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Python Outlier Detection (PyOD)

Deployment & Documentation & Stats

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PyOD is a 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. Since 2017, PyOD has been successfully used in various academic researches and commercial products [18] [19] [20]. PyOD is featured for:

  • Unified APIs, detailed documentation, and interactive examples across various algorithms.
  • Advanced models, including Neural Networks/Deep Learning and Outlier Ensembles.
  • Optimized performance with JIT and parallelization when possible, using numba and joblib.
  • Compatible with both Python 2 & 3 (scikit-learn compatible as well).

Important Notes: PyOD contains neural network based models, e.g., AutoEncoders, which are implemented in Keras. However, PyOD would NOT install Keras and/or TensorFlow automatically. This reduces the risk of damaging your local copies. If you want to use neural net based models, you should install Keras and back-end libraries like TensorFlow manually. An instruction is provided: neural-net FAQ. Similarly, some models, e.g., XGBOD, depend on xgboost, which would NOT be installed by default.

Key Links and Resources:

Table of Contents:

Citing PyOD:

If you use PyOD in a scientific publication, we would appreciate citations to the following paper:

  title={PyOD: A Python Toolbox for Scalable Outlier Detection},
  author={Zhao, Yue and Nasrullah, Zain and Li, Zheng},
  journal={arXiv preprint arXiv:1901.01588},

It is currently under review at JMLR (machine learning open-source software track). See preprint.

Quick Introduction

PyOD toolkit consists of three major groups of functionalities:

(i) Individual Detection Algorithms :

Type Abbr Algorithm Year Ref
Linear Model PCA Principal Component Analysis (the sum of weighted projected distances to the eigenvector hyperplanes) 2003 [17]
Linear Model MCD Minimum Covariance Determinant (use the mahalanobis distances as the outlier scores) 1999 [6] [16]
Linear Model OCSVM One-Class Support Vector Machines 2003 [13]
Proximity-Based LOF Local Outlier Factor 2000 [4]
Proximity-Based CBLOF Clustering-Based Local Outlier Factor 2003 [7]
Proximity-Based LOCI LOCI: Fast outlier detection using the local correlation integral 2003 [14]
Proximity-Based HBOS Histogram-based Outlier Score 2012 [5]
Proximity-Based kNN k Nearest Neighbors (use the distance to the kth nearest neighbor as the outlier score 2000 [15]
Proximity-Based AvgKNN Average kNN (use the average distance to k nearest neighbors as the outlier score) 2002 [3]
Proximity-Based MedKNN Median kNN (use the median distance to k nearest neighbors as the outlier score) 2002 [3]
Probabilistic ABOD Angle-Based Outlier Detection 2008 [9]
Probabilistic FastABOD Fast Angle-Based Outlier Detection using approximation 2008 [9]
Probabilistic SOS Stochastic Outlier Selection 2012 [8]
Outlier Ensembles IForest Isolation Forest 2008 [11]
Outlier Ensembles   Feature Bagging 2005 [10]
Outlier Ensembles LSCP LSCP: Locally Selective Combination of Parallel Outlier Ensembles 2019 [20]
Outlier Ensembles XGBOD Extreme Boosting Based Outlier Detection (Supervised) 2018 [19]
Neural Networks AutoEncoder Fully connected AutoEncoder (use reconstruction error as the outlier score)   [1] [Ch.3]
Neural Networks SO_GAAL Single-Objective Generative Adversarial Active Learning 2019 [12]
Neural Networks MO_GAAL Multiple-Objective Generative Adversarial Active Learning 2019 [12]

(ii) Outlier Ensembles & Outlier Detector Combination Frameworks:

Type Abbr Algorithm Year Ref
Outlier Ensembles   Feature Bagging 2005 [10]
Outlier Ensembles LSCP LSCP: Locally Selective Combination of Parallel Outlier Ensembles 2019 [20]
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]

(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
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


It is recommended to use pip for installation. Please make sure the latest version is installed, as PyOD is updated frequently:

pip install pyod
pip install --upgrade pyod  # make sure the latest version is installed!
pip install --pre pyod      # or include pre-release version for new features

Alternatively, install from github directly (NOT Recommended)

git clone
python install

Required Dependencies:

  • Python 2.7, 3.5, 3.6, or 3.7
  • numpy>=1.13
  • numba>=0.35
  • scipy>=0.19.1
  • scikit_learn>=0.19.1

Optional Dependencies (see details below):

  • Keras (optional, required for AutoEncoder)
  • Matplotlib (optional, required for running examples)
  • Tensorflow (optional, required for AutoEncoder, other backend works)
  • XGBoost (optional, required for XGBOD)

Known Issue 1: Running examples needs Matplotlib, which may throw errors in conda virtual environment on mac OS. See reasons and solutions issue6.

Known Issue 2: Keras and/or TensorFlow are listed as optional. However, they are both required if you want to use neural network based models, such as AutoEncoder. See reasons and solutions neural-net installation

Known Issue 3: xgboost is listed as optional. However, it is required to run XGBOD. Users are expected to install xgboost to use XGBOD model.

API Cheatsheet & Reference

Full API Reference: ( API cheatsheet for all detectors:

  • fit(X): Fit detector.
  • fit_predict(X): Fit detector first and then predict whether a particular sample is an outlier or not.
  • fit_predict_score(X, y): Fit the detector, predict on samples, and evaluate the model by predefined metrics, e.g., ROC.
  • 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.

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.

Full package structure can be found below:

Algorithm Benchmark

Comparison of all implemented models are made available below:

(Figure,, Interactive Jupyter Notebooks):

For Jupyter Notebooks, please navigate to "/notebooks/Compare All Models.ipynb"


To provide an overview and quick guidance of the implemented models, a benchmark is supplied. In total, 17 benchmark data are used for comparision, all datasets could be downloaded at ODDS.

For each dataset, it is first split into 60% for training and 40% for testing. All experiments are repeated 20 times independently with different samplings. The mean of 20 trials are taken 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 result benchmark. You are welcome to replicate this process by running

Quick Start for Outlier Detection

See examples directory for more demos. "examples/" demonstrates the basic APIs of PyOD using kNN detector. It is noted the APIs for other detectors are similar.

More detailed instruction of running examples can be found examples.

  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()
    # 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
  2. Evaluate the prediction by ROC and Precision@rank n (p@n):

    # 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

Quick Start for Combining Outlier Scores from Various Base Detectors

"examples/" illustrates the APIs for combining multiple base detectors (, Jupyter Notebooks).

For Jupyter Notebooks, please navigate to "/notebooks/Model Combination.ipynb"

Given we have n individual outlier detectors, each of them generates an individual score for all samples. The task is to combine the outputs from these detectors effectively Key Step: conducting Z-score normalization on raw scores before the combination. Four combination mechanisms are shown in this demo:

  1. Average: take the average of all base detectors.
  2. maximization : take the maximum score across all detectors as the score.
  3. Average of Maximum (AOM): first randomly split n detectors in to p groups. For each group, use the maximum within the group as the group output. Use the average of all group outputs as the final output.
  4. Maximum of Average (MOA): similarly to AOM, the same grouping is introduced. However, we use the average of a group as the group output, and use maximum of all group outputs as the final output. To better understand the merging techniques, refer to [6].

The walkthrough of the code example is provided:

  1. Import models and generate sample data

    from pyod.models.knn import KNN
    from pyod.models.combination import aom, moa, average, maximization
    from import generate_data
    X, y = generate_data(train_only=True)  # load data
  2. First initialize 20 kNN outlier detectors with different k (10 to 200), and get the outlier scores:

    # initialize 20 base detectors for combination
    k_list = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140,
                150, 160, 170, 180, 190, 200]
    train_scores = np.zeros([X_train.shape[0], n_clf])
    test_scores = np.zeros([X_test.shape[0], n_clf])
    for i in range(n_clf):
        k = k_list[i]
        clf = KNN(n_neighbors=k, method='largest')
        train_scores[:, i] = clf.decision_scores_
        test_scores[:, i] = clf.decision_function(X_test_norm)
  3. Then the output codes are standardized into zero mean and unit variance before combination.

    from pyod.utils.utility import standardizer
    train_scores_norm, test_scores_norm = standardizer(train_scores, test_scores)
  4. Then four different combination algorithms are applied as described above:

    comb_by_average = average(test_scores_norm)
    comb_by_maximization = maximization(test_scores_norm)
    comb_by_aom = aom(test_scores_norm, 5) # 5 groups
    comb_by_moa = moa(test_scores_norm, 5)) # 5 groups
  5. Finally, all four combination methods are evaluated with ROC and Precision @ Rank n:

    Combining 20 kNN detectors
    Combination by Average ROC:0.9194, precision @ rank n:0.4531
    Combination by Maximization ROC:0.9198, precision @ rank n:0.4688
    Combination by AOM ROC:0.9257, precision @ rank n:0.4844
    Combination by MOA ROC:0.9263, precision @ rank n:0.4688

How to Contribute and Collaborate

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 and follow the pull request template PR template

To make sure the code has the same style and standard, please refer to models, such as,, or feature bagging for example.

You are also welcome to share your ideas by opening an issue or dropping me an email at :)


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[2](1, 2, 3, 4, 5) Aggarwal, C.C. and Sathe, S., 2015. Theoretical foundations and algorithms for outlier ensembles.ACM SIGKDD Explorations Newsletter, 17(1), pp.24-47.
[3](1, 2) Angiulli, F. and Pizzuti, C., 2002, August. Fast outlier detection in high dimensional spaces. In European Conference on Principles of Data Mining and Knowledge Discovery pp. 15-27.
[4]Breunig, M.M., Kriegel, H.P., Ng, R.T. and Sander, J., 2000, May. LOF: identifying density-based local outliers. ACM Sigmod Record, 29(2), pp. 93-104.
[5]Goldstein, M. and Dengel, A., 2012. Histogram-based outlier score (hbos): A fast unsupervised anomaly detection algorithm. In KI-2012: Poster and Demo Track, pp.59-63.
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[9](1, 2) Kriegel, H.P. and Zimek, A., 2008, August. Angle-based outlier detection in high-dimensional data. In KDD '08, pp. 444-452. ACM.
[10](1, 2) Lazarevic, A. and Kumar, V., 2005, August. Feature bagging for outlier detection. In KDD '05. 2005.
[11]Liu, F.T., Ting, K.M. and Zhou, Z.H., 2008, December. Isolation forest. In International Conference on Data Mining, pp. 413-422. IEEE.
[12](1, 2) Liu, Y., Li, Z., Zhou, C., Jiang, Y., Sun, J., Wang, M. and He, X., 2018. Generative Adversarial Active Learning for Unsupervised Outlier Detection. arXiv preprint arXiv:1809.10816.
[13]Ma, J. and Perkins, S., 2003, July. Time-series novelty detection using one-class support vector machines. In IJCNN' 03, pp. 1741-1745. IEEE.
[14]Papadimitriou, S., Kitagawa, H., Gibbons, P.B. and Faloutsos, C., 2003, March. LOCI: Fast outlier detection using the local correlation integral. In ICDE '03, pp. 315-326. IEEE.
[15]Ramaswamy, S., Rastogi, R. and Shim, K., 2000, May. Efficient algorithms for mining outliers from large data sets. ACM Sigmod Record, 29(2), pp. 427-438).
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[18]Zhao, Y. and Hryniewicki, M.K. DCSO: Dynamic Combination of Detector Scores for Outlier Ensembles. ACM SIGKDD Workshop on Outlier Detection De-constructed (ODD v5.0), 2018.
[19](1, 2) Zhao, Y. and Hryniewicki, M.K. XGBOD: Improving Supervised Outlier Detection with Unsupervised Representation Learning. IEEE International Joint Conference on Neural Networks, 2018.
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