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Python Outlier Detection (PyOD)

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PyOD is a comprehensive and efficient Python toolkit to identify 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 [4, 8] and commercial products. PyOD is featured for:

  • Unified APIs, detailed documentation and interactive examples across various anomaly detection algorithms.
  • Advanced anomaly detection models, including Neural Networks/Deep Learning and Outlier Ensembles.
  • Optimized performance with JIT and parallelization, using numba and multiprocessing.
  • Compatibility with both Python 2 & 3. All implemented algorithms are also scikit-learn compatible.

Important Notes: PyOD contains some neural network based models, e.g., AutoEncoders, which are implemented in keras. However, PyOD would NOT install keras and tensorflow automatically. This would reduce the risk of damaging your local installations. You are responsible to install keras and tensorflow if you want to use neural net based models. An instruction is provided here.

Table of Contents:

Key Links and Resources

Quick Introduction

PyOD toolkit consists of three major groups of functionalities: (i) outlier detection algorithms; (ii) outlier ensemble frameworks and (iii) outlier detection utility functions.

Individual Detection Algorithms:

  1. Linear Models for Outlier Detection:

    1. PCA: Principal Component Analysis use the sum of weighted projected distances to the eigenvector hyperplane as the outlier outlier scores) [10]
    2. MCD: Minimum Covariance Determinant (use the mahalanobis distances as the outlier scores) [11, 12]
    3. One-Class Support Vector Machines [3]

  2. Proximity-Based Outlier Detection Models:

    1. LOF: Local Outlier Factor [1]
    2. CBLOF: Clustering-Based Local Outlier Factor [15]
    3. HBOS: Histogram-based Outlier Score [5]
    4. kNN: k Nearest Neighbors (use the distance to the kth nearest neighbor as the outlier score) [13]
    5. Average kNN or kNN Sum Outlier Detection (use the average distance to k nearest neighbors as the outlier score or sum all k distances) [14]
    6. Median kNN Outlier Detection (use the median distance to k nearest neighbors as the outlier score)

  3. Probabilistic Models for Outlier Detection:

    1. ABOD: Angle-Based Outlier Detection [7]
    2. FastABOD: Fast Angle-Based Outlier Detection using approximation [7]

  4. Outlier Ensembles and Combination Frameworks

    1. Isolation Forest [2]
    2. Feature Bagging [9]

  5. Neural Networks and Deep Learning Models (implemented in Keras)

    1. AutoEncoder with Fully Connected NN [16, Chapter 3]

      FAQ regarding AutoEncoder in PyOD and debugging advices: known issues

Outlier Detector/Scores Combination Frameworks:

  1. Feature Bagging: build various detectors on random selected features [9]
  2. Average & Weighted Average: simply combine scores by averaging [6]
  3. Maximization: simply combine scores by taking the maximum across all base detectors [6]
  4. Average of Maximum (AOM) [6]
  5. Maximum of Average (MOA) [6]
  6. Threshold Sum (Thresh) [6]

Utility Functions for Outlier Detection:

  1. score_to_lable(): convert raw outlier scores to binary labels
  2. precision_n_scores(): one of the popular evaluation metrics for outlier mining (precision @ rank n)
  3. generate_data(): generate pseudo data for outlier detection experiment
  4. wpearsonr(): weighted pearson is useful in pseudo ground truth generation

Comparison of all implemented models are made available below: (Figure, Code, Jupyter Notebooks):

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

Comparision_of_All

Installation

It is recommended to use pip for installation. Please make sure the latest version is installed since PyOD is currently updated on a daily basis:

pip install pyod
pip install --upgrade pyod # make sure the latest version is installed!

Alternatively, install from github directly (NOT Recommended)

git clone https://github.com/yzhao062/pyod.git
python setup.py install

Required Dependencies:

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

Optional Dependencies (required for running examples or AutoEncoder):

  • keras (optional, required if calling AutoEncoder, other backend works)
  • matplotlib (optional, required for running examples)
  • tensorflow (optional, required if calling AutoEncoder, other backend works)

Known Issue 1: PyOD depends on matplotlib, which would throw errors in conda virtual environment on mac OS. See reasons and solutions here.

Known Issue 2: PyOD builds on various packages, which most of them you should have already installed. If you are installing PyOD in a fresh state (virtualenv), downloading and installing the dependencies, e.g., TensorFlow, may take 3-5 mins.

Known Issue 3: If you are willing to run examples, matplotlib is required. PyOD does not list it as a required package for eliminating the dependency. Similarly, Keras and 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 here

API Cheatsheet & Reference

Full API Reference: (https://pyod.readthedocs.io/en/latest/pyod.html). API cheatsheet for all detectors:

  • fit(X): Fit detector.
  • fit_predict(X): Fit detector and predict if a particular sample is an outlier or not.
  • fit_predict_score(X, y): Fit, predict and then evaluate with predefined metrics (ROC and precision @ rank n).
  • decision_function(X): Predict anomaly score of X of the base classifiers.
  • predict(X): Predict if a particular sample is an outlier or not. The model must be fitted first.
  • predict_proba(X): Predict the probability of a sample being outlier. The model must be fitted first.

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:

Quick Start for Outlier Detection

See examples directory for more demos. "examples/knn_example.py" 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 here.

  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
  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/comb_example.py" illustrates the APIs for combining multiple base detectors (Code, 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 pyod.utils.data 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')
    clf.fit(X_train_norm)

    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, and we are pursuing to publish the toolkit in prestigious academic venues, e.g., JMLR (Track for open-source software).

If you are interested in contributing:

  • Please first check Issue lists for "help wanted" tag and comment the one you are interested

  • Fork the repository and add your improvement/modification/fix

  • Create a pull request

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

You are also welcome to share your ideas by openning an issue or dropping me an email at [email protected] :)

Algorithm Benchmark

To provide an overview and quick guidance of the implemented models, 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 here. You are welcome to replicate this process by running benchmark.py.

Reference

[1] Breunig, M.M., Kriegel, H.P., Ng, R.T. and Sander, J., 2000, May. LOF: identifying density-based local outliers. In ACM SIGMOD Record, pp. 93-104. ACM.

[2] Liu, F.T., Ting, K.M. and Zhou, Z.H., 2008, December. Isolation forest. In ICDM '08, pp. 413-422. IEEE.

[3] Ma, J. and Perkins, S., 2003, July. Time-series novelty detection using one-class support vector machines. In IJCNN' 03, pp. 1741-1745. IEEE.

[4] Y. Zhao and M.K. Hryniewicki, "DCSO: Dynamic Combination of Detector Scores for Outlier Ensembles," ACM SIGKDD Workshop on Outlier Detection De-constructed (ODD v5.0), 2018.

[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.

[6] Aggarwal, C.C. and Sathe, S., 2015. Theoretical foundations and algorithms for outlier ensembles.ACM SIGKDD Explorations Newsletter, 17(1), pp.24-47.

[7] Kriegel, H.P. and Zimek, A., 2008, August. Angle-based outlier detection in high-dimensional data. In KDD '08, pp. 444-452. ACM.

[8] Y. Zhao and M.K. Hryniewicki, "XGBOD: Improving Supervised Outlier Detection with Unsupervised Representation Learning," IEEE International Joint Conference on Neural Networks, 2018.

[9] Lazarevic, A. and Kumar, V., 2005, August. Feature bagging for outlier detection. In KDD '05. 2005.

[10] Shyu, M.L., Chen, S.C., Sarinnapakorn, K. and Chang, L., 2003. A novel anomaly detection scheme based on principal component classifier. MIAMI UNIV CORAL GABLES FL DEPT OF ELECTRICAL AND COMPUTER ENGINEERING.

[11] Rousseeuw, P.J. and Driessen, K.V., 1999. A fast algorithm for the minimum covariance determinant estimator. Technometrics, 41(3), pp.212-223.

[12] 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.

[13] 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).

[14] 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.

[15] He, Z., Xu, X. and Deng, S., 2003. Discovering cluster-based local outliers. Pattern Recognition Letters, 24(9-10), pp.1641-1650.

[16] Aggarwal, C.C., 2015. Outlier analysis. In Data mining (pp. 237-263). Springer, Cham.