Python Outlier Detection (PyOD)
Deployment & Documentation & Stats & License
News: We just released a 45page, the most comprehensive anomaly detection benchmark paper. The fully opensourced ADBench compares 30 anomaly detection algorithms on 57 benchmark datasets.
For timeseries 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 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 [46].
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 datadriven 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 = {17}, url = {http://jmlr.org/papers/v20/19011.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.17.
If you want more general insights of anomaly detection and/or algorithm performance comparison, please see our NeurIPS 2022 paper ADBench: Anomaly Detection Benchmark Paper:
@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:
Table of Contents:
 Installation
 API Cheatsheet & Reference
 ADBench Benchmark
 Model Save & Load
 Fast Train with SUOD
 Implemented Algorithms
 Quick Start for Outlier Detection
 How to Contribute
 Inclusion Criteria
Installation
It is recommended to use pip or conda for installation. Please make sure the latest version is installed, as PyOD is updated frequently:
pip install pyod # normal install
pip install upgrade pyod # or update if needed
conda install c condaforge pyod
Alternatively, you could clone and run setup.py file:
git clone https://github.com/yzhao062/pyod.git
cd pyod
pip install .
Required Dependencies:
 Python 3.6+
 joblib
 matplotlib
 numpy>=1.19
 numba>=0.51
 scipy>=1.5.1
 scikit_learn>=0.20.0
 six
 statsmodels
Optional Dependencies (see details below):
 combo (optional, required for models/combination.py and FeatureBagging)
 keras/tensorflow (optional, required for AutoEncoder, and other deep learning models)
 pandas (optional, required for running benchmark)
 suod (optional, required for running SUOD model)
 xgboost (optional, required for XGBOD)
 pythresh to use thresholding
Warning: PyOD has multiple neural network based models, e.g., AutoEncoders, which are implemented in both Tensorflow and PyTorch. However, PyOD does NOT install these deep learning libraries for you. This reduces the risk of interfering with your local copies. If you want to use neuralnet based models, please make sure these deep learning libraries are installed. Instructions are provided: neuralnet FAQ. Similarly, models depending on xgboost, e.g., XGBOD, would NOT enforce xgboost installation by default.
API Cheatsheet & Reference
Full API Reference: (https://pyod.readthedocs.io/en/latest/pyod.html). API cheatsheet for all detectors:
 fit(X): Fit detector. y is ignored in unsupervised methods.
 decision_function(X): Predict raw anomaly score of X using the fitted detector.
 predict(X): Predict if a particular sample is an outlier or not using the fitted detector.
 predict_proba(X): Predict the probability of a sample being outlier using the fitted detector.
 predict_confidence(X): Predict the model's samplewise confidence (available in predict and predict_proba) [32].
Key Attributes of a fitted model:
 decision_scores_: The outlier scores of the training data. The higher, the more abnormal. Outliers tend to have higher scores.
 labels_: The binary labels of the training data. 0 stands for inliers and 1 for outliers/anomalies.
ADBench Benchmark
We just released a 45page, the most comprehensive ADBench: Anomaly Detection Benchmark [14]. The fully opensourced ADBench compares 30 anomaly detection algorithms on 57 benchmark datasets.
The organization of ADBench is provided below:
The comparison of selected models is made available below (Figure, compare_all_models.py, Interactive Jupyter Notebooks). For Jupyter Notebooks, please navigate to "/notebooks/Compare All Models.ipynb".
Model Save & Load
PyOD takes a similar approach of sklearn regarding model persistence. See model persistence for 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:
from joblib import dump, load
# save the model
dump(clf, 'clf.joblib')
# load the model
clf = load('clf.joblib')
It is known that there are challenges in saving neural network models. Check #328 and #88 for temporary workaround.
Fast Train with SUOD
Fast training and prediction: it is possible to train and predict with a large number of detection models in PyOD by leveraging SUOD framework [46]. See SUOD Paper and SUOD example.
from pyod.models.suod import SUOD
# initialized a group of outlier detectors for acceleration
detector_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 model
clf = SUOD(base_estimators=detector_list, n_jobs=2, combination='average',
verbose=False)
Implemented Algorithms
PyOD toolkit consists of three major functional groups:
(i) Individual Detection Algorithms :
Type  Abbr  Algorithm  Year  Ref 

Probabilistic  ECOD  Unsupervised Outlier Detection Using Empirical Cumulative Distribution Functions  2022  [27] 
Probabilistic  ABOD  AngleBased Outlier Detection  2008  [21] 
Probabilistic  FastABOD  Fast AngleBased Outlier Detection using approximation  2008  [21] 
Probabilistic  COPOD  COPOD: CopulaBased Outlier Detection  2020  [26] 
Probabilistic  MAD  Median Absolute Deviation (MAD)  1993  [18] 
Probabilistic  SOS  Stochastic Outlier Selection  2012  [19] 
Probabilistic  KDE  Outlier Detection with Kernel Density Functions  2007  [23] 
Probabilistic  Sampling  Rapid distancebased outlier detection via sampling  2013  [39] 
Probabilistic  GMM  Probabilistic Mixture Modeling for Outlier Analysis  [1] [Ch.2]  
Linear Model  PCA  Principal Component Analysis (the sum of weighted projected distances to the eigenvector hyperplanes)  2003  [38] 
Linear Model  KPCA  Kernel Principal Component Analysis  2007  [17] 
Linear Model  MCD  Minimum Covariance Determinant (use the mahalanobis distances as the outlier scores)  1999  [15] [34] 
Linear Model  CD  Use Cook's distance for outlier detection  1977  [10] 
Linear Model  OCSVM  OneClass Support Vector Machines  2001  [37] 
Linear Model  LMDD  Deviationbased Outlier Detection (LMDD)  1996  [6] 
ProximityBased  LOF  Local Outlier Factor  2000  [8] 
ProximityBased  COF  ConnectivityBased Outlier Factor  2002  [40] 
ProximityBased  (Incremental) COF  Memory Efficient ConnectivityBased Outlier Factor (slower but reduce storage complexity)  2002  [40] 
ProximityBased  CBLOF  ClusteringBased Local Outlier Factor  2003  [16] 
ProximityBased  LOCI  LOCI: Fast outlier detection using the local correlation integral  2003  [30] 
ProximityBased  HBOS  Histogrambased Outlier Score  2012  [11] 
ProximityBased  kNN  k Nearest Neighbors (use the distance to the kth nearest neighbor as the outlier score)  2000  [33] 
ProximityBased  AvgKNN  Average kNN (use the average distance to k nearest neighbors as the outlier score)  2002  [5] 
ProximityBased  MedKNN  Median kNN (use the median distance to k nearest neighbors as the outlier score)  2002  [5] 
ProximityBased  SOD  Subspace Outlier Detection  2009  [22] 
ProximityBased  ROD  Rotationbased Outlier Detection  2020  [4] 
Outlier Ensembles  IForest  Isolation Forest  2008  [28] 
Outlier Ensembles  INNE  Isolationbased Anomaly Detection Using NearestNeighbor Ensembles  2018  [7] 
Outlier Ensembles  FB  Feature Bagging  2005  [24] 
Outlier Ensembles  LSCP  LSCP: Locally Selective Combination of Parallel Outlier Ensembles  2019  [45] 
Outlier Ensembles  XGBOD  Extreme Boosting Based Outlier Detection (Supervised)  2018  [44] 
Outlier Ensembles  LODA  Lightweight Online Detector of Anomalies  2016  [31] 
Outlier Ensembles  SUOD  SUOD: Accelerating Largescale Unsupervised Heterogeneous Outlier Detection (Acceleration)  2021  [46] 
Neural Networks  AutoEncoder  Fully connected AutoEncoder (use reconstruction error as the outlier score)  [1] [Ch.3]  
Neural Networks  VAE  Variational AutoEncoder (use reconstruction error as the outlier score)  2013  [20] 
Neural Networks  BetaVAE  Variational AutoEncoder (all customized loss term by varying gamma and capacity)  2018  [9] 
Neural Networks  SO_GAAL  SingleObjective Generative Adversarial Active Learning  2019  [29] 
Neural Networks  MO_GAAL  MultipleObjective Generative Adversarial Active Learning  2019  [29] 
Neural Networks  DeepSVDD  Deep OneClass Classification  2018  [35] 
Neural Networks  AnoGAN  Anomaly Detection with Generative Adversarial Networks  2017  [36] 
Neural Networks  ALAD  Adversarially learned anomaly detection  2018  [43] 
Graphbased  RGraph  Outlier detection by Rgraph  2017  [42] 
Graphbased  LUNAR  LUNAR: Unifying Local Outlier Detection Methods via Graph Neural Networks  2022  [12] 
(ii) Outlier Ensembles & Outlier Detector Combination Frameworks:
Type  Abbr  Algorithm  Year  Ref 

Outlier Ensembles  FB  Feature Bagging  2005  [24] 
Outlier Ensembles  LSCP  LSCP: Locally Selective Combination of Parallel Outlier Ensembles  2019  [45] 
Outlier Ensembles  XGBOD  Extreme Boosting Based Outlier Detection (Supervised)  2018  [44] 
Outlier Ensembles  LODA  Lightweight Online Detector of Anomalies  2016  [31] 
Outlier Ensembles  SUOD  SUOD: Accelerating Largescale Unsupervised Heterogeneous Outlier Detection (Acceleration)  2021  [46] 
Outlier Ensembles  INNE  Isolationbased Anomaly Detection Using NearestNeighbor Ensembles  2018  [7] 
Combination  Average  Simple combination by averaging the scores  2015  [2] 
Combination  Weighted Average  Simple combination by averaging the scores with detector weights  2015  [2] 
Combination  Maximization  Simple combination by taking the maximum scores  2015  [2] 
Combination  AOM  Average of Maximum  2015  [2] 
Combination  MOA  Maximization of Average  2015  [2] 
Combination  Median  Simple combination by taking the median of the scores  2015  [2] 
Combination  majority Vote  Simple combination by taking the majority vote of the labels (weights can be used)  2015  [2] 
(iii) Utility Functions:
Type  Name  Function  Documentation 

Data  generate_data  Synthesized data generation; normal data is generated by a multivariate Gaussian and outliers are generated by a uniform distribution  generate_data 
Data  generate_data_clusters  Synthesized data generation in clusters; more complex data patterns can be created with multiple clusters  generate_data_clusters 
Stat  wpearsonr  Calculate the weighted Pearson correlation of two samples  wpearsonr 
Utility  get_label_n  Turn raw outlier scores into binary labels by assign 1 to top n outlier scores  get_label_n 
Utility  precision_n_scores  calculate precision @ rank n  precision_n_scores 
Quick Start for Outlier Detection
PyOD 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 Library
KDnuggets: Intuitive Visualization of Outlier Detection Methods, An Overview of Outlier Detection Methods from PyOD
Towards Data Science: Anomaly Detection for Dummies
Computer 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 in examples directory.

Initialize a kNN detector, fit the model, and make the prediction.
from pyod.models.knn import KNN # kNN detector # train kNN detector clf_name = 'KNN' clf = KNN() clf.fit(X_train) # get the prediction label and outlier scores of the training data y_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 data y_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 well y_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).
from pyod.utils.data import evaluate_print # evaluate and print the results print("\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.
On Training Data: KNN ROC:1.0, precision @ rank n:1.0 On Test Data: KNN ROC:0.9989, precision @ rank n:0.9
visualize(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 Contribute
You 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 to development branch and follow the pull request template PR template
 Automatic 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 at zhaoy@cmu.edu :)
Inclusion Criteria
Similarly to scikitlearn, We mainly consider wellestablished 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
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