemble learning">Ensembles</a>
<ul><li><a href="Bootstrap_aggregating" title="Bootstrap aggregating">Bagging</a></li>
<li><a href="Boosting_(machine_learning)" title="Boosting (machine learning)">Boosting</a></li>
<li><a href="Random_forest" title="Random forest">Random forest</a></li></ul></li>
<li><a href="K-nearest_neighbors_algorithm" title="K-nearest neighbors algorithm"><i>k</i>-NN</a></li>
<li><a href="Linear_regression" title="Linear regression">Linear regression</a></li>
<li><a href="Naive_Bayes_classifier" title="Naive Bayes classifier">Naive Bayes</a></li>
<li><a href="Artificial_neural_network" class="mw-redirect" title="Artificial neural network">Artificial neural networks</a></li>
<li><a href="Logistic_regression" title="Logistic regression">Logistic regression</a></li>
<li><a href="Perceptron" title="Perceptron">Perceptron</a></li>
<li><a href="Relevance_vector_machine" title="Relevance vector machine">Relevance vector machine (RVM)</a></li>
<li><a href="Support_vector_machine" title="Support vector machine">Support vector machine (SVM)</a></li></ul></div></div></td>
</tr><tr><td class="sidebar-content">
<div class="sidebar-list mw-collapsible mw-collapsed machine-learning-list-title"><div class="sidebar-list-title" style="border-top:1px solid #aaa; text-align:center;;color: var(--color-base)"><a href="Cluster_analysis" title="Cluster analysis">Clustering</a></div><div class="sidebar-list-content mw-collapsible-content hlist">
<ul><li><a href="BIRCH" title="BIRCH">BIRCH</a></li>
<li><a href="CURE_algorithm" title="CURE algorithm">CURE</a></li>
<li><a href="Hierarchical_clustering" title="Hierarchical clustering">Hierarchical</a></li>
<li><a href="K-means_clustering" title="K-means clustering"><i>k</i>-means</a></li>
<li><a href="Fuzzy_clustering" title="Fuzzy clustering">Fuzzy</a></li>
<li><a href="Expectation%E2%80%93maximization_algorithm" title="Expectation–maximization algorithm">Expectation–maximization (EM)</a></li>
<li><br><a href="DBSCAN" title="DBSCAN">DBSCAN</a></li>
<li><a href="OPTICS_algorithm" title="OPTICS algorithm">OPTICS</a></li>
<li><a href="Mean_shift" title="Mean shift">Mean shift</a></li></ul></div></div></td>
</tr><tr><td class="sidebar-content">
<div class="sidebar-list mw-collapsible mw-collapsed machine-learning-list-title"><div class="sidebar-list-title" style="border-top:1px solid #aaa; text-align:center;;color: var(--color-base)"><a href="Dimensionality_reduction" title="Dimensionality reduction">Dimensionality reduction</a></div><div class="sidebar-list-content mw-collapsible-content hlist">
<ul><li><a href="Factor_analysis" title="Factor analysis">Factor analysis</a></li>
<li><a href="Canonical_correlation" title="Canonical correlation">CCA</a></li>
<li><a href="Independent_component_analysis" title="Independent component analysis">ICA</a></li>
<li><a href="Linear_discriminant_analysis" title="Linear discriminant analysis">LDA</a></li>
<li><a href="Non-negative_matrix_factorization" title="Non-negative matrix factorization">NMF</a></li>
<li><a href="Principal_component_analysis" title="Principal component analysis">PCA</a></li>
<li><a href="Proper_generalized_decomposition" title="Proper generalized decomposition">PGD</a></li>
<li><a href="T-distributed_stochastic_neighbor_embedding" title="T-distributed stochastic neighbor embedding">t-SNE</a></li>
<li><a href="Sparse_dictionary_learning" title="Sparse dictionary learning">SDL</a></li></ul></div></div></td>
</tr><tr><td class="sidebar-content">
<div class="sidebar-list mw-collapsible mw-collapsed machine-learning-list-title"><div class="sidebar-list-title" style="border-top:1px solid #aaa; text-align:center;;color: var(--color-base)"><a href="Structured_prediction" title="Structured prediction">Structured prediction</a></div><div class="sidebar-list-content mw-collapsible-content hlist">
<ul><li><a href="Graphical_model" title="Graphical model">Graphical models</a>
<ul><li><a href="Bayesian_network" title="Bayesian network">Bayes net</a></li>
<li><a href="Conditional_random_field" title="Conditional random field">Conditional random field</a></li>
<li><a href="Hidden_Markov_model" title="Hidden Markov model">Hidden Markov</a></li></ul></li></ul></div></div></td>
</tr><tr><td class="sidebar-content">
<div class="sidebar-list mw-collapsible mw-collapsed machine-learning-list-title"><div class="sidebar-list-title" style="border-top:1px solid #aaa; text-align:center;;color: var(--color-base)"><a href="Anomaly_detection" title="Anomaly detection">Anomaly detection</a></div><div class="sidebar-list-content mw-collapsible-content hlist">
<ul><li><a href="Random_sample_consensus" title="Random sample consensus">RANSAC</a></li>
<li><a href="K-nearest_neighbors_algorithm" title="K-nearest neighbors algorithm"><i>k</i>-NN</a></li>
<li><a href="Local_outlier_factor" title="Local outlier factor">Local outlier factor</a></li>
<li><a href="Isolation_forest" title="Isolation forest">Isolation forest</a></li></ul></div></div></td>
</tr><tr><td class="sidebar-content">
<div class="sidebar-list mw-collapsible mw-collapsed machine-learning-list-title"><div class="sidebar-list-title" style="border-top:1px solid #aaa; text-align:center;;color: var(--color-base)"><a href="Neural_network_(machine_learning)" title="Neural network (machine learning)">Neural networks</a></div><div class="sidebar-list-content mw-collapsible-content hlist">
<ul><li><a href="Autoencoder" title="Autoencoder">Autoencoder</a></li>
<li><a href="Deep_learning" title="Deep learning">Deep learning</a></li>
<li><a href="Feedforward_neural_network" title="Feedforward neural network">Feedforward neural network</a></li>
<li><a href="Recurrent_neural_network" title="Recurrent neural network">Recurrent neural network</a>
<ul><li><a href="Long_short-term_memory" title="Long short-term memory">LSTM</a></li>
<li><a href="Gated_recurrent_unit" title="Gated recurrent unit">GRU</a></li>
<li><a href="Echo_state_network" title="Echo state network">ESN</a></li>
<li><a href="Reservoir_computing" title="Reservoir computing">reservoir computing</a></li></ul></li>
<li><a href="Boltzmann_machine" title="Boltzmann machine">Boltzmann machine</a>
<ul><li><a href="Restricted_Boltzmann_machine" title="Restricted Boltzmann machine">Restricted</a></li></ul></li>
<li><a href="Generative_adversarial_network" title="Generative adversarial network">GAN</a></li>
<li><a href="Diffusion_model" title="Diffusion model">Diffusion model</a></li>
<li><a href="Self-organizing_map" title="Self-organizing map">SOM</a></li>
<li><a href="Convolutional_neural_network" title="Convolutional neural network">Convolutional neural network</a>
<ul><li><a href="U-Net" title="U-Net">U-Net</a></li>
<li><a href="LeNet" title="LeNet">LeNet</a></li>
<li><a href="AlexNet" title="AlexNet">AlexNet</a></li>
<li><a href="DeepDream" title="DeepDream">DeepDream</a></li></ul></li>
<li><a href="Neural_field" title="Neural field">Neural field</a>
<ul><li><a href="Neural_radiance_field" title="Neural radiance field">Neural radiance field</a></li>
<li><a href="Physics-informed_neural_networks" title="Physics-informed neural networks">Physics-informed neural networks</a></li></ul></li>
<li><a href="Transformer_(deep_learning_architecture)" title="Transformer (deep learning architecture)">Transformer</a>
<ul><li><a href="Vision_transformer" title="Vision transformer">Vision</a></li></ul></li>
<li><a href="Mamba_(deep_learning_architecture)" title="Mamba (deep learning architecture)">Mamba</a></li>
<li><a href="Spiking_neural_network" title="Spiking neural network">Spiking neural network</a></li>
<li><a href="Memtransistor" title="Memtransistor">Memtransistor</a></li>
<li><a href="Electrochemical_RAM" title="Electrochemical RAM">Electrochemical RAM</a> (ECRAM)</li></ul></div></div></td>
</tr><tr><td class="sidebar-content">
<div class="sidebar-list mw-collapsible mw-collapsed machine-learning-list-title"><div class="sidebar-list-title" style="border-top:1px solid #aaa; text-align:center;;color: var(--color-base)"><a href="Reinforcement_learning" title="Reinforcement learning">Reinforcement learning</a></div><div class="sidebar-list-content mw-collapsible-content hlist">
<ul><li><a href="Q-learning" title="Q-learning">Q-learning</a></li>
<li><a href="Policy_gradient_method" title="Policy gradient method">Policy gradient</a></li>
<li><a href="State%E2%80%93action%E2%80%93reward%E2%80%93state%E2%80%93action" title="State–action–reward–state–action">SARSA</a></li>
<li><a href="Temporal_difference_learning" title="Temporal difference learning">Temporal difference (TD)</a></li>
<li><a href="Multi-agent_reinforcement_learning" title="Multi-agent reinforcement learning">Multi-agent</a>
<ul><li><a href="Self-play_(reinforcement_learning_technique)" class="mw-redirect" title="Self-play (reinforcement learning technique)">Self-play</a></li></ul></li></ul></div></div></td>
</tr><tr><td class="sidebar-content">
<div class="sidebar-list mw-collapsible mw-collapsed machine-learning-list-title"><div class="sidebar-list-title" style="border-top:1px solid #aaa; text-align:center;;color: var(--color-base)">Learning with humans</div><div class="sidebar-list-content mw-collapsible-content hlist">
<ul><li><a href="Active_learning_(machine_learning)" title="Active learning (machine learning)">Active learning</a></li>
<li><a href="Crowdsourcing" title="Crowdsourcing">Crowdsourcing</a></li>
<li><a href="Human-in-the-loop" title="Human-in-the-loop">Human-in-the-loop</a></li>
<li><a href="Mechanistic_interpretability" title="Mechanistic interpretability">Mechanistic interpretability</a></li>
<li><a href="Reinforcement_learning_from_human_feedback" title="Reinforcement learning from human feedback">RLHF</a></li></ul></div></div></td>
</tr><tr><td class="sidebar-content">
<div class="sidebar-list mw-collapsible mw-collapsed machine-learning-list-title"><div class="sidebar-list-title" style="border-top:1px solid #aaa; text-align:center;;color: var(--color-base)">Model diagnostics</div><div class="sidebar-list-content mw-collapsible-content hlist">
<ul><li><a href="Coefficient_of_determination" title="Coefficient of determination">Coefficient of determination</a></li>
<li><a href="Confusion_matrix" title="Confusion matrix">Confusion matrix</a></li>
<li><a href="Learning_curve_(machine_learning)" title="Learning curve (machine learning)">Learning curve</a></li>
<li><a href="Receiver_operating_characteristic" title="Receiver operating characteristic">ROC curve</a></li></ul></div></div></td>
</tr><tr><td class="sidebar-content">
<div class="sidebar-list mw-collapsible mw-collapsed machine-learning-list-title"><div class="sidebar-list-title" style="border-top:1px solid #aaa; text-align:center;;color: var(--color-base)">Mathematical foundations</div><div class="sidebar-list-content mw-collapsible-content hlist">
<ul><li><a href="Kernel_machines" class="mw-redirect" title="Kernel machines">Kernel machines</a></li>
<li><a href="Bias%E2%80%93variance_tradeoff" title="Bias–variance tradeoff">Bias–variance tradeoff</a></li>
<li><a href="Computational_learning_theory" title="Computational learning theory">Computational learning theory</a></li>
<li><a href="Empirical_risk_minimization" title="Empirical risk minimization">Empirical risk minimization</a></li>
<li><a href="Occam_learning" title="Occam learning">Occam learning</a></li>
<li><a href="Probably_approximately_correct_learning" title="Probably approximately correct learning">PAC learning</a></li>
<li><a href="Statistical_learning_theory" title="Statistical learning theory">Statistical learning</a></li>
<li><a href="Vapnik%E2%80%93Chervonenkis_theory" title="Vapnik–Chervonenkis theory">VC theory</a></li>
<li><a href="Topological_deep_learning" title="Topological deep learning">Topological deep learning</a></li></ul></div></div></td>
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<div class="sidebar-list mw-collapsible mw-collapsed machine-learning-list-title"><div class="sidebar-list-title" style="border-top:1px solid #aaa; text-align:center;;color: var(--color-base)">Journals and conferences</div><div class="sidebar-list-content mw-collapsible-content hlist">
<ul><li><a href="AAAI_Conference_on_Artificial_Intelligence" title="AAAI Conference on Artificial Intelligence">AAAI</a></li>
<li><a href="ECML_PKDD" title="ECML PKDD">ECML PKDD</a></li>
<li><a href="Conference_on_Neural_Information_Processing_Systems" title="Conference on Neural Information Processing Systems">NeurIPS</a></li>
<li><a href="International_Conference_on_Machine_Learning" title="International Conference on Machine Learning">ICML</a></li>
<li><a href="International_Conference_on_Learning_Representations" title="International Conference on Learning Representations">ICLR</a></li>
<li><a href="International_Joint_Conference_on_Artificial_Intelligence" title="International Joint Conference on Artificial Intelligence">IJCAI</a></li>
<li><a href="Machine_Learning_(journal)" title="Machine Learning (journal)">ML</a></li>
<li><a href="Journal_of_Machine_Learning_Research" title="Journal of Machine Learning Research">JMLR</a></li></ul></div></div></td>
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<div class="sidebar-list mw-collapsible mw-collapsed machine-learning-list-title"><div class="sidebar-list-title" style="border-top:1px solid #aaa; text-align:center;;color: var(--color-base)">Related articles</div><div class="sidebar-list-content mw-collapsible-content hlist">
<ul><li><a href="Glossary_of_artificial_intelligence" title="Glossary of artificial intelligence">Glossary of artificial intelligence</a></li>
<li><a href="List_of_datasets_for_machine-learning_research" title="List of datasets for machine-learning research">List of datasets for machine-learning research</a>
<ul><li><a href="List_of_datasets_in_computer_vision_and_image_processing" title="List of datasets in computer vision and image processing">List of datasets in computer vision and image processing</a></li></ul></li>
<li><a href="Outline_of_machine_learning" title="Outline of machine learning">Outline of machine learning</a></li></ul></div></div></td>
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<p><b>Feature engineering</b> is a preprocessing step in <a href="Supervised_machine_learning" class="mw-redirect" title="Supervised machine learning">supervised machine learning</a> and <a href="Statistical_modeling" class="mw-redirect" title="Statistical modeling">statistical modeling</a><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> which transforms raw data into a more effective set of inputs. Each input comprises several attributes, known as features. By providing models with relevant information, feature engineering significantly enhances their predictive accuracy and decision-making capability.<sup id="cite_ref-auto1_2-0" class="reference"><a href="#cite_note-auto1-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>
</p><p>Beyond machine learning, the principles of feature engineering are applied in various scientific fields, including physics. For example, physicists construct <a href="Dimensionless_quantity" title="Dimensionless quantity">dimensionless numbers</a> such as the <a href="Reynolds_number" title="Reynolds number">Reynolds number</a> in <a href="Fluid_dynamics" title="Fluid dynamics">fluid dynamics</a>, the <a href="Nusselt_number" title="Nusselt number">Nusselt number</a> in <a href="Heat_transfer" title="Heat transfer">heat transfer</a>, and the <a href="Archimedes_number" title="Archimedes number">Archimedes number</a> in <a href="Sedimentation" title="Sedimentation">sedimentation</a>. They also develop first approximations of solutions, such as analytical solutions for the <a href="Strength_of_materials" title="Strength of materials">strength of materials</a> in mechanics.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>
</p>
<meta property="mw:PageProp/toc">
<div class="mw-heading mw-heading2"><h2 id="Clustering">Clustering</h2></div>
<p>One of the applications of feature engineering has been clustering of feature-objects or sample-objects in a dataset. Especially, feature engineering based on <a href="Matrix_decomposition" title="Matrix decomposition">matrix decomposition</a> has been extensively used for data clustering under non-negativity constraints on the feature coefficients. These include <i>Non-Negative Matrix Factorization</i> (NMF),<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> <i>Non-Negative Matrix-Tri Factorization</i> (NMTF),<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> <i>Non-Negative Tensor Decomposition/Factorization</i> (NTF/NTD),<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> etc. The non-negativity constraints on coefficients of the feature vectors mined by the above-stated algorithms yields a part-based representation, and different factor matrices exhibit natural clustering properties. Several extensions of the above-stated feature engineering methods have been reported in literature, including <i>orthogonality-constrained factorization</i> for hard clustering, and <i>manifold learning</i> to overcome inherent issues with these algorithms.
</p><p>Other classes of feature engineering algorithms include leveraging a common hidden structure across multiple inter-related datasets to obtain a consensus (common) clustering scheme. An example is <i>Multi-view Classification based on Consensus Matrix Decomposition</i> (MCMD),<sup id="cite_ref-auto1_2-1" class="reference"><a href="#cite_note-auto1-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> which mines a common clustering scheme across multiple datasets. MCMD is designed to output two types of class labels (scale-variant and scale-invariant clustering), and:
</p>
<ul><li>is <a href="Robustness_(computer_science)" title="Robustness (computer science)">computationally robust</a> to missing information,</li>
<li>can obtain shape- and scale-based outliers,</li>
<li>and can handle high-dimensional data effectively.</li></ul>
<p>Coupled matrix and tensor decompositions are popular in multi-view feature engineering.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading2"><h2 id="Predictive_modelling">Predictive modelling</h2></div>
<p>Feature engineering in <a href="Machine_learning" title="Machine learning">machine learning</a> and <a href="Statistical_modeling" class="mw-redirect" title="Statistical modeling">statistical modeling</a> involves selecting, creating, transforming, and extracting data features. Key components include feature creation from existing data, transforming and imputing missing or invalid features, reducing data dimensionality through methods like <a href="Principal_component_analysis" title="Principal component analysis">Principal Components Analysis</a> (PCA), <a href="Independent_component_analysis" title="Independent component analysis">Independent Component Analysis</a> (ICA), and <a href="Linear_discriminant_analysis" title="Linear discriminant analysis">Linear Discriminant Analysis</a> (LDA), and selecting the most relevant features for model training based on importance scores and <a href="Correlation_matrices" class="mw-redirect" title="Correlation matrices">correlation matrices</a>.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup>
</p><p>Features vary in significance.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> Even relatively insignificant features may contribute to a model. <a href="Feature_selection" title="Feature selection">Feature selection</a> can reduce the number of features to prevent a model from becoming too specific to the training data set (overfitting).<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup>
</p><p>Feature explosion occurs when the number of identified features is too large for effective model estimation or optimization. Common causes include:
</p>
<ul><li>Feature templates - implementing feature templates instead of coding new features</li>
<li>Feature combinations - combinations that cannot be represented by a linear system</li></ul>
<p>Feature explosion can be limited via techniques such as: <a href="Regularization_(mathematics)" title="Regularization (mathematics)">regularization</a>, <a href="Kernel_method" title="Kernel method">kernel methods</a>, and <a href="Feature_selection" title="Feature selection">feature selection</a>.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading2"><h2 id="Automation">Automation</h2></div>
<p>Automation of feature engineering is a research topic that dates back to the 1990s.<sup id="cite_ref-:0_14-0" class="reference"><a href="#cite_note-:0-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> Machine learning software that incorporates <a href="Automated_feature_engineering" class="mw-redirect" title="Automated feature engineering">automated feature engineering</a> has been commercially available since 2016.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> Related academic literature can be roughly separated into two types:
</p>
<ul><li>Multi-relational decision tree learning (MRDTL) uses a supervised algorithm that is similar to a <a href="Decision_tree" title="Decision tree">decision tree</a>.</li>
<li>Deep Feature Synthesis uses simpler methods.</li></ul>
<div class="mw-heading mw-heading3"><h3 id="Multi-relational_decision_tree_learning_(MRDTL)">Multi-relational decision tree learning (MRDTL)</h3></div>
<p>Multi-relational Decision Tree Learning (MRDTL) extends traditional decision tree methods to <a href="Relational_database" title="Relational database">relational databases</a>, handling complex data relationships across tables. It innovatively uses selection graphs as <a href="Decision_node" class="mw-redirect" title="Decision node">decision nodes</a>, refined systematically until a specific termination criterion is reached.<sup id="cite_ref-:0_14-1" class="reference"><a href="#cite_note-:0-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup>
</p><p>Most MRDTL studies base implementations on relational databases, which results in many redundant operations. These redundancies can be reduced by using techniques such as tuple id propagation.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading3"><h3 id="Open-source_implementations">Open-source implementations</h3></div>
<p>There are a number of open-source libraries and tools that automate feature engineering on relational data and time series:
</p>
<ul><li><b>featuretools</b> is a <a href="Python_(programming_language)" title="Python (programming language)">Python</a> library for transforming time series and relational data into feature matrices for machine learning.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup></li>
<li><b>MCMD:</b> An open-source feature engineering algorithm for joint clustering of multiple datasets . <sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-auto1_2-2" class="reference"><a href="#cite_note-auto1-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup></li>
<li><b>OneBM</b> or One-Button Machine combines feature transformations and feature selection on relational data with feature selection techniques.<sup id="cite_ref-auto2_22-0" class="reference"><a href="#cite_note-auto2-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> <style data-mw-deduplicate="TemplateStyles:r1244412712">
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</style><blockquote class="templatequote"><p>[OneBM] helps data scientists reduce data exploration time allowing them to try and error many ideas in short time. On the other hand, it enables non-experts, who are not familiar with data science, to quickly extract value from their data with a little effort, time, and cost.<sup id="cite_ref-auto2_22-1" class="reference"><a href="#cite_note-auto2-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup></p></blockquote></li>
<li><b>getML community</b> is an open source tool for automated feature engineering on time series and relational data.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-auto_24-0" class="reference"><a href="#cite_note-auto-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> It is implemented in <a href="C_(programming_language)" title="C (programming language)">C</a>/<a href="C%2B%2B" title="C++">C++</a> with a Python interface.<sup id="cite_ref-auto_24-1" class="reference"><a href="#cite_note-auto-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> It has been shown to be at least 60 times faster than tsflex, tsfresh, tsfel, featuretools or kats.<sup id="cite_ref-auto_24-2" class="reference"><a href="#cite_note-auto-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup></li>
<li><b>tsfresh</b> is a Python library for feature extraction on time series data.<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> It evaluates the quality of the features using hypothesis testing.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup></li>
<li><b>tsflex</b> is an open source Python library for extracting features from time series data.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> Despite being 100% written in Python, it has been shown to be faster and more memory efficient than tsfresh, seglearn or tsfel.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup></li>
<li><b>seglearn</b> is an extension for multivariate, sequential time series data to the <a href="Scikit-learn" title="Scikit-learn">scikit-learn</a> Python library.<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup></li>
<li><b>tsfel</b> is a Python package for feature extraction on time series data.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup></li>
<li><b>kats</b> is a Python toolkit for analyzing time series data.<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup></li></ul>
<div class="mw-heading mw-heading3"><h3 id="Deep_feature_synthesis">Deep feature synthesis</h3></div>
<p>The deep feature synthesis (DFS) algorithm beat 615 of 906 human teams in a competition.<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading2"><h2 id="Feature_stores">Feature stores</h2></div>
<p>The feature store is where the features are stored and organized for the explicit purpose of being used to either train models (by data scientists) or make predictions (by applications that have a trained model). It is a central location where you can either create or update groups of features created from multiple different data sources, or create and update new datasets from those feature groups for training models or for use in applications that do not want to compute the features but just retrieve them when it needs them to make predictions.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup>
</p><p>A feature store includes the ability to store code used to generate features, apply the code to raw data, and serve those features to models upon request. Useful capabilities include feature versioning and policies governing the circumstances under which features can be used.<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup>
</p><p>Feature stores can be standalone software tools or built into machine learning platforms.
</p>
<div class="mw-heading mw-heading2"><h2 id="Alternatives">Alternatives</h2></div>
<p>Feature engineering can be a time-consuming and error-prone process, as it requires domain expertise and often involves trial and error.<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> <a href="Deep_learning" title="Deep learning">Deep learning algorithms</a> may be used to process a large raw dataset without having to resort to feature engineering.<sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> However, deep learning algorithms still require careful preprocessing and cleaning of the input data.<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> In addition, choosing the right architecture, hyperparameters, and optimization algorithm for a deep neural network can be a challenging and iterative process.<sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2></div>
<ul><li><a href="Covariate" class="mw-redirect" title="Covariate">Covariate</a></li>
<li><a href="Data_transformation_(statistics)" title="Data transformation (statistics)">Data transformation</a></li>
<li><a href="Feature_extraction" class="mw-redirect" title="Feature extraction">Feature extraction</a></li>
<li><a href="Feature_learning" title="Feature learning">Feature learning</a></li>
<li><a href="Hashing_trick" class="mw-redirect" title="Hashing trick">Hashing trick</a></li>
<li><a href="Instrumental_variables_estimation" title="Instrumental variables estimation">Instrumental variables estimation</a></li>
<li><a href="Kernel_method" title="Kernel method">Kernel method</a></li>
<li><a href="List_of_datasets_for_machine_learning_research" class="mw-redirect" title="List of datasets for machine learning research">List of datasets for machine learning research</a></li>
<li><a href="Scale_co-occurrence_matrix" title="Scale co-occurrence matrix">Scale co-occurrence matrix</a></li>
<li><a href="Space_mapping" title="Space mapping">Space mapping</a></li></ul>
<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>
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<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>
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<ul><li><cite id="CITEREFBoehmkeGreenwell2019" class="citation book cs1">Boehmke B, Greenwell B (2019). "Feature &amp; Target Engineering". <i>Hands-On Machine Learning with R</i>. Chapman &amp; Hall. pp.&nbsp;<span class="nowrap">41–</span>75. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a>&nbsp;<bdi>978-1-138-49568-5</bdi>.</cite></li>
<li><cite id="CITEREFZhengCasari2018" class="citation book cs1">Zheng A, Casari A (2018). <i>Feature Engineering for Machine Learning: Principles and Techniques for Data Scientists</i>. O'Reilly. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a>&nbsp;<bdi>978-1-4919-5324-2</bdi>.</cite></li>
<li><cite id="CITEREFZumelMount2020" class="citation book cs1">Zumel N, Mount (2020). "Data Engineering and Data Shaping". <i>Practical Data Science with R</i> (2nd&nbsp;ed.). Manning. pp.&nbsp;<span class="nowrap">113–</span>160. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a>&nbsp;<bdi>978-1-61729-587-4</bdi>.</cite></li>
<li><cite id="CITEREFAbououf,_M.Singh,_S.Mizouni,_R.Otrok,_H.2024" class="citation cs2 cs1-prop-vanc-accept">Abououf, M., Singh, S., Mizouni, R., Otrok, H. (2024), <span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.1016/j.iot.2024.101191">"Feature engineering and deep learning-based approach for event detection in Medical Internet of Things (MIoT)"</a></span>, <i>Internet of Things</i>, <b>26</b> 101191, Elsevier BV, <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.iot.2024.101191">10.1016/j.iot.2024.101191</a></cite></li>
<li><cite id="CITEREFChiccoOnetoTavazzi2022" class="citation journal cs1">Chicco D, Oneto L, Tavazzi E (December 2022). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9754225">"Eleven quick tips for data cleaning and feature engineering"</a>. <i>PLOS Computational Biology</i>. <b>18</b> (12): e1010718. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2022PLSCB..18E0718C">2022PLSCB..18E0718C</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1371%2Fjournal.pcbi.1010718">10.1371/journal.pcbi.1010718</a></span>. <a href="PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a>&nbsp;<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9754225">9754225</a></span>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a>&nbsp;<a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/36520712">36520712</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a>&nbsp;<a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:254733288">254733288</a>.</cite></li></ul>
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