Welcome to PyOD documentation!

Deployment & Documentation & Stats

PyPI version Documentation Status Binder GitHub stars GitHub forks Downloads Downloads

Build Status & Coverage & Maintainability & License

Build status Build Status Circle CI Coverage Status Maintainability License 996.ICU

PyOD is a comprehensive and scalable Python toolkit for detecting outlying objects in multivariate data. This exciting yet challenging field is commonly referred as Outlier Detection or Anomaly Detection. Since 2017, PyOD [AZNL19] has been successfully used in various academic researches and commercial products [ARSLS19][AKW19][AZH18b][AZNHL19]. It is also well acknowledged by the machine learning community with various dedicated posts/tutorials, including Analytics Vidhya, Towards Data Science, KDnuggets, Computer Vision News, and awesome-machine-learning.

PyOD is featured for:

  • Unified APIs, detailed documentation, and interactive examples across various algorithms.
  • Advanced models, including Neural Networks/Deep Learning and Outlier Ensembles.
  • Optimized performance with JIT and parallelization when possible, using numba and joblib.
  • Compatible with both Python 2 & 3.

Note on Python 2.7: The maintenance of Python 2.7 will be stopped by January 1, 2020 (see official announcement) To be consistent with the Python change and PyOD’s dependent libraries, e.g., scikit-learn, we will stop supporting Python 2.7 in the near future (dates are still to be decided). We encourage you to use Python 3.5 or newer for the latest functions and bug fixes. More information can be found at Moving to require Python 3.

API Demo:

# train the KNN detector
from pyod.models.knn import KNN
clf = KNN()

# get outlier scores
y_train_scores = clf.decision_scores_  # raw outlier scores
y_test_scores = clf.decision_function(X_test)  # outlier scores

Citing PyOD:

PyOD paper is published in JMLR (machine learning open-source software track). If you use PyOD in a scientific publication, we would appreciate citations to the following paper:

  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}


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.

Key Links and Resources:

Implemented Algorithms

PyOD toolkit consists of three major functional groups:

(i) Individual Detection Algorithms :

  1. Linear Models for Outlier Detection:
Type Abbr Algorithm Year Class Ref
Linear Model PCA Principal Component Analysis (the sum of weighted projected distances to the eigenvector hyperplanes) 2003 pyod.models.pca.PCA [ASCSC03]
Linear Model MCD Minimum Covariance Determinant (use the mahalanobis distances as the outlier scores) 1999 pyod.models.mcd.MCD [ARD99][AHR04]
Linear Model OCSVM One-Class Support Vector Machines 2001 pyod.models.ocsvm.OCSVM [AScholkopfPST+01]
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 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 [ARRS00][AAP02]
Proximity-Based AvgKNN Average kNN (use the average distance to k nearest neighbors as the outlier score) 2002 pyod.models.knn.KNN [ARRS00][AAP02]
Proximity-Based MedKNN Median kNN (use the median distance to k nearest neighbors as the outlier score) 2002 pyod.models.knn.KNN [ARRS00][AAP02]
Proximity-Based SOD Subspace Outlier Detection 2009 pyod.models.sod.SOD [BKKrogerSZ09]
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 SOS Stochastic Outlier Selection 2012 pyod.models.sos.SOS [AJHuszarPvdH12]
Outlier Ensembles IForest Isolation Forest 2008 pyod.models.iforest.IForest [ALTZ08][ALTZ12]
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 [AZH18a]
Neural Networks AutoEncoder Fully connected AutoEncoder (use reconstruction error as the outlier score) 2015 pyod.models.auto_encoder.AutoEncoder [AAgg15]
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]

(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]
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]

(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”.

Comparison of selected models

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.

Key Attributes of a fitted model:

Note : fit_predict() and fit_predict_score() are deprecated in V0.6.9 due to consistency issue and will be removed in V0.8.0. To get the binary labels of the training data X_train, one should call clf.fit(X_train) and use pyod.models.base.BaseDetector.labels_, instead of calling clf.predict(X_train).


[AAgg15]Charu C Aggarwal. Outlier analysis. In Data mining, 75–79. Springer, 2015.
[AAS15](1, 2, 3, 4, 5) Charu C Aggarwal and Saket Sathe. Theoretical foundations and algorithms for outlier ensembles. ACM SIGKDD Explorations Newsletter, 17(1):24–47, 2015.
[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.
[ABKNS00]Markus M Breunig, Hans-Peter Kriegel, Raymond T Ng, and Jörg Sander. Lof: identifying density-based local outliers. In ACM sigmod record, volume 29, 93–104. ACM, 2000.
[AGD12]Markus Goldstein and Andreas Dengel. Histogram-based outlier score (hbos): a fast unsupervised anomaly detection algorithm. KI-2012: Poster and Demo Track, pages 59–63, 2012.
[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.
[AJHuszarPvdH12]JHM Janssens, Ferenc Huszár, EO Postma, and HJ van den Herik. Stochastic outlier selection. Technical Report, Technical report TiCC TR 2012-001, Tilburg University, Tilburg Center for Cognition and Communication, Tilburg, The Netherlands, 2012.
[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.
[AKW19]Sanjay Krishnan and Eugene Wu. Alphaclean: automatic generation of data cleaning pipelines. arXiv preprint arXiv:1904.11827, 2019.
[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.
[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.
[ALTZ12]Fei Tony Liu, Kai Ming Ting, and Zhi-Hua Zhou. Isolation-based anomaly detection. ACM Transactions on Knowledge Discovery from Data (TKDD), 6(1):3, 2012.
[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.
[ARSLS19]Jagdish Ramakrishnan, Elham Shaabani, Chao Li, and Mátyás A Sustik. Anomaly detection for an e-commerce pricing system. arXiv preprint arXiv:1902.09566, 2019.
[ARRS00](1, 2, 3) Sridhar Ramaswamy, Rajeev Rastogi, and Kyuseok Shim. Efficient algorithms for mining outliers from large data sets. In ACM Sigmod Record, volume 29, 427–438. ACM, 2000.
[ARD99]Peter J Rousseeuw and Katrien Van Driessen. A fast algorithm for the minimum covariance determinant estimator. Technometrics, 41(3):212–223, 1999.
[AScholkopfPST+01]Bernhard Schölkopf, John C Platt, John Shawe-Taylor, Alex J Smola, and Robert C Williamson. Estimating the support of a high-dimensional distribution. Neural computation, 13(7):1443–1471, 2001.
[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.
[ATCFC02]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.
[AZH18a]Yue Zhao and Maciej K Hryniewicki. Xgbod: improving supervised outlier detection with unsupervised representation learning. In Neural Networks, 2018. Proceedings of the International Joint Conference on. IEEE, 2018.
[AZH18b]Yue Zhao and Maciej K. Hryniewicki. Dcso: dynamic combination of detector scores for outlier ensembles. In ACM SIGKDD Workshop on Outlier Detection De-constructed (ODD v5.0). ACM, 2018.
[AZNHL19](1, 2, 3) 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. arXiv preprint arXiv:1901.01588, 2019.