A Comprehensive and Scalable Python Library for Outlier Detection (Anomaly Detection)
Project description
Deployment & Documentation & Stats & License
PyOD is the most 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.
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 [38] [39] with more than 6 million downloads. It is also well acknowledged by the machine learning community with various dedicated posts/tutorials, including Analytics Vidhya, KDnuggets, Towards Data Science, and awesomemachinelearning.
PyOD is featured for:
Unified APIs, detailed documentation, and interactive examples across various algorithms.
Advanced models, including classical ones by 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 [39].
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
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.
Key Links and Resources:
Table of Contents:
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+
combo>=0.1.3
joblib
numpy>=1.13
numba>=0.35
scipy>=1.3.1
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)
matplotlib (optional, required for running examples)
pandas (optional, required for running benchmark)
suod (optional, required for running SUOD model)
xgboost (optional, required for XGBOD)
Warning 1: PyOD has multiple neural network based models, e.g., AutoEncoders, which are implemented in both PyTorch and Tensorflow. However, PyOD does NOT install DL libraries for you. This reduces the risk of interfering with your local copies. If you want to use neuralnet based models, please make sure Keras and a backend library, e.g., TensorFlow, are installed. Instructions are provided: neuralnet FAQ. Similarly, models depending on xgboost, e.g., XGBOD, would NOT enforce xgboost installation by default.
Warning 2: PyOD contains multiple models that also exist in scikitlearn. However, these two libraries’ API is not exactly the same–it is recommended to use only one of them for consistency but not mix the results. Refer Differences between scikitlearn and PyOD for more information.
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) [28].
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.
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 [39]. 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 

Probabilistic 
ABOD 
AngleBased Outlier Detection 
2008 

Probabilistic 
FastABOD 
Fast AngleBased Outlier Detection using approximation 
2008 

Probabilistic 
COPOD 
COPOD: CopulaBased Outlier Detection 
2020 

Probabilistic 
MAD 
Median Absolute Deviation (MAD) 
1993 

Probabilistic 
SOS 
Stochastic Outlier Selection 
2012 

Probabilistic 
KDE 
Outlier Detection with Kernel Density Functions 
2007 

Probabilistic 
Sampling 
Rapid distancebased outlier detection via sampling 
2013 

Linear Model 
PCA 
Principal Component Analysis (the sum of weighted projected distances to the eigenvector hyperplanes) 
2003 

Linear Model 
MCD 
Minimum Covariance Determinant (use the mahalanobis distances as the outlier scores) 
1999 

Linear Model 
CD 
Use Cook’s distance for outlier detection 
1977 

Linear Model 
OCSVM 
OneClass Support Vector Machines 
2001 

Linear Model 
LMDD 
Deviationbased Outlier Detection (LMDD) 
1996 

ProximityBased 
LOF 
Local Outlier Factor 
2000 

ProximityBased 
COF 
ConnectivityBased Outlier Factor 
2002 

ProximityBased 
(Incremental) COF 
Memory Efficient ConnectivityBased Outlier Factor (slower but reduce storage complexity) 
2002 

ProximityBased 
CBLOF 
ClusteringBased Local Outlier Factor 
2003 

ProximityBased 
LOCI 
LOCI: Fast outlier detection using the local correlation integral 
2003 

ProximityBased 
HBOS 
Histogrambased Outlier Score 
2012 

ProximityBased 
kNN 
k Nearest Neighbors (use the distance to the kth nearest neighbor as the outlier score) 
2000 

ProximityBased 
AvgKNN 
Average kNN (use the average distance to k nearest neighbors as the outlier score) 
2002 

ProximityBased 
MedKNN 
Median kNN (use the median distance to k nearest neighbors as the outlier score) 
2002 

ProximityBased 
SOD 
Subspace Outlier Detection 
2009 

ProximityBased 
ROD 
Rotationbased Outlier Detection 
2020 

Outlier Ensembles 
IForest 
Isolation Forest 
2008 

Outlier Ensembles 
FB 
Feature Bagging 
2005 

Outlier Ensembles 
LSCP 
LSCP: Locally Selective Combination of Parallel Outlier Ensembles 
2019 

Outlier Ensembles 
XGBOD 
Extreme Boosting Based Outlier Detection (Supervised) 
2018 

Outlier Ensembles 
LODA 
Lightweight Online Detector of Anomalies 
2016 

Outlier Ensembles 
SUOD 
SUOD: Accelerating Largescale Unsupervised Heterogeneous Outlier Detection (Acceleration) 
2021 

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 

Neural Networks 
BetaVAE 
Variational AutoEncoder (all customized loss term by varying gamma and capacity) 
2018 

Neural Networks 
SO_GAAL 
SingleObjective Generative Adversarial Active Learning 
2019 

Neural Networks 
MO_GAAL 
MultipleObjective Generative Adversarial Active Learning 
2019 

Neural Networks 
DeepSVDD 
Deep OneClass Classification 
2018 
(ii) Outlier Ensembles & Outlier Detector Combination Frameworks:
Type 
Abbr 
Algorithm 
Year 
Ref 

Outlier Ensembles 
Feature Bagging 
2005 

Outlier Ensembles 
LSCP 
LSCP: Locally Selective Combination of Parallel Outlier Ensembles 
2019 

Outlier Ensembles 
XGBOD 
Extreme Boosting Based Outlier Detection (Supervised) 
2018 

Outlier Ensembles 
LODA 
Lightweight Online Detector of Anomalies 
2016 

Outlier Ensembles 
SUOD 
SUOD: Accelerating Largescale Unsupervised Heterogeneous Outlier Detection (Acceleration) 
2021 

Combination 
Average 
Simple combination by averaging the scores 
2015 

Combination 
Weighted Average 
Simple combination by averaging the scores with detector weights 
2015 

Combination 
Maximization 
Simple combination by taking the maximum scores 
2015 

Combination 
AOM 
Average of Maximum 
2015 

Combination 
MOA 
Maximization of Average 
2015 

Combination 
Median 
Simple combination by taking the median of the scores 
2015 

Combination 
majority Vote 
Simple combination by taking the majority vote of the labels (weights can be used) 
2015 
(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 

Data 
generate_data_clusters 
Synthesized data generation in clusters; more complex data patterns can be created with multiple clusters 

Stat 
wpearsonr 
Calculate the weighted Pearson correlation of two samples 

Utility 
get_label_n 
Turn raw outlier scores into binary labels by assign 1 to top n outlier scores 

Utility 
precision_n_scores 
calculate precision @ rank n 
Algorithm Benchmark
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”.
A benchmark is supplied for select algorithms to provide an overview of the implemented models. In total, 17 benchmark datasets are used for comparison, which can be downloaded at ODDS.
For each dataset, it is first split into 60% for training and 40% for testing. All experiments are repeated 10 times independently with random splits. The mean of 10 trials is regarded as the final result. Three evaluation metrics are provided:
The area under receiver operating characteristic (ROC) curve
Precision @ rank n (P@N)
Execution time
Check the latest benchmark. You could replicate this process by running benchmark.py.
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.
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