Python Outlier Detection (PyOD)

Deployment & Documentation & Stats & License

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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 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 [48].

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 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:

• View the latest codes on Github
• Anomaly Detection Resources

Table of Contents:

• Installation
• API Cheatsheet & Reference
• ADBench Benchmark
• Model Save & Load
• Fast Train with SUOD
• Thresholding Outlier Scores
• Implemented Algorithms
• Quick Start for Outlier Detection
• How to Contribute
• Inclusion Criteria

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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 conda-forge 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

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 neural-net based models, please make sure these deep learning libraries are installed. Instructions are provided: neural-net FAQ. Similarly, models depending on xgboost, e.g., XGBOD, would NOT enforce xgboost installation by default.

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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 sample-wise confidence (available in predict and predict_proba) [33].

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.

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ADBench Benchmark

We just released a 45-page, the most comprehensive ADBench: Anomaly Detection Benchmark [15]. The fully open-sourced 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".

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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.

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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 [48]. 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)

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Thresholding Outlier Scores

A 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 to PyThresh for a more in depth look at thresholding.

from pyod.models.knn import KNN
from pyod.models.thresholds import FILTER

# Set the outlier detection and thresholding methods
clf = KNN(contamination=FILTER())

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Implemented Algorithms

PyOD toolkit consists of four major functional groups:

(i) Individual Detection Algorithms :

Type	Abbr	Algorithm	Year	Ref
Probabilistic	ECOD	Unsupervised Outlier Detection Using Empirical Cumulative Distribution Functions	2022	[28]
Probabilistic	ABOD	Angle-Based Outlier Detection	2008	[22]
Probabilistic	FastABOD	Fast Angle-Based Outlier Detection using approximation	2008	[22]
Probabilistic	COPOD	COPOD: Copula-Based Outlier Detection	2020	[27]
Probabilistic	MAD	Median Absolute Deviation (MAD)	1993	[19]
Probabilistic	SOS	Stochastic Outlier Selection	2012	[20]
Probabilistic	QMCD	Quasi-Monte Carlo Discrepancy outlier detection	2001	[11]
Probabilistic	KDE	Outlier Detection with Kernel Density Functions	2007	[24]
Probabilistic	Sampling	Rapid distance-based outlier detection via sampling	2013	[40]
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	[39]
Linear Model	KPCA	Kernel Principal Component Analysis	2007	[18]
Linear Model	MCD	Minimum Covariance Determinant (use the mahalanobis distances as the outlier scores)	1999	[16] [35]
Linear Model	CD	Use Cook's distance for outlier detection	1977	[10]
Linear Model	OCSVM	One-Class Support Vector Machines	2001	[38]
Linear Model	LMDD	Deviation-based Outlier Detection (LMDD)	1996	[6]
Proximity-Based	LOF	Local Outlier Factor	2000	[8]
Proximity-Based	COF	Connectivity-Based Outlier Factor	2002	[41]
Proximity-Based	(Incremental) COF	Memory Efficient Connectivity-Based Outlier Factor (slower but reduce storage complexity)	2002	[41]
Proximity-Based	CBLOF	Clustering-Based Local Outlier Factor	2003	[17]
Proximity-Based	LOCI	LOCI: Fast outlier detection using the local correlation integral	2003	[31]
Proximity-Based	HBOS	Histogram-based Outlier Score	2012	[12]
Proximity-Based	kNN	k Nearest Neighbors (use the distance to the kth nearest neighbor as the outlier score)	2000	[34]
Proximity-Based	AvgKNN	Average kNN (use the average distance to k nearest neighbors as the outlier score)	2002	[5]
Proximity-Based	MedKNN	Median kNN (use the median distance to k nearest neighbors as the outlier score)	2002	[5]
Proximity-Based	SOD	Subspace Outlier Detection	2009	[23]
Proximity-Based	ROD	Rotation-based Outlier Detection	2020	[4]
Outlier Ensembles	IForest	Isolation Forest	2008	[29]
Outlier Ensembles	INNE	Isolation-based Anomaly Detection Using Nearest-Neighbor Ensembles	2018	[7]
Outlier Ensembles	DIF	Deep Isolation Forest for Anomaly Detection	2023	[43]
Outlier Ensembles	FB	Feature Bagging	2005	[25]
Outlier Ensembles	LSCP	LSCP: Locally Selective Combination of Parallel Outlier Ensembles	2019	[47]
Outlier Ensembles	XGBOD	Extreme Boosting Based Outlier Detection (Supervised)	2018	[46]
Outlier Ensembles	LODA	Lightweight On-line Detector of Anomalies	2016	[32]
Outlier Ensembles	SUOD	SUOD: Accelerating Large-scale Unsupervised Heterogeneous Outlier Detection (Acceleration)	2021	[48]
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	[21]
Neural Networks	Beta-VAE	Variational AutoEncoder (all customized loss term by varying gamma and capacity)	2018	[9]
Neural Networks	SO_GAAL	Single-Objective Generative Adversarial Active Learning	2019	[30]
Neural Networks	MO_GAAL	Multiple-Objective Generative Adversarial Active Learning	2019	[30]
Neural Networks	DeepSVDD	Deep One-Class Classification	2018	[36]
Neural Networks	AnoGAN	Anomaly Detection with Generative Adversarial Networks	2017	[37]
Neural Networks	ALAD	Adversarially learned anomaly detection	2018	[45]
Graph-based	R-Graph	Outlier detection by R-graph	2017	[44]
Graph-based	LUNAR	LUNAR: Unifying Local Outlier Detection Methods via Graph Neural Networks	2022	[13]

(ii) Outlier Ensembles & Outlier Detector Combination Frameworks:

Type	Abbr	Algorithm	Year	Ref
Outlier Ensembles	FB	Feature Bagging	2005	[25]
Outlier Ensembles	LSCP	LSCP: Locally Selective Combination of Parallel Outlier Ensembles	2019	[47]
Outlier Ensembles	XGBOD	Extreme Boosting Based Outlier Detection (Supervised)	2018	[46]
Outlier Ensembles	LODA	Lightweight On-line Detector of Anomalies	2016	[32]
Outlier Ensembles	SUOD	SUOD: Accelerating Large-scale Unsupervised Heterogeneous Outlier Detection (Acceleration)	2021	[48]
Outlier Ensembles	INNE	Isolation-based Anomaly Detection Using Nearest-Neighbor 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) Outlier Detection Score Thresholding Methods:

Type	Abbr	Algorithm	Documentation
Kernel-Based	AUCP	Area Under Curve Percentage	AUCP
Statistical Moment-Based	BOOT	Bootstrapping	BOOT
Normality-Based	CHAU	Chauvenet's Criterion	CHAU
Linear Model	CLF	Trained Linear Classifier	CLF
cluster-Based	CLUST	Clustering Based	CLUST
Kernel-Based	CPD	Change Point Detection	CPD
Transformation-Based	DECOMP	Decomposition	DECOMP
Normality-Based	DSN	Distance Shift from Normal	DSN
Curve-Based	EB	Elliptical Boundary	EB
Kernel-Based	FGD	Fixed Gradient Descent	FGD
Filter-Based	FILTER	Filtering Based	FILTER
Curve-Based	FWFM	Full Width at Full Minimum	FWFM
Statistical Test-Based	GESD	Generalized Extreme Studentized Deviate	GESD
Filter-Based	HIST	Histogram Based	HIST
Quantile-Based	IQR	Inter-Quartile Region	IQR
Statistical Moment-Based	KARCH	Karcher mean (Riemannian Center of Mass)	KARCH
Statistical Moment-Based	MAD	Median Absolute Deviation	MAD
Statistical Test-Based	MCST	Monte Carlo Shapiro Tests	MCST
Ensembles-Based	META	Meta-model Trained Classifier	META
Transformation-Based	MOLL	Friedrichs' Mollifier	MOLL
Statistical Test-Based	MTT	Modified Thompson Tau Test	MTT
Linear Model	OCSVM	One-Class Support Vector Machine	OCSVM
Quantile-Based	QMCD	Quasi-Monte Carlo Discrepancy	QMCD
Linear Model	REGR	Regression Based	REGR
Neural Networks	VAE	Variational Autoencoder	VAE
Curve-Based	WIND	Topological Winding Number	WIND
Transformation-Based	YJ	Yeo-Johnson Transformation	YJ
Normality-Based	ZSCORE	Z-score	ZSCORE

(iV) 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

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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.

1. 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]

2. 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)

3. 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):

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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 [email protected] :)

Inclusion Criteria

Similarly to scikit-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.

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Reference

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