class kenchi.outlier_detection.statistical.GMM(contamination=0.1, covariance_type='full', init_params='kmeans', max_iter=100, means_init=None, n_components=1, n_init=1, precisions_init=None, random_state=None, reg_covar=1e-06, tol=0.001, warm_start=False, weights_init=None)[source]

Bases: kenchi.outlier_detection.base.BaseOutlierDetector

Outlier detector using Gaussian Mixture Models (GMMs).

Parameters:
  • contamination (float, default 0.1) – Proportion of outliers in the data set. Used to define the threshold.
  • covariance_type (str, default 'full') – String describing the type of covariance parameters to use. Valid options are [‘full’|’tied’|’diag’|’spherical’].
  • init_params (str, default 'kmeans') – Method used to initialize the weights, the means and the precisions. Valid options are [‘kmeans’|’random’].
  • max_iter (int, default 100) – Maximum number of iterations.
  • means_init (array-like of shape (n_components, n_features), default None) – User-provided initial means.
  • n_init (int, default 1) – Number of initializations to perform.
  • n_components (int, default 1) – Number of mixture components.
  • precisions_init (array-like, default None) – User-provided initial precisions.
  • random_state (int or RandomState instance, default None) – Seed of the pseudo random number generator.
  • reg_covar (float, default 1e-06) – Non-negative regularization added to the diagonal of covariance.
  • tol (float, default 1e-03) – Tolerance to declare convergence.
  • warm_start (bool, default False) – If True, the solution of the last fitting is used as initialization for the next call of fit.
  • weights_init (array-like of shape (n_components,), default None) – User-provided initial weights.
anomaly_score_

array-like of shape (n_samples,) – Anomaly score for each training data.

contamination_

float – Actual proportion of outliers in the data set.

threshold_

float – Threshold.

Examples

>>> import numpy as np
>>> from kenchi.outlier_detection import GMM
>>> X = np.array([
...     [0., 0.], [1., 1.], [2., 0.], [3., -1.], [4., 0.],
...     [5., 1.], [6., 0.], [7., -1.], [8., 0.], [1000., 1.]
... ])
>>> det = GMM(random_state=0)
>>> det.fit_predict(X)
array([ 1,  1,  1,  1,  1,  1,  1,  1,  1, -1])
converged_

bool – True when convergence was reached in fit, False otherwise.

covariances_

array-like – Covariance of each mixture component.

lower_bound_

float – Log-likelihood of the best fit of EM.

means_

array-like of shape (n_components, n_features) – Mean of each mixture component.

n_iter_

int – Number of step used by the best fit of EM to reach the convergence.

precisions_

array-like – Precision matrix for each component in the mixture.

precisions_cholesky_

array-like – Cholesky decomposition of the precision matrices of each mixture component.

weights_

array-like of shape (n_components,) – Weight of each mixture components.

class kenchi.outlier_detection.statistical.HBOS(bins='auto', contamination=0.1, novelty=False)[source]

Bases: kenchi.outlier_detection.base.BaseOutlierDetector

Histogram-based outlier detector.

Parameters:
  • bins (int or str, default 'auto') – Number of hist bins.
  • contamination (float, default 0.1) – Proportion of outliers in the data set. Used to define the threshold.
  • novelty (bool, default False) – If True, you can use predict, decision_function and anomaly_score on new unseen data and not on the training data.
anomaly_score_

array-like of shape (n_samples,) – Anomaly score for each training data.

contamination_

float – Actual proportion of outliers in the data set.

threshold_

float – Threshold.

bin_edges_

array-like – Bin edges.

data_max_

array-like of shape (n_features,) – Per feature maximum seen in the data.

data_min_

array-like of shape (n_features,) – Per feature minimum seen in the data.

hist_

array-like – Values of the histogram.

References

[1]Goldstein, M., and Dengel, A., “Histogram-based outlier score (HBOS): A fast unsupervised anomaly detection algorithm,” KI: Poster and Demo Track, pp. 59-63, 2012.

Examples

>>> import numpy as np
>>> from kenchi.outlier_detection import HBOS
>>> X = np.array([
...     [0., 0.], [1., 1.], [2., 0.], [3., -1.], [4., 0.],
...     [5., 1.], [6., 0.], [7., -1.], [8., 0.], [1000., 1.]
... ])
>>> det = HBOS()
>>> det.fit_predict(X)
array([ 1,  1,  1,  1,  1,  1,  1,  1,  1, -1])
class kenchi.outlier_detection.statistical.KDE(algorithm='auto', atol=0.0, bandwidth=1.0, breadth_first=True, contamination=0.1, kernel='gaussian', leaf_size=40, metric='euclidean', rtol=0.0, metric_params=None)[source]

Bases: kenchi.outlier_detection.base.BaseOutlierDetector

Outlier detector using Kernel Density Estimation (KDE).

Parameters:
  • algorithm (str, default 'auto') – Tree algorithm to use. Valid algorithms are [‘kd_tree’|’ball_tree’|’auto’].
  • atol (float, default 0.0) – Desired absolute tolerance of the result.
  • bandwidth (float, default 1.0) – Bandwidth of the kernel.
  • breadth_first (bool, default True) – If true, use a breadth-first approach to the problem. Otherwise use a depth-first approach.
  • contamination (float, default 0.1) – Proportion of outliers in the data set. Used to define the threshold.
  • kernel (str, default 'gaussian') – Kernel to use. Valid kernels are [‘gaussian’|’tophat’|’epanechnikov’|’exponential’|’linear’|’cosine’].
  • leaf_size (int, default 40) – Leaf size of the underlying tree.
  • metric (str, default 'euclidean') – Distance metric to use.
  • rtol (float, default 0.0) – Desired relative tolerance of the result.
  • metric_params (dict, default None) – Additional parameters to be passed to the requested metric.
anomaly_score_

array-like of shape (n_samples,) – Anomaly score for each training data.

contamination_

float – Actual proportion of outliers in the data set.

threshold_

float – Threshold.

References

[2]Parzen, E., “On estimation of a probability density function and mode,” Ann. Math. Statist., 33(3), pp. 1065-1076, 1962.

Examples

>>> import numpy as np
>>> from kenchi.outlier_detection import KDE
>>> X = np.array([
...     [0., 0.], [1., 1.], [2., 0.], [3., -1.], [4., 0.],
...     [5., 1.], [6., 0.], [7., -1.], [8., 0.], [1000., 1.]
... ])
>>> det = KDE()
>>> det.fit_predict(X)
array([ 1,  1,  1,  1,  1,  1,  1,  1,  1, -1])
X_

array-like of shape (n_samples, n_features) – Training data.

class kenchi.outlier_detection.statistical.SparseStructureLearning(alpha=0.01, assume_centered=False, contamination=0.1, enet_tol=0.0001, max_iter=100, mode='cd', tol=0.0001, apcluster_params=None)[source]

Bases: kenchi.outlier_detection.base.BaseOutlierDetector

Outlier detector using sparse structure learning.

Parameters:
  • alpha (float, default 0.01) – Regularization parameter.
  • assume_centered (bool, default False) – If True, data are not centered before computation.
  • contamination (float, default 0.1) – Proportion of outliers in the data set. Used to define the threshold.
  • enet_tol (float, default 1e-04) – Tolerance for the elastic net solver used to calculate the descent direction. This parameter controls the accuracy of the search direction for a given column update, not of the overall parameter estimate. Only used for mode=’cd’.
  • max_iter (integer, default 100) – Maximum number of iterations.
  • mode (str, default 'cd') – Lasso solver to use: coordinate descent or LARS.
  • tol (float, default 1e-04) – Tolerance to declare convergence.
  • apcluster_params (dict, default None) – Additional parameters passed to sklearn.cluster.affinity_propagation.
anomaly_score_

array-like of shape (n_samples,) – Anomaly score for each training data.

contamination_

float – Actual proportion of outliers in the data set.

threshold_

float – Threshold.

labels_

array-like of shape (n_features,) – Label of each feature.

References

[3]Ide, T., Lozano, C., Abe, N., and Liu, Y., “Proximity-based anomaly detection using sparse structure learning,” In Proceedings of SDM, pp. 97-108, 2009.

Examples

>>> import numpy as np
>>> from kenchi.outlier_detection import SparseStructureLearning
>>> X = np.array([
...     [0., 0.], [1., 1.], [2., 0.], [3., -1.], [4., 0.],
...     [5., 1.], [6., 0.], [7., -1.], [8., 0.], [1000., 1.]
... ])
>>> det = SparseStructureLearning()
>>> det.fit_predict(X)
array([ 1,  1,  1,  1,  1,  1,  1,  1,  1, -1])
covariance_

array-like of shape (n_features, n_features) – Estimated covariance matrix.

featurewise_anomaly_score(X)[source]

Compute the feature-wise anomaly scores for each sample.

Parameters:X (array-like of shape (n_samples, n_features)) – Data.
Returns:anomaly_score – Feature-wise anomaly scores for each sample.
Return type:array-like of shape (n_samples, n_features)
graphical_model_

networkx Graph – GGM.

isolates_

array-like of shape (n_isolates,) – Indices of isolates.

location_

array-like of shape (n_features,) – Estimated location.

n_iter_

int – Number of iterations run.

partial_corrcoef_

array-like of shape (n_features, n_features) – Partial correlation coefficient matrix.

plot_graphical_model(**kwargs)[source]

Plot the Gaussian Graphical Model (GGM).

Parameters:
  • ax (matplotlib Axes, default None) – Target axes instance.
  • figsize (tuple, default None) – Tuple denoting figure size of the plot.
  • filename (str, default None) – If provided, save the current figure.
  • random_state (int, RandomState instance, default None) – Seed of the pseudo random number generator.
  • title (string, default 'GGM (n_clusters, n_features, n_isolates)') – Axes title. To disable, pass None.
  • **kwargs (dict) – Other keywords passed to nx.draw_networkx.
Returns:

ax – Axes on which the plot was drawn.
Return type:

matplotlib Axes
plot_partial_corrcoef(**kwargs)[source]

Plot the partial correlation coefficient matrix.

Parameters:
  • ax (matplotlib Axes, default None) – Target axes instance.
  • cbar (bool, default True.) – If Ture, to draw a colorbar.
  • figsize (tuple, default None) – Tuple denoting figure size of the plot.
  • filename (str, default None) – If provided, save the current figure.
  • title (string, default 'Partial correlation') – Axes title. To disable, pass None.
  • **kwargs (dict) – Other keywords passed to ax.pcolormesh.
Returns:

ax – Axes on which the plot was drawn.
Return type:

matplotlib Axes
precision_

array-like of shape (n_features, n_features) – Estimated pseudo inverse matrix.