Python Outlier Detection (PyOD)

Note: PyOD has been successfully used in various academic researches [8, 9] and under active development. However, full documentation and unit tests are temporarily unavailable yet planned for future release. The purpose of the toolkit is for quick exploration. Using it as the final output should be cautious. Fine-tunning may be needed to generate meaningful results.

The authours can be reached out by yuezhao@cs.toronto.edu. Please feel free to drop an email if you have any questions. PR and issue are also welcome for feature requests and bugs. Apologies for incomplete ducomentation.

• Current version on PyPI.

• Github repository with examples.

• More anomaly detection related resources, e.g., books, papers and videos, can be found at anomaly-detection-resources.

Table of Contents:

Python Outlier Detection (PyOD)

• Quick Introduction
• Installation
• API Cheatsheet
• Quick Start for Outlier Detection
• Quick Start for Combining Outlier Scores from Various Base Detectors
• Reference

Quick Introduction

PyOD is a Python-based toolkit to identify outliers in data with both unsupervised and supervised algorithms. It strives to provide unified APIs across for different anomaly detection algorithms. The 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. Local Outlier Factor, LOF [1]
  2. Isolation Forest, iForest [2]
  3. One-Class Support Vector Machines [3]
  4. kNN Outlier Detection (use the distance to the kth nearst neighbor as the outlier score)
  5. Average KNN Outlier Detection (use the average distance to k nearst neighbors as the outlier score)
  6. Median KNN Outlier Detection (use the median distance to k nearst neighbors as the outlier score)
  7. Broken, to fix: Global-Local Outlier Score From Hierarchies [4]
  8. Histogram-based Outlier Score, HBOS [5]
  9. Angle-Based Outlier Setection, ABOD [7]
  10. More to add...

• Outlier Ensemble Framework (Outlier Score Combination Frameworks)

  1. Feature bagging
  2. Average of Maximum (AOM) [6]
  3. Maximum of Average (MOA) [6]
  4. Threshold Sum (Thresh) [6]

• Utility functions:

  1. scores_to_lables(): converting raw outlier scores to binary labels
  2. precision_n_scores(): one of the popular evaluation metrics for outlier mining (precision @ rank n)

Installation

It is advised to use pip to install the latest version:

pip install pyod
pip install --upgrade pyod

or

pip install pyod==x.y.z

Please check the version number(x.y.z) is consistent with the current version number. Pypi can be unstable sometimes. Alternatively, downloading/cloning the Github repository also works. You could unzip the files and execute the following command in the folder where the files get decompressed.

python setup.py install

Library Dependency (work only with Python 3):

• scipy>=0.19.1
• pandas>=0.21
• numpy>=1.13
• scikit_learn>=0.19.1
• matplotlib>=2.0.2 (optional but required for running examples)

API Cheatsheet

For all algorithms implemented/wrapped in PyOD, the similar API is forced for consistency.

• fit(): fit the model with the training data
• fit_predict(): fit and return the binary outlier lables (0 is normal and 1 is outliers)
• decision_function(): return raw outlier scores
• predict(): return binary outlier labels of test data. The model must be fitted first.
• predict_proba(): return outlier probability of test data (0 to 1). The model must be fitted first.
• predict_rank(): return outlier rank of test data (data outlyness rank in training data)
• evaluate(): print out the roc and precision @ rank n of the data

Import outlier detection models, such like:

from pyod.models.knn import Knn
from pyod.models.abod import ABOD
from pyod.models.hbos import HBOS
...

Import utility functions:

from pyod.util.utility import precision_n_scores
...

Full package structure can be found below:

examples (excluded from installation, only available on Github)
│
│
├───abod_example.py: Example of using ABOD for outlier detection
│   comb_example.py: Example of combining multiple base outlier scores
│   hbos_example.py: Example of using HBOS for outlier detection
│   iforest_example.py: Example of using Isolation Forest for outlier detection
│   knn_example.py: Example of using kNN for outlier detection
│   lof_example.py: Example of using LOF for outlier detection
│   ocsvm_example.py: Example of using one-class SVM for outlier detection
│
│
pyod (main package)
├───models
│       abod.py: 
│           class ABOD(), from pyod.models.abod import ABOD
│       combination.py
│           amo(), from pyod.models.combination import aom
│           moa(), from pyod.models.combination import moa
│       glosh.py: class Glosh(), from pyod.models.glosh import Glosh
│       hbos.py: class HBOS(), from pyod.models.hbos import HBOS
│       iforest: class IForest(), from pyod.models.iforest import IForest
│       knn.py: class KNN(), from pyod.models.knn import Knn
│       lof.py: class LOF(), from pyod.models.lof import LOF
│       ocsvm.py: class OCSVM(), from pyod.models.ocsvm import OCSVM
│
├───utils
│       stat_models.py
│       utility.py
│           standardizer(): z- normalization function
│           scores_to_lables(): turn raw outlier scores to binary labels (0 or 1)
│           precision_n_scores(): Utlity function to calculate precision@n
│       load_data.py
│           generate_data(): generate sample data
│  
├───test (excluded from installation, only available on Github)
│       test_abod.py
|       test_combination.py
│       test_hbos.py
│       test_knn.py
│       test_lof.py
│       test_iforest.py
│       test_ocsvm.py
│       test_utility.py

Quick Start for Outlier Detection

See examples 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.

0. Import models

   from pyod.models.knn import KNN  # kNN detector
   
   from pyod.utils.load_data import generate_data
   from pyod.utils.utility import precision_n_scores
   from sklearn.metrics import roc_auc_score
   

1. Generate sample data first; normal data is generated by a 2-d gaussian distribution, and outliers are generated by a 2-d uniform distribution.

   contamination = 0.1  # percentage of outliers
   n_train = 1000  # number of training points
   n_test = 500  # number of testing points
   
   X_train, y_train, c_train, X_test, y_test, c_test = generate_data(
       n_train=n_train, n_test=n_test, contamination=contamination)
   

2. Initialize a kNN detector, fit the model, and make the prediction.

   # train a k-NN detector (default parameters, k=10)
   clf = KNN()
   clf.fit(X_train)
   
   # get the prediction label and scores on the training data
   y_train_pred = clf.y_pred
   y_train_score = clf.decision_scores
   
   # get the prediction on the test data
   y_test_pred = clf.predict(X_test)  # outlier label (0 or 1)
   y_test_score = clf.decision_function(X_test)  # outlier scores
   

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

   print(n_train.format(
       roc=roc_auc_score(y_train, y_train_score),
       prn=precision_n_scores(y_train, y_train_score)))
   
   print(n_train.format(
       roc=roc_auc_score(y_test, y_test_score),
       prn=precision_n_scores(y_test, y_test_score)))
   

   See a sample output:

   Train ROC:0.9473, precision@n:0.7857
   Test ROC:0.992, precision@n:0.9
   

To check the result of the classification visually (knn_figure):

Quick Start for Combining Outlier Scores from Various Base Detectors

"examples/comb_example.py" is a quick demo for showing the API for combining multiple algorithms. 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 effectivelly.

Key Step: conducting Z-score normalization on raw scores before the combination. Four combination mechanisms are shown in this demo:

1. Mean: use the mean value of all scores as the final output.
2. Max: use the max value of all scores as the final output.
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:

0. Import models and generate sample data

   from pyod.models.knn import Knn
   from pyod.models.combination import aom, moa # combination methods
   from pyod.utils.load_data import generate_data
   from pyod.utils.utility import precision_n_scores
   from pyod.utils.utility import standardizer
   from sklearn.metrics import roc_auc_score
   
   X, y, _ = generate_data(train_only=True)  # load data
   

1. 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.ravel()
       test_scores[:, i] = clf.decision_function(X_test_norm).ravel()
   

2. Then the output codes are standardized into zero mean and unit std before combination.

   # scores have to be normalized before combination
   train_scores_norm, test_scores_norm = standardizer(train_scores, test_scores)
   

3. Then four different combination algorithms are applied as described above:

   comb_by_mean = np.mean(test_scores_norm, axis=1)
   comb_by_max = np.max(test_scores_norm, axis=1)
   comb_by_aom = aom(test_scores_norm, 5) # 5 groups
   comb_by_moa = moa(test_scores_norm, 5)) # 5 groups
   

4. Finally, all four combination methods are evaluated with 20 iterations:

   Combining 20 kNN detectors
   ite 1 comb by mean, ROC: 0.9014 precision@n_train: 0.4531
   ite 1 comb by max, ROC: 0.9014 precision@n_train: 0.5
   ite 1 comb by aom, ROC: 0.9081 precision@n_train: 0.5
   ite 1 comb by moa, ROC: 0.9052 precision@n_train: 0.4843
   ...
   
   Summary of 10 iterations
   comb by mean, ROC: 0.9196, precision@n: 0.5464
   comb by max, ROC: 0.9198, precision@n: 0.5532
   comb by aom, ROC: 0.9260, precision@n: 0.5630
   comb by moa, ROC: 0.9244, precision@n: 0.5523
   

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] Campello, R.J., Moulavi, D., Zimek, A. and Sander, J., 2015. Hierarchical density estimates for data clustering, visualization, and outlier detection. TKDD, 10(1), pp.5.

[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] Y. Zhao and M.K. Hryniewicki, "DCSO: Dynamic Combination of Detector Scores for Outlier Ensembles," ACM SIGKDD Workshop on Outlier Detection De-constructed, 2018. Submitted, under review.