Welcome to PyOD documentation!#

Deployment & Documentation & Stats & License

News: We just released a 45-page, the most comprehensive anomaly detection benchmark paper. The fully open-sourced ADBench compares 30 anomaly detection algorithms on 57 benchmark datasets.

For time-series outlier detection, please use TODS. For graph outlier detection, please use PyGOD.

PyOD is the most comprehensive and scalable Python library for detecting outlying objects in multivariate data. This exciting yet challenging field is commonly referred as Outlier Detection or Anomaly Detection.

PyOD includes more than 40 detection algorithms, from classical LOF (SIGMOD 2000) to the latest ECOD (TKDE 2022). Since 2017, PyOD [AZNL19] has been successfully used in numerous academic researches and commercial products with more than 10 million downloads. It is also well acknowledged by the machine learning community with various dedicated posts/tutorials, including Analytics Vidhya, KDnuggets, and Towards Data Science.

PyOD is featured for:

Unified APIs, detailed documentation, and interactive examples across various algorithms.
Advanced models, including classical distance and density estimation, latest deep learning methods, and emerging algorithms like ECOD.
Optimized performance with JIT and parallelization using numba and joblib.
Fast training & prediction with SUOD [AZHC+21].

Outlier Detection with 5 Lines of Code:

# train an ECOD detector
from pyod.models.ecod import ECOD
clf = ECOD()
clf.fit(X_train)

# get outlier scores
y_train_scores = clf.decision_scores_  # raw outlier scores on the train data
y_test_scores = clf.decision_function(X_test)  # predict raw outlier scores on test

Personal suggestion on selecting an OD algorithm. If you do not know which algorithm to try, go with:

ECOD: Example of using ECOD for outlier detection
Isolation Forest: Example of using Isolation Forest for outlier detection

They are both fast and interpretable. Or, you could try more data-driven approach MetaOD.

Citing PyOD:

PyOD paper is published in Journal 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.

If you want more general insights of anomaly detection and/or algorithm performance comparison, please see our NeurIPS 2022 paper ADBench: Anomaly Detection Benchmark:

@inproceedings{han2022adbench,
    title={ADBench: Anomaly Detection Benchmark},
    author={Songqiao Han and Xiyang Hu and Hailiang Huang and Mingqi Jiang and Yue Zhao},
    booktitle={Neural Information Processing Systems (NeurIPS)}
    year={2022},
}

Key Links and Resources:

Benchmark#

We just released a 45-page, the most comprehensive ADBench: Anomaly Detection Benchmark. The fully open-sourced ADBench compares 30 anomaly detection algorithms on 57 benchmark datasets.

The organization of ADBench is provided below:

Implemented Algorithms#

PyOD toolkit consists of three major functional groups:

(i) Individual Detection Algorithms :

Type	Abbr	Algorithm	Year	Class	Ref
Probabilistic	ECOD	Unsupervised Outlier Detection Using Empirical Cumulative Distribution Functions	2022	`pyod.models.ecod.ECOD`	[ALZH+22]
Probabilistic	COPOD	COPOD: Copula-Based Outlier Detection	2020	`pyod.models.copod.COPOD`	[ALZB+20]
Probabilistic	ABOD	Angle-Based Outlier Detection	2008	`pyod.models.abod.ABOD`	[AKZ+08]
Probabilistic	FastABOD	Fast Angle-Based Outlier Detection using approximation	2008	`pyod.models.abod.ABOD`	[AKZ+08]
Probabilistic	MAD	Median Absolute Deviation (MAD)	1993	`pyod.models.mad.MAD`	[AIH93]
Probabilistic	SOS	Stochastic Outlier Selection	2012	`pyod.models.sos.SOS`	[AJHuszarPvdH12]
Probabilistic	QMCD	Quasi-Monte Carlo Discrepancy outlier detection	2001	`pyod.models.qmcd.QMCD`	[AFM01]
Probabilistic	KDE	Outlier Detection with Kernel Density Functions	2007	`pyod.models.kde.KDE`	[ALLP07]
Probabilistic	Sampling	Rapid distance-based outlier detection via sampling	2013	`pyod.models.sampling.Sampling`	[ASB13]
Probabilistic	GMM	Probabilistic Mixture Modeling for Outlier Analysis		`pyod.models.gmm.GMM`	[AAgg15] [Ch.2]
Linear Model	PCA	Principal Component Analysis (the sum of weighted projected distances to the eigenvector hyperplanes)	2003	`pyod.models.pca.PCA`	[ASCSC03]
Linear Model	KPCA	Kernel Principal Component Analysis	2007	`pyod.models.kpca.KPCA`	[AHof07]
Linear Model	MCD	Minimum Covariance Determinant (use the mahalanobis distances as the outlier scores)	1999	`pyod.models.mcd.MCD`	[AHR04, ARD99]
Linear Model	CD	Use Cook’s distance for outlier detection	1977	`pyod.models.cd.CD`	[ACoo77]
Linear Model	OCSVM	One-Class Support Vector Machines	2001	`pyod.models.ocsvm.OCSVM`	[AScholkopfPST+01]
Linear Model	LMDD	Deviation-based Outlier Detection (LMDD)	1996	`pyod.models.lmdd.LMDD`	[AAAR96]
Proximity-Based	LOF	Local Outlier Factor	2000	`pyod.models.lof.LOF`	[ABKNS00]
Proximity-Based	COF	Connectivity-Based Outlier Factor	2002	`pyod.models.cof.COF`	[ATCFC02]
Proximity-Based	Incr. COF	Memory Efficient Connectivity-Based Outlier Factor (slower but reduce storage complexity)	2002	`pyod.models.cof.COF`	[ATCFC02]
Proximity-Based	CBLOF	Clustering-Based Local Outlier Factor	2003	`pyod.models.cblof.CBLOF`	[AHXD03]
Proximity-Based	LOCI	LOCI: Fast outlier detection using the local correlation integral	2003	`pyod.models.loci.LOCI`	[APKGF03]
Proximity-Based	HBOS	Histogram-based Outlier Score	2012	`pyod.models.hbos.HBOS`	[AGD12]
Proximity-Based	kNN	k Nearest Neighbors (use the distance to the kth nearest neighbor as the outlier score	2000	`pyod.models.knn.KNN`	[AAP02, ARRS00]
Proximity-Based	AvgKNN	Average kNN (use the average distance to k nearest neighbors as the outlier score)	2002	`pyod.models.knn.KNN`	[AAP02, ARRS00]
Proximity-Based	MedKNN	Median kNN (use the median distance to k nearest neighbors as the outlier score)	2002	`pyod.models.knn.KNN`	[AAP02, ARRS00]
Proximity-Based	SOD	Subspace Outlier Detection	2009	`pyod.models.sod.SOD`	[AKKrogerSZ09]
Proximity-Based	ROD	Rotation-based Outlier Detection	2020	`pyod.models.rod.ROD`	[AABC20]
Outlier Ensembles	IForest	Isolation Forest	2008	`pyod.models.iforest.IForest`	[ALTZ08, ALTZ12]
Outlier Ensembles	INNE	Isolation-based Anomaly Detection Using Nearest-Neighbor Ensembles	2018	`pyod.models.inne.INNE`	[ABTA+18]
Outlier Ensembles	FB	Feature Bagging	2005	`pyod.models.feature_bagging.FeatureBagging`	[ALK05]
Outlier Ensembles	LSCP	LSCP: Locally Selective Combination of Parallel Outlier Ensembles	2019	`pyod.models.lscp.LSCP`	[AZNHL19]
Outlier Ensembles	XGBOD	Extreme Boosting Based Outlier Detection (Supervised)	2018	`pyod.models.xgbod.XGBOD`	[AZH18]
Outlier Ensembles	LODA	Lightweight On-line Detector of Anomalies	2016	`pyod.models.loda.LODA`	[APevny16]
Outlier Ensembles	SUOD	SUOD: Accelerating Large-scale Unsupervised Heterogeneous Outlier Detection (Acceleration)	2021	`pyod.models.suod.SUOD`	[AZHC+21]
Neural Networks	AutoEncoder	Fully connected AutoEncoder (use reconstruction error as the outlier score)	2015	`pyod.models.auto_encoder.AutoEncoder`	[AAgg15] [Ch.3]
Neural Networks	VAE	Variational AutoEncoder (use reconstruction error as the outlier score)	2013	`pyod.models.vae.VAE`	[AKW13]
Neural Networks	Beta-VAE	Variational AutoEncoder (all customized loss term by varying gamma and capacity)	2018	`pyod.models.vae.VAE`	[ABHP+18]
Neural Networks	SO_GAAL	Single-Objective Generative Adversarial Active Learning	2019	`pyod.models.so_gaal.SO_GAAL`	[ALLZ+19]
Neural Networks	MO_GAAL	Multiple-Objective Generative Adversarial Active Learning	2019	`pyod.models.mo_gaal.MO_GAAL`	[ALLZ+19]
Neural Networks	DeepSVDD	Deep One-Class Classification	2018	`pyod.models.deep_svdd.DeepSVDD`	[ARVG+18]
Neural Networks	AnoGAN	Anomaly Detection with Generative Adversarial Networks	2017	`pyod.models.anogan.AnoGAN`	[ASSeebockW+17]
Neural Networks	ALAD	Adversarially learned anomaly detection	2018	`pyod.models.alad.ALAD`	[AZRF+18]
Graph-based	R-Graph	Outlier detection by R-graph	2017	`pyod.models.rgraph.RGraph`	[BYRV17]
Graph-based	LUNAR	LUNAR: Unifying Local Outlier Detection Methods via Graph Neural Networks	2022	`pyod.models.lunar.LUNAR`	[AGHNN22]

(ii) Outlier Ensembles & Outlier Detector Combination Frameworks:

Type	Abbr	Algorithm	Year	Ref
Outlier Ensembles		Feature Bagging	2005	`pyod.models.feature_bagging.FeatureBagging`	[ALK05]
Outlier Ensembles	LSCP	LSCP: Locally Selective Combination of Parallel Outlier Ensembles	2019	`pyod.models.lscp.LSCP`	[AZNHL19]
Outlier Ensembles	XGBOD	Extreme Boosting Based Outlier Detection (Supervised)	2018	`pyod.models.xgbod.XGBOD`	[AZH18]
Outlier Ensembles	LODA	Lightweight On-line Detector of Anomalies	2016	`pyod.models.loda.LODA`	[APevny16]
Outlier Ensembles	SUOD	SUOD: Accelerating Large-scale Unsupervised Heterogeneous Outlier Detection (Acceleration)	2021	`pyod.models.suod.SUOD`	[AZHC+21]
Combination	Average	Simple combination by averaging the scores	2015	`pyod.models.combination.average()`	[AAS15]
Combination	Weighted Average	Simple combination by averaging the scores with detector weights	2015	`pyod.models.combination.average()`	[AAS15]
Combination	Maximization	Simple combination by taking the maximum scores	2015	`pyod.models.combination.maximization()`	[AAS15]
Combination	AOM	Average of Maximum	2015	`pyod.models.combination.aom()`	[AAS15]
Combination	MOA	Maximum of Average	2015	`pyod.models.combination.moa()`	[AAS15]
Combination	Median	Simple combination by taking the median of the scores	2015	`pyod.models.combination.median()`	[AAS15]
Combination	majority Vote	Simple combination by taking the majority vote of the labels (weights can be used)	2015	`pyod.models.combination.majority_vote()`	[AAS15]

(iii) Utility Functions:

Type	Name	Function
Data	`pyod.utils.data.generate_data()`	Synthesized data generation; normal data is generated by a multivariate Gaussian and outliers are generated by a uniform distribution
Data	`pyod.utils.data.generate_data_clusters()`	Synthesized data generation in clusters; more complex data patterns can be created with multiple clusters
Stat	`pyod.utils.stat_models.wpearsonr()`	Calculate the weighted Pearson correlation of two samples
Utility	`pyod.utils.utility.get_label_n()`	Turn raw outlier scores into binary labels by assign 1 to top n outlier scores
Utility	`pyod.utils.utility.precision_n_scores()`	calculate precision @ rank n

The comparison among of implemented models is made available below (Figure, compare_all_models.py, Interactive Jupyter Notebooks). For Jupyter Notebooks, please navigate to “/notebooks/Compare All Models.ipynb”.

Check the latest benchmark. You could replicate this process by running benchmark.py.

API Cheatsheet & Reference#

The following APIs are applicable for all detector models for easy use.

pyod.models.base.BaseDetector.fit(): Fit detector. y is ignored in unsupervised methods.
pyod.models.base.BaseDetector.decision_function(): Predict raw anomaly score of X using the fitted detector.
pyod.models.base.BaseDetector.predict(): Predict if a particular sample is an outlier or not using the fitted detector.
pyod.models.base.BaseDetector.predict_proba(): Predict the probability of a sample being outlier using the fitted detector.
pyod.models.base.BaseDetector.predict_confidence(): Predict the model’s sample-wise confidence (available in predict and predict_proba).

Key Attributes of a fitted model:

pyod.models.base.BaseDetector.decision_scores_: The outlier scores of the training data. The higher, the more abnormal. Outliers tend to have higher scores.
pyod.models.base.BaseDetector.labels_: The binary labels of the training data. 0 stands for inliers and 1 for outliers/anomalies.

References

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AAS15(1,2,3,4,5,6,7): Charu C Aggarwal and Saket Sathe. Theoretical foundations and algorithms for outlier ensembles. ACM SIGKDD Explorations Newsletter, 17(1):24–47, 2015.
AABC20: Yahya Almardeny, Noureddine Boujnah, and Frances Cleary. A novel outlier detection method for multivariate data. IEEE Transactions on Knowledge and Data Engineering, 2020.
AAP02(1,2,3): Fabrizio Angiulli and Clara Pizzuti. Fast outlier detection in high dimensional spaces. In European Conference on Principles of Data Mining and Knowledge Discovery, 15–27. Springer, 2002.
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ABTA+18: Tharindu R Bandaragoda, Kai Ming Ting, David Albrecht, Fei Tony Liu, Ye Zhu, and Jonathan R Wells. Isolation-based anomaly detection using nearest-neighbor ensembles. Computational Intelligence, 34(4):968–998, 2018.
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ABHP+18: Christopher P Burgess, Irina Higgins, Arka Pal, Loic Matthey, Nick Watters, Guillaume Desjardins, and Alexander Lerchner. Understanding disentangling in betvae. arXiv preprint arXiv:1804.03599, 2018.
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AGHNN22: Adam Goodge, Bryan Hooi, See-Kiong Ng, and Wee Siong Ng. Lunar: unifying local outlier detection methods via graph neural networks. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 36, 6737–6745. 2022.
AHHH+22: Songqiao Han, Xiyang Hu, Hailiang Huang, Mingqi Jiang, and Yue Zhao. Adbench: anomaly detection benchmark. arXiv preprint arXiv:2206.09426, 2022.
AHR04: Johanna Hardin and David M Rocke. Outlier detection in the multiple cluster setting using the minimum covariance determinant estimator. Computational Statistics & Data Analysis, 44(4):625–638, 2004.
AHXD03: Zengyou He, Xiaofei Xu, and Shengchun Deng. Discovering cluster-based local outliers. Pattern Recognition Letters, 24(9-10):1641–1650, 2003.
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AKW13: Diederik P Kingma and Max Welling. Auto-encoding variational bayes. arXiv preprint arXiv:1312.6114, 2013.
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AKZ+08(1,2): Hans-Peter Kriegel, Arthur Zimek, and others. Angle-based outlier detection in high-dimensional data. In Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining, 444–452. ACM, 2008.
ALLP07: Longin Jan Latecki, Aleksandar Lazarevic, and Dragoljub Pokrajac. Outlier detection with kernel density functions. In International Workshop on Machine Learning and Data Mining in Pattern Recognition, 61–75. Springer, 2007.
ALK05(1,2): Aleksandar Lazarevic and Vipin Kumar. Feature bagging for outlier detection. In Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining, 157–166. ACM, 2005.
ALZB+20: Zheng Li, Yue Zhao, Nicola Botta, Cezar Ionescu, and Xiyang Hu. COPOD: copula-based outlier detection. In IEEE International Conference on Data Mining (ICDM). IEEE, 2020.
ALZH+22: Zheng Li, Yue Zhao, Xiyang Hu, Nicola Botta, Cezar Ionescu, and H. George Chen. Ecod: unsupervised outlier detection using empirical cumulative distribution functions. IEEE Transactions on Knowledge and Data Engineering, 2022.
ALTZ08: Fei Tony Liu, Kai Ming Ting, and Zhi-Hua Zhou. Isolation forest. In Data Mining, 2008. ICDM'08. Eighth IEEE International Conference on, 413–422. IEEE, 2008.
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ALLZ+19(1,2): Yezheng Liu, Zhe Li, Chong Zhou, Yuanchun Jiang, Jianshan Sun, Meng Wang, and Xiangnan He. Generative adversarial active learning for unsupervised outlier detection. IEEE Transactions on Knowledge and Data Engineering, 2019.
APKGF03: Spiros Papadimitriou, Hiroyuki Kitagawa, Phillip B Gibbons, and Christos Faloutsos. Loci: fast outlier detection using the local correlation integral. In Data Engineering, 2003. Proceedings. 19th International Conference on, 315–326. IEEE, 2003.
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ASSeebockW+17: Thomas Schlegl, Philipp Seeböck, Sebastian M Waldstein, Ursula Schmidt-Erfurth, and Georg Langs. Unsupervised anomaly detection with generative adversarial networks to guide marker discovery. In International conference on information processing in medical imaging, 146–157. Springer, 2017.
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ASCSC03: Mei-Ling Shyu, Shu-Ching Chen, Kanoksri Sarinnapakorn, and LiWu Chang. A novel anomaly detection scheme based on principal component classifier. Technical Report, MIAMI UNIV CORAL GABLES FL DEPT OF ELECTRICAL AND COMPUTER ENGINEERING, 2003.
ASB13: Mahito Sugiyama and Karsten Borgwardt. Rapid distance-based outlier detection via sampling. Advances in neural information processing systems, 2013.
ATCFC02(1,2): Jian Tang, Zhixiang Chen, Ada Wai-Chee Fu, and David W Cheung. Enhancing effectiveness of outlier detections for low density patterns. In Pacific-Asia Conference on Knowledge Discovery and Data Mining, 535–548. Springer, 2002.
AZRF+18: Houssam Zenati, Manon Romain, Chuan-Sheng Foo, Bruno Lecouat, and Vijay Chandrasekhar. Adversarially learned anomaly detection. In 2018 IEEE International conference on data mining (ICDM), 727–736. IEEE, 2018.
AZH18(1,2): Yue Zhao and Maciej K Hryniewicki. Xgbod: improving supervised outlier detection with unsupervised representation learning. In International Joint Conference on Neural Networks (IJCNN). IEEE, 2018.
AZHC+21(1,2,3): Yue Zhao, Xiyang Hu, Cheng Cheng, Cong Wang, Changlin Wan, Wen Wang, Jianing Yang, Haoping Bai, Zheng Li, Cao Xiao, Yunlong Wang, Zhi Qiao, Jimeng Sun, and Leman Akoglu. Suod: accelerating large-scale unsupervised heterogeneous outlier detection. Proceedings of Machine Learning and Systems, 2021.
AZNHL19(1,2): Yue Zhao, Zain Nasrullah, Maciej K Hryniewicki, and Zheng Li. LSCP: locally selective combination in parallel outlier ensembles. In Proceedings of the 2019 SIAM International Conference on Data Mining, SDM 2019, 585–593. Calgary, Canada, May 2019. SIAM. URL: https://doi.org/10.1137/1.9781611975673.66, doi:10.1137/1.9781611975673.66.
AZNL19: Yue Zhao, Zain Nasrullah, and Zheng Li. PyOD: a python toolbox for scalable outlier detection. Journal of Machine Learning Research, 20(96):1–7, 2019.