Python Outlier Detection (PyOD)

Deployment & Documentation & Stats & License

Read Me First

Welcome to PyOD, a comprehensive but easy-to-use Python library for detecting anomalies in multivariate data. Whether you're tackling a small-scale project or large datasets, PyOD offers a range of algorithms to suit your needs.

For time-series outlier detection, please use TODS.
For graph outlier detection, please use PyGOD.
Performance Comparison & Datasets: We have a 45-page, comprehensive anomaly detection benchmark paper. The fully open-sourced ADBench compares 30 anomaly detection algorithms on 57 benchmark datasets.
Learn more about anomaly detection at Anomaly Detection Resources
PyOD on Distributed Systems: you can also run PyOD on databricks.

About PyOD

PyOD, established in 2017, has become a go-to Python library for detecting anomalous/outlying objects in multivariate data. This exciting yet challenging field is commonly referred to as Outlier Detection or Anomaly Detection.

PyOD includes more than 50 detection algorithms, from classical LOF (SIGMOD 2000) to the cutting-edge ECOD and DIF (TKDE 2022 and 2023). Since 2017, PyOD has been successfully used in numerous academic research projects and commercial products with more than 22 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, User-Friendly Interface across various algorithms.
Wide Range of Models, from classic techniques to the latest deep learning methods in PyTorch.
High Performance & Efficiency, leveraging numba and joblib for JIT compilation and parallel processing.
Fast Training & Prediction, achieved through the SUOD framework [50].

Outlier Detection with 5 Lines of Code:

# Example: Training an ECOD detector
from pyod.models.ecod import ECOD
clf = ECOD()
clf.fit(X_train)
y_train_scores = clf.decision_scores_  # Outlier scores for training data
y_test_scores = clf.decision_function(X_test)  # Outlier scores for test data

Selecting the Right Algorithm: Unsure where to start? Consider these robust and interpretable options:

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

Alternatively, explore MetaOD for a data-driven approach.

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.

For a broader perspective on anomaly detection, see our NeurIPS papers ADBench: Anomaly Detection Benchmark Paper and ADGym: Design Choices for Deep Anomaly Detection:

@article{han2022adbench,
    title={Adbench: Anomaly detection benchmark},
    author={Han, Songqiao and Hu, Xiyang and Huang, Hailiang and Jiang, Minqi and Zhao, Yue},
    journal={Advances in Neural Information Processing Systems},
    volume={35},
    pages={32142--32159},
    year={2022}
}

@article{jiang2023adgym,
    title={ADGym: Design Choices for Deep Anomaly Detection},
    author={Jiang, Minqi and Hou, Chaochuan and Zheng, Ao and Han, Songqiao and Huang, Hailiang and Wen, Qingsong and Hu, Xiyang and Zhao, Yue},
    journal={Advances in Neural Information Processing Systems},
    volume={36},
    year={2023}
}

Table of Contents:

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

Installation

PyOD is designed for easy installation using either pip or conda. We recommend using the latest version of PyOD due to frequent updates and enhancements:

pip install pyod            # normal install
pip install --upgrade pyod  # or update if needed

conda install -c conda-forge pyod

Alternatively, you can clone and run the setup.py file:

git clone https://github.com/yzhao062/pyod.git
cd pyod
pip install .

Required Dependencies:

Python 3.8 or higher
joblib
matplotlib
numpy>=1.19
numba>=0.51
scipy>=1.5.1
scikit_learn>=0.22.0

Optional Dependencies (see details below):

combo (optional, required for models/combination.py and FeatureBagging)
pytorch (optional, required for AutoEncoder, and other deep learning models)
suod (optional, required for running SUOD model)
xgboost (optional, required for XGBOD)
pythresh (optional, required for thresholding)

API Cheatsheet & Reference

The full API Reference is available at PyOD Documentation. Below is a quick cheatsheet for all detectors:

fit(X): Fit the detector. The parameter y is ignored in unsupervised methods.
decision_function(X): Predict raw anomaly scores for X using the fitted detector.
predict(X): Determine whether a sample is an outlier or not as binary labels using the fitted detector.
predict_proba(X): Estimate the probability of a sample being an outlier using the fitted detector.
predict_confidence(X): Assess the model's confidence on a per-sample basis (applicable in predict and predict_proba) [35].

Key Attributes of a fitted model:

decision_scores_: Outlier scores of the training data. Higher scores typically indicate more abnormal behavior. Outliers usually have higher scores.
labels_: Binary labels of the training data, where 0 indicates inliers and 1 indicates outliers/anomalies.

ADBench Benchmark and Datasets

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:

For a simpler visualization, we make the comparison of selected models via compare_all_models.py.

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 [50]. 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)

Thresholding Outlier Scores

A more data-based approach can be taken when setting the contamination level. By using a thresholding method, guessing an arbitrary value can be replaced with tested techniques for separating 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())

See supported thresholding methods in thresholding.

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	[42]
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	[41]
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] [37]
Linear Model	CD	Use Cook's distance for outlier detection	1977	[10]
Linear Model	OCSVM	One-Class Support Vector Machines	2001	[40]
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	[43]
Proximity-Based	(Incremental) COF	Memory Efficient Connectivity-Based Outlier Factor (slower but reduce storage complexity)	2002	[43]
Proximity-Based	CBLOF	Clustering-Based Local Outlier Factor	2003	[17]
Proximity-Based	LOCI	LOCI: Fast outlier detection using the local correlation integral	2003	[33]
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	[36]
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	[45]
Outlier Ensembles	FB	Feature Bagging	2005	[25]
Outlier Ensembles	LSCP	LSCP: Locally Selective Combination of Parallel Outlier Ensembles	2019	[49]
Outlier Ensembles	XGBOD	Extreme Boosting Based Outlier Detection (Supervised)	2018	[48]
Outlier Ensembles	LODA	Lightweight On-line Detector of Anomalies	2016	[34]
Outlier Ensembles	SUOD	SUOD: Accelerating Large-scale Unsupervised Heterogeneous Outlier Detection (Acceleration)	2021	[50]
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	[38]
Neural Networks	AnoGAN	Anomaly Detection with Generative Adversarial Networks	2017	[39]
Neural Networks	ALAD	Adversarially learned anomaly detection	2018	[47]
Neural Networks	AE1SVM	Autoencoder-based One-class Support Vector Machine	2019	[31]
Neural Networks	DevNet	Deep Anomaly Detection with Deviation Networks	2019	[32]
Graph-based	R-Graph	Outlier detection by R-graph	2017	[46]
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	[49]
Outlier Ensembles	XGBOD	Extreme Boosting Based Outlier Detection (Supervised)	2018	[48]
Outlier Ensembles	LODA	Lightweight On-line Detector of Anomalies	2016	[34]
Outlier Ensembles	SUOD	SUOD: Accelerating Large-scale Unsupervised Heterogeneous Outlier Detection (Acceleration)	2021	[50]
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) 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

"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):

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