{ "info": { "author": "Yue Zhao", "author_email": "zhaoy@cmu.edu", "bugtrack_url": null, "classifiers": [ "Development Status :: 5 - Production/Stable", "Intended Audience :: Developers", "Intended Audience :: Education", "Intended Audience :: Financial and Insurance Industry", "Intended Audience :: Information Technology", "Intended Audience :: Science/Research", "License :: OSI Approved :: BSD License", "Programming Language :: Python :: 2.7", "Programming Language :: Python :: 3.5", "Programming Language :: Python :: 3.6", "Programming Language :: Python :: 3.7" ], "description": "Python Outlier Detection (PyOD)\n===============================\n\n**Deployment & Documentation & Stats**\n\n.. image:: https://img.shields.io/pypi/v/pyod.svg?color=brightgreen\n :target: https://pypi.org/project/pyod/\n :alt: PyPI version\n\n\n.. image:: https://readthedocs.org/projects/pyod/badge/?version=latest\n :target: https://pyod.readthedocs.io/en/latest/?badge=latest\n :alt: Documentation Status\n\n\n.. image:: https://mybinder.org/badge_logo.svg\n :target: https://mybinder.org/v2/gh/yzhao062/pyod/master\n :alt: Binder\n\n\n.. image:: https://img.shields.io/github/stars/yzhao062/pyod.svg\n :target: https://github.com/yzhao062/pyod/stargazers\n :alt: GitHub stars\n\n\n.. image:: https://img.shields.io/github/forks/yzhao062/pyod.svg?color=blue\n :target: https://github.com/yzhao062/pyod/network\n :alt: GitHub forks\n\n\n.. image:: https://pepy.tech/badge/pyod\n :target: https://pepy.tech/project/pyod\n :alt: Downloads\n\n\n.. image:: https://pepy.tech/badge/pyod/month\n :target: https://pepy.tech/project/pyod\n :alt: Downloads\n\n-----\n\n**Build Status & Coverage & Maintainability & License**\n\n\n.. image:: https://ci.appveyor.com/api/projects/status/1kupdy87etks5n3r/branch/master?svg=true\n :target: https://ci.appveyor.com/project/yzhao062/pyod/branch/master\n :alt: Build status\n\n\n.. image:: https://travis-ci.org/yzhao062/pyod.svg?branch=master\n :target: https://travis-ci.org/yzhao062/pyod\n :alt: Build Status\n\n\n.. image:: https://circleci.com/gh/yzhao062/pyod.svg?style=svg\n :target: https://circleci.com/gh/yzhao062/pyod\n :alt: Circle CI\n\n\n.. image:: https://coveralls.io/repos/github/yzhao062/pyod/badge.svg\n :target: https://coveralls.io/github/yzhao062/pyod\n :alt: Coverage Status\n\n\n.. image:: https://api.codeclimate.com/v1/badges/bdc3d8d0454274c753c4/maintainability\n :target: https://codeclimate.com/github/yzhao062/Pyod/maintainability\n :alt: Maintainability\n\n\n.. image:: https://img.shields.io/github/license/yzhao062/pyod.svg\n :target: https://github.com/yzhao062/pyod/blob/master/LICENSE\n :alt: License\n\n\n-----\n\nPyOD is a comprehensive and scalable **Python toolkit** for **detecting outlying objects** in \nmultivariate data. This exciting yet challenging field is commonly referred as \n`Outlier Detection `_\nor `Anomaly Detection `_.\nSince 2017, PyOD has been successfully used in various academic researches and\ncommercial products [#Li2019MADGAN]_ [#Zhao2019LSCP]_.\nIt is also well acknowledged by the machine learning community with various dedicated posts/tutorials, including\n`Analytics Vidhya `_,\n`KDnuggets `_,\n`Towards Data Science `_,\n`Computer Vision News `_, and\n`awesome-machine-learning `_.\n\n\nPyOD is featured for:\n\n* **Unified APIs, detailed documentation, and interactive examples** across various algorithms.\n* **Advanced models**\\ , including **Neural Networks/Deep Learning** and **Outlier Ensembles**.\n* **Optimized performance with JIT and parallelization** when possible, using `numba `_ and `joblib `_.\n* **Compatible with both Python 2 & 3**.\n\n\n**Note on Python 2.7**\\ :\nThe maintenance of Python 2.7 will be stopped by January 1, 2020 (see `official announcement `_).\nTo be consistent with the Python change and PyOD's dependent libraries, e.g., scikit-learn, we will\nstop supporting Python 2.7 in the near future (dates are still to be decided). We encourage you to use\nPython 3.5 or newer for the latest functions and bug fixes. More information can\nbe found at `Moving to require Python 3 `_.\n\n\n**API Demo**\\ :\n\n\n .. code-block:: python\n\n\n # train the KNN detector\n from pyod.models.knn import KNN\n clf = KNN()\n clf.fit(X_train)\n\n # get outlier scores\n y_train_scores = clf.decision_scores_ # raw outlier scores\n y_test_scores = clf.decision_function(X_test) # outlier scores\n\n\n**Citing PyOD**\\ :\n\n`PyOD paper `_ is published in\n`JMLR `_ (machine learning open-source software track).\nIf you use PyOD in a scientific publication, we would appreciate\ncitations to the following paper::\n\n @article{zhao2019pyod,\n author = {Zhao, Yue and Nasrullah, Zain and Li, Zheng},\n title = {PyOD: A Python Toolbox for Scalable Outlier Detection},\n journal = {Journal of Machine Learning Research},\n year = {2019},\n volume = {20},\n number = {96},\n pages = {1-7},\n url = {http://jmlr.org/papers/v20/19-011.html}\n }\n\nor::\n\n 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.\n\n\n**Key Links and Resources**\\ :\n\n\n* `View the latest codes on Github `_\n* `Execute Interactive Jupyter Notebooks `_\n* `Anomaly Detection Resources `_\n\n\n**Table of Contents**\\ :\n\n\n* `Installation <#installation>`_\n* `API Cheatsheet & Reference <#api-cheatsheet--reference>`_\n* `Implemented Algorithms <#implemented-algorithms>`_\n* `Algorithm Benchmark <#algorithm-benchmark>`_\n* `Quick Start for Outlier Detection <#quick-start-for-outlier-detection>`_\n* `Quick Start for Combining Outlier Scores from Various Base Detectors <#quick-start-for-combining-outlier-scores-from-various-base-detectors>`_\n* `How to Contribute <#how-to-contribute>`_\n* `Inclusion Criteria <#inclusion-criteria>`_\n\n\n----\n\n\nInstallation\n^^^^^^^^^^^^\n\nIt is recommended to use **pip** for installation. Please make sure\n**the latest version** is installed, as PyOD is updated frequently:\n\n.. code-block:: bash\n\n pip install pyod # normal install\n pip install --upgrade pyod # or update if needed\n pip install --pre pyod # or include pre-release version for new features\n\nAlternatively, you could clone and run setup.py file:\n\n.. code-block:: bash\n\n git clone https://github.com/yzhao062/pyod.git\n cd pyod\n pip install .\n\n\n**Note on Python 2.7**\\ :\nThe maintenance of Python 2.7 will be stopped by January 1, 2020 (see `official announcement `_)\nTo be consistent with the Python change and PyOD's dependent libraries, e.g., scikit-learn, we will\nstop supporting Python 2.7 in the near future (dates are still to be decided). We encourage you to use\nPython 3.5 or newer for the latest functions and bug fixes. More information can\nbe found at `Moving to require Python 3 `_.\n\n\n**Required Dependencies**\\ :\n\n\n* Python 2.7, 3.5, 3.6, or 3.7\n* numpy>=1.13\n* numba>=0.35\n* scipy>=0.19.1\n* scikit_learn>=0.19.1\n\n**Optional Dependencies (see details below)**\\ :\n\n\n* keras (optional, required for AutoEncoder)\n* matplotlib (optional, required for running examples)\n* pandas (optional, required for running benchmark)\n* tensorflow (optional, required for AutoEncoder, other backend works)\n* xgboost (optional, required for XGBOD)\n\n**Warning 1**\\ :\nPyOD has multiple neural network based models, e.g., AutoEncoders, which are\nimplemented in Keras. However, PyOD does **NOT** install **keras** and/or\n**tensorFlow** for you. This reduces the risk of interfering with your local copies.\nIf you want to use neural-net based models, please make sure Keras and a backend library, e.g., TensorFlow, are installed.\nInstructions are provided: `neural-net FAQ `_.\nSimilarly, models depending on **xgboost**, e.g., XGBOD, would **NOT** enforce xgboost installation by default.\n\n**Warning 2**\\ :\nRunning examples needs **matplotlib**, which may throw errors in conda\nvirtual environment on mac OS. See reasons and solutions `mac_matplotlib `_.\n\n**Warning 3**\\ :\nPyOD contains multiple models that also exist in scikit-learn. However, these two\nlibraries' API is not exactly the same--it is recommended to use only one of them\nfor consistency but not mix the results. Refer `Differences between sckit-learn and PyOD `_\nfor more information.\n\n\n----\n\n\nAPI Cheatsheet & Reference\n^^^^^^^^^^^^^^^^^^^^^^^^^^\n\nFull API Reference: (https://pyod.readthedocs.io/en/latest/pyod.html). API cheatsheet for all detectors:\n\n\n* **fit(X)**\\ : Fit detector.\n* **decision_function(X)**\\ : Predict raw anomaly score of X using the fitted detector.\n* **predict(X)**\\ : Predict if a particular sample is an outlier or not using the fitted detector.\n* **predict_proba(X)**\\ : Predict the probability of a sample being outlier using the fitted detector.\n* **fit_predict(X)**\\ : **[Deprecated in V0.6.9]** Fit detector first and then predict whether a particular sample is an outlier or not.\n* **fit_predict_score(X, y)**\\ : **[Deprecated in V0.6.9]** Fit the detector, predict on samples, and evaluate the model by predefined metrics, e.g., ROC.\n\n\nKey Attributes of a fitted model:\n\n\n* **decision_scores_**\\ : The outlier scores of the training data. The higher, the more abnormal.\n Outliers tend to have higher scores.\n* **labels_**\\ : The binary labels of the training data. 0 stands for inliers and 1 for outliers/anomalies.\n\n\n**Note** \\ : fit_predict() and fit_predict_score() are deprecated in V0.6.9 due\nto consistency issue and will be removed in V0.8.0. To get the binary labels\nof the training data X_train, one should call clf.fit(X_train) and use\nclf.labels\\_, instead of calling clf.predict(X_train).\n\n\n----\n\nImplemented Algorithms\n^^^^^^^^^^^^^^^^^^^^^^\n\nPyOD toolkit consists of three major functional groups:\n\n**(i) Individual Detection Algorithms** :\n\n=================== ================ ====================================================================================================== ===== ========================================\nType Abbr Algorithm Year Ref\n=================== ================ ====================================================================================================== ===== ========================================\nLinear Model PCA Principal Component Analysis (the sum of weighted projected distances to the eigenvector hyperplanes) 2003 [#Shyu2003A]_\nLinear Model MCD Minimum Covariance Determinant (use the mahalanobis distances as the outlier scores) 1999 [#Hardin2004Outlier]_ [#Rousseeuw1999A]_\nLinear Model OCSVM One-Class Support Vector Machines 2001 [#Scholkopf2001Estimating]_\nProximity-Based LOF Local Outlier Factor 2000 [#Breunig2000LOF]_\nProximity-Based COF Connectivity-Based Outlier Factor 2002 [#Tang2002Enhancing]_\nProximity-Based CBLOF Clustering-Based Local Outlier Factor 2003 [#He2003Discovering]_\nProximity-Based LOCI LOCI: Fast outlier detection using the local correlation integral 2003 [#Papadimitriou2003LOCI]_\nProximity-Based HBOS Histogram-based Outlier Score 2012 [#Goldstein2012Histogram]_\nProximity-Based kNN k Nearest Neighbors (use the distance to the kth nearest neighbor as the outlier score) 2000 [#Ramaswamy2000Efficient]_\nProximity-Based AvgKNN Average kNN (use the average distance to k nearest neighbors as the outlier score) 2002 [#Angiulli2002Fast]_\nProximity-Based MedKNN Median kNN (use the median distance to k nearest neighbors as the outlier score) 2002 [#Angiulli2002Fast]_\nProximity-Based SOD Subspace Outlier Detection 2009 [#Kriegel2009Outlier]_\nProbabilistic ABOD Angle-Based Outlier Detection 2008 [#Kriegel2008Angle]_\nProbabilistic FastABOD Fast Angle-Based Outlier Detection using approximation 2008 [#Kriegel2008Angle]_\nProbabilistic SOS Stochastic Outlier Selection 2012 [#Janssens2012Stochastic]_\nOutlier Ensembles IForest Isolation Forest 2008 [#Liu2008Isolation]_\nOutlier Ensembles Feature Bagging 2005 [#Lazarevic2005Feature]_\nOutlier Ensembles LSCP LSCP: Locally Selective Combination of Parallel Outlier Ensembles 2019 [#Zhao2019LSCP]_\nOutlier Ensembles XGBOD Extreme Boosting Based Outlier Detection **(Supervised)** 2018 [#Zhao2018XGBOD]_\nNeural Networks AutoEncoder Fully connected AutoEncoder (use reconstruction error as the outlier score) [#Aggarwal2015Outlier]_ [Ch.3]\nNeural Networks SO_GAAL Single-Objective Generative Adversarial Active Learning 2019 [#Liu2019Generative]_\nNeural Networks MO_GAAL Multiple-Objective Generative Adversarial Active Learning 2019 [#Liu2019Generative]_\n=================== ================ ====================================================================================================== ===== ========================================\n\n\n**(ii) Outlier Ensembles & Outlier Detector Combination Frameworks**:\n\n=================== ================ ===================================================================================================== ===== ========================================\nType Abbr Algorithm Year Ref\n=================== ================ ===================================================================================================== ===== ========================================\nOutlier Ensembles Feature Bagging 2005 [#Lazarevic2005Feature]_\nOutlier Ensembles LSCP LSCP: Locally Selective Combination of Parallel Outlier Ensembles 2019 [#Zhao2019LSCP]_\nCombination Average Simple combination by averaging the scores 2015 [#Aggarwal2015Theoretical]_\nCombination Weighted Average Simple combination by averaging the scores with detector weights 2015 [#Aggarwal2015Theoretical]_\nCombination Maximization Simple combination by taking the maximum scores 2015 [#Aggarwal2015Theoretical]_\nCombination AOM Average of Maximum 2015 [#Aggarwal2015Theoretical]_\nCombination MOA Maximization of Average 2015 [#Aggarwal2015Theoretical]_\n=================== ================ ===================================================================================================== ===== ========================================\n\n\n**(iii) Utility Functions**:\n\n=================== ====================== ===================================================================================================================================================== ======================================================================================================================================\nType Name Function Documentation\n=================== ====================== ===================================================================================================================================================== ======================================================================================================================================\nData generate_data Synthesized data generation; normal data is generated by a multivariate Gaussian and outliers are generated by a uniform distribution `generate_data `_\nData generate_data_clusters Synthesized data generation in clusters; more complex data patterns can be created with multiple clusters `generate_data_clusters `_\nStat wpearsonr Calculate the weighted Pearson correlation of two samples `wpearsonr `_\nUtility get_label_n Turn raw outlier scores into binary labels by assign 1 to top n outlier scores `get_label_n `_\nUtility precision_n_scores calculate precision @ rank n `precision_n_scores `_\n=================== ====================== ===================================================================================================================================================== ======================================================================================================================================\n\n----\n\n\nAlgorithm Benchmark\n^^^^^^^^^^^^^^^^^^^\n\n**The comparison among of implemented models** is made available below\n(\\ `Figure `_\\ ,\n`compare_all_models.py `_\\ ,\n`Interactive Jupyter Notebooks `_\\ ).\nFor Jupyter Notebooks, please navigate to **\"/notebooks/Compare All Models.ipynb\"**.\n\n\n.. image:: https://raw.githubusercontent.com/yzhao062/pyod/master/examples/ALL.png\n :target: https://raw.githubusercontent.com/yzhao062/pyod/master/examples/ALL.png\n :alt: Comparision_of_All\n\nA benchmark is supplied for select algorithms to provide an overview of the implemented models.\nIn total, 17 benchmark datasets are used for comparison, which\ncan be downloaded at `ODDS `_.\n\nFor each dataset, it is first split into 60% for training and 40% for testing.\nAll experiments are repeated 10 times independently with random splits.\nThe mean of 10 trials is regarded as the final result. Three evaluation metrics\nare provided:\n\n- The area under receiver operating characteristic (ROC) curve\n- Precision @ rank n (P@N)\n- Execution time\n\nCheck the latest `benchmark `_. You could replicate this process by running\n`benchmark.py `_.\n\n\n----\n\n\nQuick Start for Outlier Detection\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n\nPyOD has been well acknowledged by the machine learning community with a few featured posts and tutorials.\n\n**Analytics Vidhya**: `An Awesome Tutorial to Learn Outlier Detection in Python using PyOD Library `_\n\n**KDnuggets**: `Intuitive Visualization of Outlier Detection Methods `_, `An Overview of Outlier Detection Methods from PyOD `_\n\n**Towards Data Science**: `Anomaly Detection for Dummies `_\n\n**Computer Vision News (March 2019)**: `Python Open Source Toolbox for Outlier Detection `_\n\n`\"examples/knn_example.py\" `_\ndemonstrates the basic API of using kNN detector. **It is noted that the API across all other algorithms are consistent/similar**.\n\nMore detailed instructions for running examples can be found in `examples directory `_.\n\n\n#. Initialize a kNN detector, fit the model, and make the prediction.\n\n .. code-block:: python\n\n\n from pyod.models.knn import KNN # kNN detector\n\n # train kNN detector\n clf_name = 'KNN'\n clf = KNN()\n clf.fit(X_train)\n\n # get the prediction label and outlier scores of the training data\n y_train_pred = clf.labels_ # binary labels (0: inliers, 1: outliers)\n y_train_scores = clf.decision_scores_ # raw outlier scores\n\n # get the prediction on the test data\n y_test_pred = clf.predict(X_test) # outlier labels (0 or 1)\n y_test_scores = clf.decision_function(X_test) # outlier scores\n\n#. Evaluate the prediction by ROC and Precision @ Rank n (p@n).\n\n .. code-block:: python\n\n\n # evaluate and print the results\n print(\"\\nOn Training Data:\")\n evaluate_print(clf_name, y_train, y_train_scores)\n print(\"\\nOn Test Data:\")\n evaluate_print(clf_name, y_test, y_test_scores)\n\n\n#. See a sample output & visualization.\n\n\n .. code-block:: python\n\n\n On Training Data:\n KNN ROC:1.0, precision @ rank n:1.0\n\n On Test Data:\n KNN ROC:0.9989, precision @ rank n:0.9\n\n .. code-block:: python\n\n\n visualize(clf_name, X_train, y_train, X_test, y_test, y_train_pred,\n y_test_pred, show_figure=True, save_figure=False)\n\nVisualization (\\ `knn_figure `_\\ ):\n\n.. image:: https://raw.githubusercontent.com/yzhao062/pyod/master/examples/KNN.png\n :target: https://raw.githubusercontent.com/yzhao062/pyod/master/examples/KNN.png\n :alt: kNN example figure\n\n\n----\n\nQuick Start for Combining Outlier Scores from Various Base Detectors\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n\nOutlier detection often suffers from model instability due to its unsupervised\nnature. Thus, it is recommended to combine various detector outputs, e.g., by averaging,\nto improve its robustness. Detector combination is a subfield of outlier ensembles;\nrefer [#Aggarwal2017Outlier]_ for more information.\n\n\nFour score combination mechanisms are shown in this demo:\n\n\n#. **Average**: average scores of all detectors.\n#. **maximization**: maximum score across all detectors.\n#. **Average of Maximum (AOM)**: divide base detectors into subgroups and take the maximum score for each subgroup. The final score is the average of all subgroup scores.\n#. **Maximum of Average (MOA)**: divide base detectors into subgroups and take the average score for each subgroup. The final score is the maximum of all subgroup scores.\n\n\n\"examples/comb_example.py\" illustrates the API for combining the output of multiple base detectors\n(\\ `comb_example.py `_\\ ,\n`Jupyter Notebooks `_\\ ). For Jupyter Notebooks,\nplease navigate to **\"/notebooks/Model Combination.ipynb\"**\n\n\n#. Import models and generate sample data.\n\n .. code-block:: python\n\n from pyod.models.knn import KNN\n from pyod.models.combination import aom, moa, average, maximization\n from pyod.utils.data import generate_data\n\n X, y = generate_data(train_only=True) # load data\n\n#. First initialize 20 kNN outlier detectors with different k (10 to 200), and get the outlier scores.\n\n .. code-block:: python\n\n # initialize 20 base detectors for combination\n k_list = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140,\n 150, 160, 170, 180, 190, 200]\n\n train_scores = np.zeros([X_train.shape[0], n_clf])\n test_scores = np.zeros([X_test.shape[0], n_clf])\n\n for i in range(n_clf):\n k = k_list[i]\n\n clf = KNN(n_neighbors=k, method='largest')\n clf.fit(X_train_norm)\n\n train_scores[:, i] = clf.decision_scores_\n test_scores[:, i] = clf.decision_function(X_test_norm)\n\n#. Then the output scores are standardized into zero mean and unit variance before combination.\n This step is crucial to adjust the detector outputs to the same scale.\n\n\n .. code-block:: python\n\n from pyod.utils.utility import standardizer\n train_scores_norm, test_scores_norm = standardizer(train_scores, test_scores)\n\n#. Then four different combination algorithms are applied as described above.\n\n .. code-block:: python\n\n comb_by_average = average(test_scores_norm)\n comb_by_maximization = maximization(test_scores_norm)\n comb_by_aom = aom(test_scores_norm, 5) # 5 groups\n comb_by_moa = moa(test_scores_norm, 5)) # 5 groups\n\n#. Finally, all four combination methods are evaluated with ROC and Precision @ Rank n.\n\n .. code-block:: bash\n\n Combining 20 kNN detectors\n Combination by Average ROC:0.9194, precision @ rank n:0.4531\n Combination by Maximization ROC:0.9198, precision @ rank n:0.4688\n Combination by AOM ROC:0.9257, precision @ rank n:0.4844\n Combination by MOA ROC:0.9263, precision @ rank n:0.4688\n\n----\n\nHow to Contribute\n^^^^^^^^^^^^^^^^^\n\nYou are welcome to contribute to this exciting project:\n\n\n* Please first check Issue lists for \"help wanted\" tag and comment the one\n you are interested. We will assign the issue to you.\n\n* Fork the master branch and add your improvement/modification/fix.\n\n* Create a pull request to **development branch** and follow the pull request template `PR template `_\n\n* Automatic tests will be triggered. Make sure all tests are passed. Please make sure all added modules are accompanied with proper test functions.\n\n\nTo make sure the code has the same style and standard, please refer to abod.py, hbos.py, or feature_bagging.py for example.\n\nYou are also welcome to share your ideas by opening an issue or dropping me an email at zhaoy@cmu.edu :)\n\n\nInclusion Criteria\n^^^^^^^^^^^^^^^^^^\n\nSimilarly to `scikit-learn `_,\nWe mainly consider well-established algorithms for inclusion.\nA rule of thumb is at least two years since publication, 50+ citations, and usefulness.\n\nHowever, we encourage the author(s) of newly proposed models to share and add your implementation into PyOD\nfor boosting ML accessibility and reproducibility.\nThis exception only applies if you could commit to the maintenance of your model for at least two year period.\n\n\n----\n\nReference\n^^^^^^^^^\n\n\n.. [#Aggarwal2015Outlier] Aggarwal, C.C., 2015. Outlier analysis. In Data mining (pp. 237-263). Springer, Cham.\n\n.. [#Aggarwal2015Theoretical] Aggarwal, C.C. and Sathe, S., 2015. Theoretical foundations and algorithms for outlier ensembles.\\ *ACM SIGKDD Explorations Newsletter*\\ , 17(1), pp.24-47.\n\n.. [#Aggarwal2017Outlier] Aggarwal, C.C. and Sathe, S., 2017. Outlier ensembles: An introduction. Springer.\n\n.. [#Angiulli2002Fast] 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.\n\n.. [#Breunig2000LOF] 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.\n\n.. [#Goldstein2012Histogram] 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.\n\n.. [#Hardin2004Outlier] Hardin, J. and Rocke, D.M., 2004. Outlier detection in the multiple cluster setting using the minimum covariance determinant estimator. *Computational Statistics & Data Analysis*\\ , 44(4), pp.625-638.\n\n.. [#He2003Discovering] He, Z., Xu, X. and Deng, S., 2003. Discovering cluster-based local outliers. *Pattern Recognition Letters*\\ , 24(9-10), pp.1641-1650.\n\n.. [#Janssens2012Stochastic] Janssens, J.H.M., Husz\u00e1r, F., Postma, E.O. and van den Herik, H.J., 2012. Stochastic outlier selection. Technical report TiCC TR 2012-001, Tilburg University, Tilburg Center for Cognition and Communication, Tilburg, The Netherlands.\n\n.. [#Kriegel2008Angle] Kriegel, H.P. and Zimek, A., 2008, August. Angle-based outlier detection in high-dimensional data. In *KDD '08*\\ , pp. 444-452. ACM.\n\n.. [#Kriegel2009Outlier] Kriegel, H.P., Kr\u00f6ger, P., Schubert, E. and Zimek, A., 2009, April. Outlier detection in axis-parallel subspaces of high dimensional data. In *Pacific-Asia Conference on Knowledge Discovery and Data Mining*\\ , pp. 831-838. Springer, Berlin, Heidelberg.\n\n.. [#Lazarevic2005Feature] Lazarevic, A. and Kumar, V., 2005, August. Feature bagging for outlier detection. In *KDD '05*. 2005.\n\n.. [#Li2019MADGAN] Li, D., Chen, D., Jin, B., Shi, L., Goh, J. and Ng, S.K., 2019, September. MAD-GAN: Multivariate anomaly detection for time series data with generative adversarial networks. In *International Conference on Artificial Neural Networks* (pp. 703-716). Springer, Cham.\n\n.. [#Liu2008Isolation] Liu, F.T., Ting, K.M. and Zhou, Z.H., 2008, December. Isolation forest. In *International Conference on Data Mining*\\ , pp. 413-422. IEEE.\n\n.. [#Liu2019Generative] Liu, Y., Li, Z., Zhou, C., Jiang, Y., Sun, J., Wang, M. and He, X., 2019. Generative adversarial active learning for unsupervised outlier detection. *IEEE Transactions on Knowledge and Data Engineering*.\n\n.. [#Papadimitriou2003LOCI] 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.\n\n.. [#Ramaswamy2000Efficient] 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.\n\n.. [#Rousseeuw1999A] Rousseeuw, P.J. and Driessen, K.V., 1999. A fast algorithm for the minimum covariance determinant estimator. *Technometrics*\\ , 41(3), pp.212-223.\n\n.. [#Scholkopf2001Estimating] Scholkopf, B., Platt, J.C., Shawe-Taylor, J., Smola, A.J. and Williamson, R.C., 2001. Estimating the support of a high-dimensional distribution. *Neural Computation*, 13(7), pp.1443-1471.\n\n.. [#Shyu2003A] Shyu, M.L., Chen, S.C., Sarinnapakorn, K. and Chang, L., 2003. 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