Package: pyod
Deployment & Documentation & Stats & LicenseRead Me FirstWelcome to PyOD, a versatile Python library for detecting anomalies in multivariate data. Whether you’re tackling a small-scale project or large datasets, PyOD offers a range of algorithms to suit your needs.For time-series outlier detection, please useTODS.For graph outlier detection, please usePyGOD.Performance Comparison & Datasets: We have a 45-page, the most comprehensiveanomaly detection benchmark paper. The fullyopen-sourced ADBenchcompares 30 anomaly detection algorithms on 57 benchmark datasets.Learn more about anomaly detection@Anomaly Detection ResourcesPyOD on Distributed Systems: you could also runPyOD on databricks.About PyODPyOD, established in 2017, has become a go-toPython libraryfordetecting anomalous/outlying objectsin
multivariate data. This exciting yet challenging field is commonly referred asOutlier DetectionorAnomaly Detection.PyOD includes more than 50 detection algorithms, from classical LOF (SIGMOD 2000) to
the cutting-edge ECOD and DIF (TKDE 2022 and 2023). Since 2017, PyOD has been successfully used in numerous academic researches and
commercial products with more than17 million downloads.
It is also well acknowledged by the machine learning community with various dedicated posts/tutorials, includingAnalytics Vidhya,KDnuggets, andTowards Data Science.PyOD is featured for:Unified, User-Friendly Interfaceacross various algorithms.Wide Range of Models, from classic techniques to the latest deep learning methods.High Performance & Efficiency, leveragingnumbaandjoblibfor JIT compilation and parallel processing.Fast Training & Prediction, achieved through the SUOD framework[48].Outlier Detection with 5 Lines of Code:# Example: Training an ECOD detectorfrompyod.models.ecodimportECODclf=ECOD()clf.fit(X_train)y_train_scores=clf.decision_scores_# Outlier scores for training datay_test_scores=clf.decision_function(X_test)# Outlier scores for test dataSelecting the Right Algorithm:. Unsure where to start? Consider these robust and interpretable options:ECOD: Example of using ECOD for outlier detectionIsolation Forest: Example of using Isolation Forest for outlier detectionAlternatively, exploreMetaODfor a data-driven approach.Citing PyOD:PyOD paperis published inJournal of Machine Learning Research (JMLR)(MLOSS track).
If you use PyOD in a scientific publication, we would appreciate
citations to the following paper:@article{zhao2019pyod,
    author  = {Zhao, Yue and Nasrullah, Zain and Li, Zheng},
    title   = {PyOD: A Python Toolbox for Scalable Outlier Detection},
    journal = {Journal of Machine Learning Research},
    year    = {2019},
    volume  = {20},
    number  = {96},
    pages   = {1-7},
    url     = {http://jmlr.org/papers/v20/19-011.html}
}or:Zhao, Y., Nasrullah, Z. and Li, Z., 2019. PyOD: A Python Toolbox for Scalable Outlier Detection. Journal of machine learning research (JMLR), 20(96), pp.1-7.For a broader perspective on anomaly detection, see our NeurIPS papersADBench: Anomaly Detection Benchmark Paper&ADGym: Design Choices for Deep Anomaly Detection:@article{han2022adbench,
    title={Adbench: Anomaly detection benchmark},
    author={Han, Songqiao and Hu, Xiyang and Huang, Hailiang and Jiang, Minqi and Zhao, Yue},
    journal={Advances in Neural Information Processing Systems},
    volume={35},
    pages={32142--32159},
    year={2022}
}

@article{jiang2023adgym,
    title={ADGym: Design Choices for Deep Anomaly Detection},
    author={Jiang, Minqi and Hou, Chaochuan and Zheng, Ao and Han, Songqiao and Huang, Hailiang and Wen, Qingsong and Hu, Xiyang and Zhao, Yue},
    journal={Advances in Neural Information Processing Systems},
    volume={36},
    year={2023}
}Table of Contents:InstallationAPI Cheatsheet & ReferenceADBench Benchmark and DatasetsModel Save & LoadFast Train with SUODThresholding Outlier ScoresImplemented AlgorithmsQuick Start for Outlier DetectionHow to ContributeInclusion CriteriaInstallationPyOD is designed for easy installation using eitherpiporconda.
We recommend using the latest version of PyOD due to frequent updates and enhancements:pipinstallpyod# normal installpipinstall--upgradepyod# or update if neededcondainstall-cconda-forgepyodAlternatively, you could clone and run setup.py file:gitclonehttps://github.com/yzhao062/pyod.gitcdpyodpipinstall.Required Dependencies:Python 3.6 or higherjoblibmatplotlibnumpy>=1.19numba>=0.51scipy>=1.5.1scikit_learn>=0.22.0sixOptional Dependencies (see details below):combo (optional, required for models/combination.py and FeatureBagging)keras/tensorflow (optional, required for AutoEncoder, and other deep learning models)suod (optional, required for running SUOD model)xgboost (optional, required for XGBOD)pythresh (optional, required for thresholding)Warning:
PyOD includes several neural network-based models, such as AutoEncoders, implemented in Tensorflow and PyTorch. These deep learning libraries are not automatically installed by PyOD to avoid conflicts with existing installations. If you plan to use neural-net based models, please ensure these libraries are installed. See theneural-net FAQfor guidance. Additionally, xgboost is not installed by default but is required for models like XGBOD.API Cheatsheet & ReferenceThe full API Reference is available atPyOD Documentation. Below is a quick cheatsheet for all detectors:fit(X): Fit the detector. The parameter y is ignored in unsupervised methods.decision_function(X): Predict raw anomaly scores for X using the fitted detector.predict(X): Determine whether a sample is an outlier or not as binary labels using the fitted detector.predict_proba(X): Estimate the probability of a sample being an outlier using the fitted detector.predict_confidence(X): Assess the model’s confidence on a per-sample basis (applicable in predict and predict_proba)[33].Key Attributes of a fitted model:decision_scores_: Outlier scores of the training data. Higher scores typically indicate more abnormal behavior. Outliers usually have higher scores.labels_: Binary labels of the training data, where 0 indicates inliers and 1 indicates outliers/anomalies.ADBench Benchmark and DatasetsWe just released a 45-page, the most comprehensiveADBench: Anomaly Detection Benchmark[15].
The fullyopen-sourced ADBenchcompares 30 anomaly detection algorithms on 57 benchmark datasets.The organization ofADBenchis provided below:For a simpler visualization, we makethe comparison of selected modelsviacompare_all_models.py.Model Save & LoadPyOD takes a similar approach of sklearn regarding model persistence.
Seemodel persistencefor clarification.In short, we recommend to use joblib or pickle for saving and loading PyOD models.
See“examples/save_load_model_example.py”for an example.
In short, it is simple as below:fromjoblibimportdump,load# save the modeldump(clf,'clf.joblib')# load the modelclf=load('clf.joblib')It is known that there are challenges in saving neural network models.
Check#328and#88for temporary workaround.Fast Train with SUODFast training and prediction: it is possible to train and predict with
a large number of detection models in PyOD by leveraging SUOD framework[48].
SeeSUOD PaperandSUOD example.frompyod.models.suodimportSUOD# initialized a group of outlier detectors for accelerationdetector_list=[LOF(n_neighbors=15),LOF(n_neighbors=20),LOF(n_neighbors=25),LOF(n_neighbors=35),COPOD(),IForest(n_estimators=100),IForest(n_estimators=200)]# decide the number of parallel process, and the combination method# then clf can be used as any outlier detection modelclf=SUOD(base_estimators=detector_list,n_jobs=2,combination='average',verbose=False)Thresholding Outlier ScoresA more data based approach can be taken when setting the contamination level.
By using a thresholding method, guessing an abritrary value can be replaced
with tested techniques for seperating inliers and outliers. Refer toPyThreshfor
a more in depth look at thresholding.frompyod.models.knnimportKNNfrompyod.models.thresholdsimportFILTER# Set the outlier detection and thresholding methodsclf=KNN(contamination=FILTER())Implemented AlgorithmsPyOD toolkit consists of four major functional groups:(i) Individual Detection Algorithms:TypeAbbrAlgorithmYearRefProbabilisticECODUnsupervised Outlier Detection Using Empirical Cumulative Distribution Functions2022[28]ProbabilisticABODAngle-Based Outlier Detection2008[22]ProbabilisticFastABODFast Angle-Based Outlier Detection using approximation2008[22]ProbabilisticCOPODCOPOD: Copula-Based Outlier Detection2020[27]ProbabilisticMADMedian Absolute Deviation (MAD)1993[19]ProbabilisticSOSStochastic Outlier Selection2012[20]ProbabilisticQMCDQuasi-Monte Carlo Discrepancy outlier detection2001[11]ProbabilisticKDEOutlier Detection with Kernel Density Functions2007[24]ProbabilisticSamplingRapid distance-based outlier detection via sampling2013[40]ProbabilisticGMMProbabilistic Mixture Modeling for Outlier Analysis[1][Ch.2]Linear ModelPCAPrincipal Component Analysis (the sum of weighted projected distances to the eigenvector hyperplanes)2003[39]Linear ModelKPCAKernel Principal Component Analysis2007[18]Linear ModelMCDMinimum Covariance Determinant (use the mahalanobis distances as the outlier scores)1999[16][35]Linear ModelCDUse Cook’s distance for outlier detection1977[10]Linear ModelOCSVMOne-Class Support Vector Machines2001[38]Linear ModelLMDDDeviation-based Outlier Detection (LMDD)1996[6]Proximity-BasedLOFLocal Outlier Factor2000[8]Proximity-BasedCOFConnectivity-Based Outlier Factor2002[41]Proximity-Based(Incremental) COFMemory Efficient Connectivity-Based Outlier Factor (slower but reduce storage complexity)2002[41]Proximity-BasedCBLOFClustering-Based Local Outlier Factor2003[17]Proximity-BasedLOCILOCI: Fast outlier detection using the local correlation integral2003[31]Proximity-BasedHBOSHistogram-based Outlier Score2012[12]Proximity-BasedkNNk Nearest Neighbors (use the distance to the kth nearest neighbor as the outlier score)2000[34]Proximity-BasedAvgKNNAverage kNN (use the average distance to k nearest neighbors as the outlier score)2002[5]Proximity-BasedMedKNNMedian kNN (use the median distance to k nearest neighbors as the outlier score)2002[5]Proximity-BasedSODSubspace Outlier Detection2009[23]Proximity-BasedRODRotation-based Outlier Detection2020[4]Outlier EnsemblesIForestIsolation Forest2008[29]Outlier EnsemblesINNEIsolation-based Anomaly Detection Using Nearest-Neighbor Ensembles2018[7]Outlier EnsemblesDIFDeep Isolation Forest for Anomaly Detection2023[43]Outlier EnsemblesFBFeature Bagging2005[25]Outlier EnsemblesLSCPLSCP: Locally Selective Combination of Parallel Outlier Ensembles2019[47]Outlier EnsemblesXGBODExtreme Boosting Based Outlier Detection(Supervised)2018[46]Outlier EnsemblesLODALightweight On-line Detector of Anomalies2016[32]Outlier EnsemblesSUODSUOD: Accelerating Large-scale Unsupervised Heterogeneous Outlier Detection(Acceleration)2021[48]Neural NetworksAutoEncoderFully connected AutoEncoder (use reconstruction error as the outlier score)[1][Ch.3]Neural NetworksVAEVariational AutoEncoder (use reconstruction error as the outlier score)2013[21]Neural NetworksBeta-VAEVariational AutoEncoder (all customized loss term by varying gamma and capacity)2018[9]Neural NetworksSO_GAALSingle-Objective Generative Adversarial Active Learning2019[30]Neural NetworksMO_GAALMultiple-Objective Generative Adversarial Active Learning2019[30]Neural NetworksDeepSVDDDeep One-Class Classification2018[36]Neural NetworksAnoGANAnomaly Detection with Generative Adversarial Networks2017[37]Neural NetworksALADAdversarially learned anomaly detection2018[45]Graph-basedR-GraphOutlier detection by R-graph2017[44]Graph-basedLUNARLUNAR: Unifying Local Outlier Detection Methods via Graph Neural Networks2022[13](ii) Outlier Ensembles & Outlier Detector Combination Frameworks:TypeAbbrAlgorithmYearRefOutlier EnsemblesFBFeature Bagging2005[25]Outlier EnsemblesLSCPLSCP: Locally Selective Combination of Parallel Outlier Ensembles2019[47]Outlier EnsemblesXGBODExtreme Boosting Based Outlier Detection(Supervised)2018[46]Outlier EnsemblesLODALightweight On-line Detector of Anomalies2016[32]Outlier EnsemblesSUODSUOD: Accelerating Large-scale Unsupervised Heterogeneous Outlier Detection(Acceleration)2021[48]Outlier EnsemblesINNEIsolation-based Anomaly Detection Using Nearest-Neighbor Ensembles2018[7]CombinationAverageSimple combination by averaging the scores2015[2]CombinationWeighted AverageSimple combination by averaging the scores with detector weights2015[2]CombinationMaximizationSimple combination by taking the maximum scores2015[2]CombinationAOMAverage of Maximum2015[2]CombinationMOAMaximization of Average2015[2]CombinationMedianSimple combination by taking the median of the scores2015[2]Combinationmajority VoteSimple combination by taking the majority vote of the labels (weights can be used)2015[2](iii) Outlier Detection Score Thresholding Methods:TypeAbbrAlgorithmDocumentationKernel-BasedAUCPArea Under Curve PercentageAUCPStatistical Moment-BasedBOOTBootstrappingBOOTNormality-BasedCHAUChauvenet’s CriterionCHAULinear ModelCLFTrained Linear ClassifierCLFcluster-BasedCLUSTClustering BasedCLUSTKernel-BasedCPDChange Point DetectionCPDTransformation-BasedDECOMPDecompositionDECOMPNormality-BasedDSNDistance Shift from NormalDSNCurve-BasedEBElliptical BoundaryEBKernel-BasedFGDFixed Gradient DescentFGDFilter-BasedFILTERFiltering BasedFILTERCurve-BasedFWFMFull Width at Full MinimumFWFMStatistical Test-BasedGESDGeneralized Extreme Studentized DeviateGESDFilter-BasedHISTHistogram BasedHISTQuantile-BasedIQRInter-Quartile RegionIQRStatistical Moment-BasedKARCHKarcher mean (Riemannian Center of Mass)KARCHStatistical Moment-BasedMADMedian Absolute DeviationMADStatistical Test-BasedMCSTMonte Carlo Shapiro TestsMCSTEnsembles-BasedMETAMeta-model Trained ClassifierMETATransformation-BasedMOLLFriedrichs’ MollifierMOLLStatistical Test-BasedMTTModified Thompson Tau TestMTTLinear ModelOCSVMOne-Class Support Vector MachineOCSVMQuantile-BasedQMCDQuasi-Monte Carlo DiscrepancyQMCDLinear ModelREGRRegression BasedREGRNeural NetworksVAEVariational AutoencoderVAECurve-BasedWINDTopological Winding NumberWINDTransformation-BasedYJYeo-Johnson TransformationYJNormality-BasedZSCOREZ-scoreZSCORE(iV) Utility Functions:TypeNameFunctionDocumentationDatagenerate_dataSynthesized data generation; normal data is generated by a multivariate Gaussian and outliers are generated by a uniform distributiongenerate_dataDatagenerate_data_clustersSynthesized data generation in clusters; more complex data patterns can be created with multiple clustersgenerate_data_clustersStatwpearsonrCalculate the weighted Pearson correlation of two sampleswpearsonrUtilityget_label_nTurn raw outlier scores into binary labels by assign 1 to top n outlier scoresget_label_nUtilityprecision_n_scorescalculate precision @ rank nprecision_n_scoresQuick Start for Outlier DetectionPyOD has been well acknowledged by the machine learning community with a few featured posts and tutorials.Analytics Vidhya:An Awesome Tutorial to Learn Outlier Detection in Python using PyOD LibraryKDnuggets:Intuitive Visualization of Outlier Detection Methods,An Overview of Outlier Detection Methods from PyODTowards Data Science:Anomaly Detection for DummiesComputer Vision News (March 2019):Python Open Source Toolbox for Outlier Detection“examples/knn_example.py”demonstrates the basic API of using kNN detector.It is noted that the API across all other algorithms are consistent/similar.More detailed instructions for running examples can be found inexamples directory.Initialize a kNN detector, fit the model, and make the prediction.frompyod.models.knnimportKNN# kNN detector# train kNN detectorclf_name='KNN'clf=KNN()clf.fit(X_train)# get the prediction label and outlier scores of the training datay_train_pred=clf.labels_# binary labels (0: inliers, 1: outliers)y_train_scores=clf.decision_scores_# raw outlier scores# get the prediction on the test datay_test_pred=clf.predict(X_test)# outlier labels (0 or 1)y_test_scores=clf.decision_function(X_test)# outlier scores# it is possible to get the prediction confidence as welly_test_pred,y_test_pred_confidence=clf.predict(X_test,return_confidence=True)# outlier labels (0 or 1) and confidence in the range of [0,1]Evaluate the prediction by ROC and Precision @ Rank n (p@n).frompyod.utils.dataimportevaluate_print# evaluate and print the resultsprint("\nOn Training Data:")evaluate_print(clf_name,y_train,y_train_scores)print("\nOn Test Data:")evaluate_print(clf_name,y_test,y_test_scores)See a sample output & visualization.OnTrainingData:KNNROC:1.0,precision@rankn:1.0OnTestData:KNNROC:0.9989,precision@rankn:0.9visualize(clf_name,X_train,y_train,X_test,y_test,y_train_pred,y_test_pred,show_figure=True,save_figure=False)Visualization (knn_figure):How to ContributeYou are welcome to contribute to this exciting project:Please first check Issue lists for “help wanted” tag and comment the one
you are interested. We will assign the issue to you.Fork the master branch and add your improvement/modification/fix.Create a pull request todevelopment branchand follow the pull request templatePR templateAutomatic tests will be triggered. Make sure all tests are passed. Please make sure all added modules are accompanied with proper test functions.To make sure the code has the same style and standard, please refer to abod.py, hbos.py, or feature_bagging.py for example.You are also welcome to share your ideas by opening an issue or dropping me an email atzhaoy@cmu.edu:)Inclusion CriteriaSimilarly toscikit-learn,
We mainly consider well-established algorithms for inclusion.
A rule of thumb is at least two years since publication, 50+ citations, and usefulness.However, we encourage the author(s) of newly proposed models to share and add your implementation into PyOD
for boosting ML accessibility and reproducibility.
This exception only applies if you could commit to the maintenance of your model for at least two year period.Reference[1](1,2)Aggarwal, C.C., 2015. Outlier analysis. In Data mining (pp. 237-263). Springer, Cham.[2](1,2,3,4,5,6,7)Aggarwal, C.C. and Sathe, S., 2015. Theoretical foundations and algorithms for outlier ensembles.ACM SIGKDD Explorations Newsletter, 17(1), pp.24-47.[3]Aggarwal, C.C. and Sathe, S., 2017. Outlier ensembles: An introduction. Springer.[4]Almardeny, Y., Boujnah, N. and Cleary, F., 2020. A Novel Outlier Detection Method for Multivariate Data.IEEE Transactions on Knowledge and Data Engineering.[5](1,2)Angiulli, F. and Pizzuti, C., 2002, August. Fast outlier detection in high dimensional spaces. InEuropean Conference on Principles of Data Mining and Knowledge Discoverypp. 15-27.[6]Arning, A., Agrawal, R. and Raghavan, P., 1996, August. A Linear Method for Deviation Detection in Large Databases. InKDD(Vol. 1141, No. 50, pp. 972-981).[7](1,2)Bandaragoda, T. 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