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A Comprehensive and Scalable Python Library for Outlier Detection (Anomaly Detection)

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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 [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 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:

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 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

  • 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)

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.


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) [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 45-page, the most comprehensive ADBench: Anomaly Detection Benchmark [14]. The fully open-sourced ADBench compares 30 anomaly detection algorithms on 57 benchmark datasets.

The organization of ADBench is provided below:

benchmark-fig

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”.

Comparision_of_All

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

Angle-Based Outlier Detection

2008

[21]

Probabilistic

FastABOD

Fast Angle-Based Outlier Detection using approximation

2008

[21]

Probabilistic

COPOD

COPOD: Copula-Based 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 distance-based 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

One-Class Support Vector Machines

2001

[37]

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

[40]

Proximity-Based

(Incremental) COF

Memory Efficient Connectivity-Based Outlier Factor (slower but reduce storage complexity)

2002

[40]

Proximity-Based

CBLOF

Clustering-Based Local Outlier Factor

2003

[16]

Proximity-Based

LOCI

LOCI: Fast outlier detection using the local correlation integral

2003

[30]

Proximity-Based

HBOS

Histogram-based Outlier Score

2012

[11]

Proximity-Based

kNN

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

2000

[33]

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

[22]

Proximity-Based

ROD

Rotation-based Outlier Detection

2020

[4]

Outlier Ensembles

IForest

Isolation Forest

2008

[28]

Outlier Ensembles

INNE

Isolation-based Anomaly Detection Using Nearest-Neighbor 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 On-line Detector of Anomalies

2016

[31]

Outlier Ensembles

SUOD

SUOD: Accelerating Large-scale 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

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

[29]

Neural Networks

MO_GAAL

Multiple-Objective Generative Adversarial Active Learning

2019

[29]

Neural Networks

DeepSVDD

Deep One-Class Classification

2018

[35]

Neural Networks

AnoGAN

Anomaly Detection with Generative Adversarial Networks

2017

[36]

Neural Networks

ALAD

Adversarially learned anomaly detection

2018

[43]

Graph-based

R-Graph

Outlier detection by R-graph

2017

[42]

Graph-based

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 On-line Detector of Anomalies

2016

[31]

Outlier Ensembles

SUOD

SUOD: Accelerating Large-scale Unsupervised Heterogeneous Outlier Detection (Acceleration)

2021

[46]

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

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):

kNN example 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 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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