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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 [ALCJ+19][AWDL+19][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()
clf.fit(X_train)

# 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:

@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.

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

[AZH18]

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).



References

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.

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.

ALCJ+19

Dan Li, Dacheng Chen, Baihong Jin, Lei Shi, Jonathan Goh, and See-Kiong Ng. Mad-gan: multivariate anomaly detection for time series data with generative adversarial networks. In International Conference on Artificial Neural Networks, 703–716. Springer, 2019.

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.

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.

AWDL+19

Xuhong Wang, Ying Du, Shijie Lin, Ping Cui, Yuntian Shen, and Yupu Yang. Advae: a self-adversarial variational autoencoder with gaussian anomaly prior knowledge for anomaly detection. Knowledge-Based Systems, 2019.

AZH18

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.

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. Journal of Machine Learning Research, 20(96):1–7, 2019.