Example of Comparing All Implemented Outlier Detection Models¶
PyOD is a comprehensive Python toolkit to identify outlying objects in multivariate data with both unsupervised and supervised approaches. The model covered in this example includes:
Linear Models for Outlier Detection:
- PCA: Principal Component Analysis use the sum of
weighted projected distances to the eigenvector hyperplane as the outlier outlier scores) 2. MCD: Minimum Covariance Determinant (use the mahalanobis distances as the outlier scores) 3. OCSVM: One-Class Support Vector Machines
Proximity-Based Outlier Detection Models:
- LOF: Local Outlier Factor
- CBLOF: Clustering-Based Local Outlier Factor
- kNN: k Nearest Neighbors (use the distance to the kth nearest
neighbor as the outlier score) 4. Median kNN Outlier Detection (use the median distance to k nearest neighbors as the outlier score) 5. HBOS: Histogram-based Outlier Score
Probabilistic Models for Outlier Detection:
- ABOD: Angle-Based Outlier Detection
Outlier Ensembles and Combination Frameworks
- Isolation Forest
- Feature Bagging
- LSCP
Corresponding file could be found at /examples/compare_all_models.py
In [1]:
from __future__ import division
from __future__ import print_function
import os
import sys
from time import time
# temporary solution for relative imports in case pyod is not installed
# if pyod is installed, no need to use the following line
sys.path.append(
os.path.abspath(os.path.join(os.path.dirname("__file__"), '..')))
import numpy as np
from scipy import stats
import matplotlib.pyplot as plt
import matplotlib.font_manager
# Import all models
from pyod.models.abod import ABOD
from pyod.models.cblof import CBLOF
from pyod.models.feature_bagging import FeatureBagging
from pyod.models.hbos import HBOS
from pyod.models.iforest import IForest
from pyod.models.knn import KNN
from pyod.models.lof import LOF
from pyod.models.mcd import MCD
from pyod.models.ocsvm import OCSVM
from pyod.models.pca import PCA
from pyod.models.lscp import LSCP
In [2]:
# Define the number of inliers and outliers
n_samples = 200
outliers_fraction = 0.25
clusters_separation = [0]
# Compare given detectors under given settings
# Initialize the data
xx, yy = np.meshgrid(np.linspace(-7, 7, 100), np.linspace(-7, 7, 100))
n_inliers = int((1. - outliers_fraction) * n_samples)
n_outliers = int(outliers_fraction * n_samples)
ground_truth = np.zeros(n_samples, dtype=int)
ground_truth[-n_outliers:] = 1
# initialize a set of detectors for LSCP
detector_list = [LOF(n_neighbors=5), LOF(n_neighbors=10), LOF(n_neighbors=15),
LOF(n_neighbors=20), LOF(n_neighbors=25), LOF(n_neighbors=30),
LOF(n_neighbors=35), LOF(n_neighbors=40), LOF(n_neighbors=45),
LOF(n_neighbors=50)]
In [3]:
# Show the statics of the data
print('Number of inliers: %i' % n_inliers)
print('Number of outliers: %i' % n_outliers)
print('Ground truth shape is {shape}. Outlier are 1 and inliers are 0.\n'.format(shape=ground_truth.shape))
print(ground_truth)
Number of inliers: 150 Number of outliers: 50 Ground truth shape is (200,). Outlier are 1 and inliers are 0. [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
In [4]:
random_state = np.random.RandomState(42)
# Define nine outlier detection tools to be compared
classifiers = {
'Angle-based Outlier Detector (ABOD)':
ABOD(contamination=outliers_fraction),
'Cluster-based Local Outlier Factor (CBLOF)':
CBLOF(contamination=outliers_fraction,
check_estimator=False, random_state=random_state),
'Feature Bagging':
FeatureBagging(LOF(n_neighbors=35),
contamination=outliers_fraction,
check_estimator=False,
random_state=random_state),
'Histogram-base Outlier Detection (HBOS)': HBOS(
contamination=outliers_fraction),
'Isolation Forest': IForest(contamination=outliers_fraction,
random_state=random_state),
'K Nearest Neighbors (KNN)': KNN(
contamination=outliers_fraction),
'Average KNN': KNN(method='mean',
contamination=outliers_fraction),
# 'Median KNN': KNN(method='median',
# contamination=outliers_fraction),
'Local Outlier Factor (LOF)':
LOF(n_neighbors=35, contamination=outliers_fraction),
# 'Local Correlation Integral (LOCI)':
# LOCI(contamination=outliers_fraction),
'Minimum Covariance Determinant (MCD)': MCD(
contamination=outliers_fraction, random_state=random_state),
'One-class SVM (OCSVM)': OCSVM(contamination=outliers_fraction,
random_state=random_state),
'Principal Component Analysis (PCA)': PCA(
contamination=outliers_fraction, random_state=random_state),
# 'Stochastic Outlier Selection (SOS)': SOS(
# contamination=outliers_fraction),
'Locally Selective Combination (LSCP)': LSCP(
detector_list, contamination=outliers_fraction,
random_state=random_state)
}
In [5]:
# Show all detectors
for i, clf in enumerate(classifiers.keys()):
print('Model', i + 1, clf)
Model 1 Angle-based Outlier Detector (ABOD) Model 2 Cluster-based Local Outlier Factor (CBLOF) Model 3 Feature Bagging Model 4 Histogram-base Outlier Detection (HBOS) Model 5 Isolation Forest Model 6 K Nearest Neighbors (KNN) Model 7 Average KNN Model 8 Local Outlier Factor (LOF) Model 9 Minimum Covariance Determinant (MCD) Model 10 One-class SVM (OCSVM) Model 11 Principal Component Analysis (PCA) Model 12 Locally Selective Combination (LSCP)
In [6]:
# Fit the models with the generated data and
# compare model performances
for i, offset in enumerate(clusters_separation):
np.random.seed(42)
# Data generation
X1 = 0.3 * np.random.randn(n_inliers // 2, 2) - offset
X2 = 0.3 * np.random.randn(n_inliers // 2, 2) + offset
X = np.r_[X1, X2]
# Add outliers
X = np.r_[X, np.random.uniform(low=-6, high=6, size=(n_outliers, 2))]
# Fit the model
plt.figure(figsize=(15, 12))
for i, (clf_name, clf) in enumerate(classifiers.items()):
print(i + 1, 'fitting', clf_name)
# fit the data and tag outliers
clf.fit(X)
scores_pred = clf.decision_function(X) * -1
y_pred = clf.predict(X)
threshold = stats.scoreatpercentile(scores_pred,
100 * outliers_fraction)
n_errors = (y_pred != ground_truth).sum()
# plot the levels lines and the points
Z = clf.decision_function(np.c_[xx.ravel(), yy.ravel()]) * -1
Z = Z.reshape(xx.shape)
subplot = plt.subplot(3, 4, i + 1)
subplot.contourf(xx, yy, Z, levels=np.linspace(Z.min(), threshold, 7),
cmap=plt.cm.Blues_r)
a = subplot.contour(xx, yy, Z, levels=[threshold],
linewidths=2, colors='red')
subplot.contourf(xx, yy, Z, levels=[threshold, Z.max()],
colors='orange')
b = subplot.scatter(X[:-n_outliers, 0], X[:-n_outliers, 1], c='white',
s=20, edgecolor='k')
c = subplot.scatter(X[-n_outliers:, 0], X[-n_outliers:, 1], c='black',
s=20, edgecolor='k')
subplot.axis('tight')
subplot.legend(
[a.collections[0], b, c],
['learned decision function', 'true inliers', 'true outliers'],
prop=matplotlib.font_manager.FontProperties(size=10),
loc='lower right')
subplot.set_xlabel("%d. %s (errors: %d)" % (i + 1, clf_name, n_errors))
subplot.set_xlim((-7, 7))
subplot.set_ylim((-7, 7))
plt.subplots_adjust(0.04, 0.1, 0.96, 0.94, 0.1, 0.26)
plt.suptitle("Outlier detection")
plt.show()
1 fitting Angle-based Outlier Detector (ABOD) 2 fitting Cluster-based Local Outlier Factor (CBLOF) 3 fitting Feature Bagging 4 fitting Histogram-base Outlier Detection (HBOS) 5 fitting Isolation Forest 6 fitting K Nearest Neighbors (KNN) 7 fitting Average KNN 8 fitting Local Outlier Factor (LOF) 9 fitting Minimum Covariance Determinant (MCD) 10 fitting One-class SVM (OCSVM) 11 fitting Principal Component Analysis (PCA) 12 fitting Locally Selective Combination (LSCP)
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