Welcome to kenchi’s documentation!

kenchi package

Subpackages

kenchi.datasets package

Submodules

kenchi.datasets.base module

kenchi.datasets.base.load_wdbc(contamination=0.0272, random_state=None, shuffle=True)

Load and return the breast cancer wisconsin dataset.

contamination : float, default 0.0272

Proportion of outliers in the data set.

random_state : int, RandomState instance, default None

Seed of the pseudo random number generator.

shuffle : bool, default True

If True, shuffle samples.

Returns:

• X (ndarray of shape (n_samples, n_features)) – Data.
• y (ndarray of shape (n_samples,)) – Return -1 (malignant) for outliers and +1 (benign) for inliers.

References

[1]	Kriegel, H.-P., Kroger, P., Schubert E., and Zimek, A., “Interpreting and unifying outlier scores,” In Proceedings of SDM‘11, pp. 13-24, 2011.

kenchi.datasets.base.load_pendigits(contamination=0.002, random_state=None, shuffle=True)

Load and return the pendigits dataset.

contamination : float, default 0.002

Proportion of outliers in the data set.

random_state : int, RandomState instance, default None

Seed of the pseudo random number generator.

shuffle : bool, default True

If True, shuffle samples.

Returns:

• X (ndarray of shape (n_samples, n_features)) – Data.
• y (ndarray of shape (n_samples,)) – Return -1 (digit 4) for outliers and +1 (otherwise) for inliers.

References

[2]	Kriegel, H.-P., Kroger, P., Schubert E., and Zimek, A., “Interpreting and unifying outlier scores,” In Proceedings of SDM‘11, pp. 13-24, 2011.

kenchi.datasets.sample_generator module

kenchi.datasets.sample_generator.make_blobs(centers=5, center_box=(-10.0, 10.0), cluster_std=1.0, contamination=0.02, n_features=25, n_samples=500, random_state=None, shuffle=True)

Generate isotropic Gaussian blobs with outliers.

Parameters:

• centers (int or array-like of shape (n_centers, n_features), default 5) – Number of centers to generate, or the fixed center locations.
• center_box (pair of floats (min, max), default (-10.0, 10.0)) – Bounding box for each cluster center when centers are generated at random.
• cluster_std (float or array-like of shape (n_centers,), default 1.0) – Standard deviation of the clusters.
• contamination (float, default 0.02) – Proportion of outliers in the data set.
• n_features (int, default 25) – Number of features for each sample.
• n_samples (int, default 500) – Number of samples.
• random_state (int, RandomState instance, default None) – Seed of the pseudo random number generator.
• shuffle (bool, default True) – If True, shuffle samples.

Returns:

• X (ndarray of shape (n_samples, n_features)) – Generated data.
• y (ndarray of shape (n_samples,)) – Return -1 for outliers and +1 for inliers.

References

[1]	Kriegel, H.-P., Kroger, P., Schubert E., and Zimek, A., “Interpreting and unifying outlier scores,” In Proceedings of SDM‘11, pp. 13-24, 2011.

Module contents

kenchi.outlier_detection package

Submodules

kenchi.outlier_detection.angle_based module

class kenchi.outlier_detection.angle_based.FastABOD(algorithm='auto', contamination=0.1, leaf_size=30, metric='minkowski', novelty=False, n_jobs=1, n_neighbors=20, p=2, metric_params=None)

Bases: kenchi.outlier_detection.base.BaseOutlierDetector

Fast Angle-Based Outlier Detector (FastABOD).

Parameters:

• algorithm (str, default 'auto') – Tree algorithm to use. Valid algorithms are [‘kd_tree’|’ball_tree’|’auto’].
• contamination (float, default 0.1) – Proportion of outliers in the data set. Used to define the threshold.
• leaf_size (int, default 30) – Leaf size of the underlying tree.
• metric (str or callable, default 'minkowski') – Distance metric to use.
• 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.
• n_jobs (int, default 1) – Number of jobs to run in parallel. If -1, then the number of jobs is set to the number of CPU cores.
• n_neighbors (int, default 20) – Number of neighbors.
• p (int, default 2) – Power parameter for the Minkowski metric.
• metric_params (dict, default None) – Additioal parameters passed to the requested metric.

anomaly_score_

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

threshold_

float – Threshold.

n_neighbors_

int – Actual number of neighbors used for kneighbors queries.

X_

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

References

[1]	Kriegel, H.-P., Kroger, P., Schubert E., and Zimek, A., “Interpreting and unifying outlier scores,” In Proceedings of SDM‘11, pp. 13-24, 2011.

[2]	Kriegel, H.-P., Schubert M., and Zimek, A., “Angle-based outlier detection in high-dimensional data,” In Proceedings of SIGKDD‘08, pp. 444-452, 2008.

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kenchi.outlier_detection.base module

kenchi.outlier_detection.base.is_outlier_detector(estimator)

Return True if the given estimator is (probably) an outlier detector.

Parameters:estimator (object) – Estimator object to test. Returns:out – True if estimator is an outlier detector and False otherwise. Return type:bool

class kenchi.outlier_detection.base.BaseOutlierDetector(contamination=0.1)

Bases: sklearn.base.BaseEstimator, abc.ABC

Base class for all outlier detectors in kenchi.

References

[1]	Kriegel, H.-P., Kroger, P., Schubert E., and Zimek, A., “Interpreting and unifying outlier scores,” In Proceedings of SDM‘11, pp. 13-24, 2011.

anomaly_score(X=None, normalize=False)

Compute the anomaly score for each sample.

Parameters:

• X (array-like of shape (n_samples, n_features), default None) – Data. If None, compute the anomaly score for each training sample.
• normalize (bool, default False) – If True, return the normalized anomaly score.

Returns:

anomaly_score – Anomaly score for each sample.

Return type:

array-like of shape (n_samples,)

decision_function(X=None, threshold=None)

Compute the decision function of the given samples.

Parameters:

• X (array-like of shape (n_samples, n_features), default None) – Data. If None, compute the decision function of the given training samples.
• threshold (float, default None) – User-provided threshold.

Returns:

y_score – Shifted opposite of the anomaly score for each sample. Negative scores represent outliers and positive scores represent inliers.

Return type:

array-like of shape (n_samples,)

fit(X, y=None)

Fit the model according to the given training data.

Parameters:

• X (array-like of shape (n_samples, n_features)) – Training data.
• y (ignored) –

Returns:

self – Return self.

Return type:

object

fit_predict(X, y=None)

Fit the model according to the given training data and predict if a particular training sample is an outlier or not.

Parameters:

• X (array-like of shape (n_samples, n_features)) – Training Data.
• y (ignored) –

Returns:

y_pred – Return -1 for outliers and +1 for inliers.

Return type:

array-like of shape (n_samples,)

plot_anomaly_score(X=None, normalize=False, **kwargs)

Plot the anomaly score for each sample.

Parameters:

• X (array-like of shape (n_samples, n_features), default None) – Data. If None, plot the anomaly score for each training samples.
• normalize (bool, default False) – If True, return the normalized anomaly score.
• ax (matplotlib Axes, default None) – Target axes instance.
• bins (int, str or array-like, default 'auto') – Number of hist bins.
• figsize (tuple, default None) – Tuple denoting figure size of the plot.
• filename (str, default None) – If provided, save the current figure.
• hist (bool, default True) – If True, plot a histogram of anomaly scores.
• kde (bool, default True) – If True, plot a gaussian kernel density estimate.
• title (string, default None) – Axes title. To disable, pass None.
• xlabel (string, default 'Samples') – X axis title label. To disable, pass None.
• xlim (tuple, default None) – Tuple passed to ax.xlim.
• ylabel (string, default 'Anomaly score') – Y axis title label. To disable, pass None.
• ylim (tuple, default None) – Tuple passed to ax.ylim.
• **kwargs (dict) – Other keywords passed to ax.plot.

Returns:

ax – Axes on which the plot was drawn.

Return type:

matplotlib Axes

plot_roc_curve(X, y, **kwargs)

Plot the Receiver Operating Characteristic (ROC) curve.

Parameters:

• X (array-like of shape (n_samples, n_features)) – Data.
• y (array-like of shape (n_samples,)) – Labels.
• 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.
• title (string, default 'ROC curve') – Axes title. To disable, pass None.
• xlabel (string, default 'FPR') – X axis title label. To disable, pass None.
• ylabel (string, default 'TPR') – Y axis title label. To disable, pass None.
• **kwargs (dict) – Other keywords passed to ax.plot.

Returns:

ax – Axes on which the plot was drawn.

Return type:

matplotlib Axes

predict(X=None, threshold=None)

Predict if a particular sample is an outlier or not.

Parameters:

• X (array-like of shape (n_samples, n_features), default None) – Data. If None, predict if a particular training sample is an outlier or not.
• threshold (float, default None) – User-provided threshold.

Returns:

y_pred – Return -1 for outliers and +1 for inliers.

Return type:

array-like of shape (n_samples,)

kenchi.outlier_detection.clustering_based module

class kenchi.outlier_detection.clustering_based.MiniBatchKMeans(batch_size=100, contamination=0.1, init='k-means++', init_size=None, max_iter=100, max_no_improvement=10, n_clusters=8, n_init=3, random_state=None, reassignment_ratio=0.01, tol=0.0)

Bases: kenchi.outlier_detection.base.BaseOutlierDetector

Outlier detector using K-means clustering.

Parameters:

• batch_size (int, optional, default 100) – Size of the mini batches.
• contamination (float, default 0.1) – Proportion of outliers in the data set. Used to define the threshold.
• init (str or array-like, default 'k-means++') – Method for initialization. Valid options are [‘k-means++’|’random’].
• init_size (int, default: 3 * batch_size) – Number of samples to randomly sample for speeding up the initialization.
• max_iter (int, default 100) – Maximum number of iterations.
• max_no_improvement (int, default 10) – Control early stopping based on the consecutive number of mini batches that does not yield an improvement on the smoothed inertia. To disable convergence detection based on inertia, set max_no_improvement to None.
• n_clusters (int, default 8) – Number of clusters.
• n_init (int, default 3) – Number of initializations to perform.
• random_state (int or RandomState instance, default None) – Seed of the pseudo random number generator.
• reassignment_ratio (float, default 0.01) – Control the fraction of the maximum number of counts for a center to be reassigned.
• tol (float, default 0.0) – Tolerance to declare convergence.

anomaly_score_

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

threshold_

float – Threshold.

cluster_centers_

array-like of shape (n_clusters, n_features) – Coordinates of cluster centers.

inertia_

float – Value of the inertia criterion associated with the chosen partition.

labels_

array-like of shape (n_samples,) – Label of each point.

cluster_centers_

inertia_

labels_

score(X, y=None)

Compute the opposite value of the given data on the K-means objective.

Parameters:

• X (array-like of shape (n_samples, n_features)) – Data.
• y (ignored) –

Returns:

score – Opposite value of the given data on the K-means objective.

Return type:

float

kenchi.outlier_detection.density_based module

class kenchi.outlier_detection.density_based.LOF(algorithm='auto', contamination=0.1, leaf_size=30, metric='minkowski', novelty=False, n_jobs=1, n_neighbors=20, p=2, metric_params=None)

Bases: kenchi.outlier_detection.base.BaseOutlierDetector

Local Outlier Factor.

Parameters:

• algorithm (str, default 'auto') – Tree algorithm to use. Valid algorithms are [‘kd_tree’|’ball_tree’|’auto’].
• contamination (float, default 0.1) – Proportion of outliers in the data set. Used to define the threshold.
• leaf_size (int, default 30) – Leaf size of the underlying tree.
• metric (str or callable, default 'minkowski') – Distance metric to use.
• 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.
• n_jobs (int, default 1) – Number of jobs to run in parallel. If -1, then the number of jobs is set to the number of CPU cores.
• n_neighbors (int, default 20) – Number of neighbors.
• p (int, default 2) – Power parameter for the Minkowski metric.
• metric_params (dict, default None) – Additioal parameters passed to the requested metric.

anomaly_score_

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

threshold_

float – Threshold.

negative_outlier_factor_

array-like of shape (n_samples,) – Opposite LOF of the training samples.

n_neighbors_

int – Actual number of neighbors used for kneighbors queries.

X_

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

References

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

[2]	Kriegel, H.-P., Kroger, P., Schubert E., and Zimek, A., “Interpreting and unifying outlier scores,” In Proceedings of SDM‘11, pp. 13-24, 2011.

X_

n_neighbors_

negative_outlier_factor_

kenchi.outlier_detection.distance_based module

class kenchi.outlier_detection.distance_based.KNN(aggregate=False, algorithm='auto', contamination=0.1, leaf_size=30, metric='minkowski', novelty=False, n_jobs=1, n_neighbors=20, p=2, metric_params=None)

Bases: kenchi.outlier_detection.base.BaseOutlierDetector

Outlier detector using k-nearest neighbors algorithm.

Parameters:

• aggregate (bool, default False) – If True, return the sum of the distances from k nearest neighbors as the anomaly score.
• algorithm (str, default 'auto') – Tree algorithm to use. Valid algorithms are [‘kd_tree’|’ball_tree’|’auto’].
• contamination (float, default 0.1) – Proportion of outliers in the data set. Used to define the threshold.
• leaf_size (int, default 30) – Leaf size of the underlying tree.
• metric (str or callable, default 'minkowski') – Distance metric to use.
• 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.
• n_jobs (int, default 1) – Number of jobs to run in parallel. If -1, then the number of jobs is set to the number of CPU cores.
• n_neighbors (int, default 20) – Number of neighbors.
• p (int, default 2) – Power parameter for the Minkowski metric.
• metric_params (dict, default None) – Additioal parameters passed to the requested metric.

anomaly_score_

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

threshold_

float – Threshold.

n_neighbors_

int – Actual number of neighbors used for kneighbors queries.

X_

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

References

[1]	Angiulli, F., and Pizzuti, C., “Fast outlier detection in high dimensional spaces,” In Proceedings of PKDD‘02, pp. 15-27, 2002.

[2]	Ramaswamy, S., Rastogi R., and Shim, K., “Efficient algorithms for mining outliers from large data sets,” In Proceedings of SIGMOD‘00, pp. 427-438, 2000.

X_

class kenchi.outlier_detection.distance_based.OneTimeSampling(contamination=0.1, metric='euclidean', novelty=False, n_subsamples=20, random_state=None, metric_params=None)

Bases: kenchi.outlier_detection.base.BaseOutlierDetector

One-time sampling.

Parameters:

• contamination (float, default 0.1) – Proportion of outliers in the data set. Used to define the threshold.
• metric (str, default 'euclidean') – Distance metric to use.
• 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.
• n_subsamples (int, default 20) – Number of random samples to be used.
• random_state (int, RandomState instance, default None) – Seed of the pseudo random number generator.
• metric_params (dict, default None) – Additional parameters passed to the requested metric.

anomaly_score_

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

threshold_

float – Threshold.

subsamples_

array-like of shape (n_subsamples,) – Indices of subsamples.

S_

array-like of shape (n_subsamples, n_features) – Subset of the given training data.

References

[3]	Sugiyama M., and Borgwardt, K., “Rapid distance-based outlier detection via sampling,” Advances in NIPS‘13, pp. 467-475, 2013.

kenchi.outlier_detection.ensemble module

class kenchi.outlier_detection.ensemble.IForest(bootstrap=False, contamination=0.1, max_features=1.0, max_samples='auto', n_estimators=100, n_jobs=1, random_state=None)

Bases: kenchi.outlier_detection.base.BaseOutlierDetector

Isolation forest (iForest).

Parameters:

• bootstrap (bool, False) – If True, individual trees are fit on random subsets of the training data sampled with replacement. If False, sampling without replacement is performed.
• contamination (float, default 0.1) – Proportion of outliers in the data set. Used to define the threshold.
• max_features (int or float, default 1.0) – Number of features to draw from X to train each base estimator.
• max_samples (int ,float or str, default 'auto') – Number of samples to draw from X to train each base estimator.
• n_estimators (int, default 100) – Number of base estimators in the ensemble.
• n_jobs (int) – Number of jobs to run in parallel. If -1, then the number of jobs is set to the number of CPU cores.
• random_state (int or RandomState instance, default None) – Seed of the pseudo random number generator.

anomaly_score_

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

threshold_

float – Threshold.

estimators_

list – Collection of fitted sub-estimators.

estimators_samples_

int – Subset of drawn samples for each base estimator.

max_samples_

int – Actual number of samples.

References

[1]	Liu, F. T., Ting K. M., and Zhou, Z.-H., “Isolation forest,” In Proceedings of ICDM‘08, pp. 413-422, 2008.

estimators_

estimators_samples_

max_samples_

kenchi.outlier_detection.reconstruction_based module

class kenchi.outlier_detection.reconstruction_based.PCA(contamination=0.1, iterated_power='auto', n_components=None, random_state=None, svd_solver='auto', tol=0.0, whiten=False)

Bases: kenchi.outlier_detection.base.BaseOutlierDetector

Outlier detector using Principal Component Analysis (PCA).

Parameters:

• contamination (float, default 0.1) – Proportion of outliers in the data set. Used to define the threshold.
• iterated_power (int, default 'auto') – Number of iterations for the power method computed by svd_solver == ‘randomized’.
• n_components (int, float, or string, default None) – Number of components to keep.
• random_state (int or RandomState instance, default None) – Seed of the pseudo random number generator.
• svd_solver (string, default 'auto') – SVD solver to use. Valid solvers are [‘auto’|’full’|’arpack’|’randomized’].
• tol (float, default 0.0) – Tolerance to declare convergence for singular values computed by svd_solver == ‘arpack’.
• whiten (bool, default False) – When True the components_ vectors are multiplied by the square root of n_samples and then divided by the singular values to ensure uncorrelated outputs with unit component-wise variances.

anomaly_score_

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

threshold_

float – Threshold.

components_

array-like of shape (n_components, n_features) – Principal axes in feature space, representing the directions of maximum variance in the data.

explained_variance_

array-like of shape (n_components,) – Amount of variance explained by each of the selected components.

explained_variance_ratio_

array-like of shape (n_components,) – Percentage of variance explained by each of the selected components.

mean_

array-like of shape (n_features,) – Per-feature empirical mean, estimated from the training set.

noise_variance_

float – Estimated noise covariance following the Probabilistic PCA model from Tipping and Bishop 1999.

n_components_

int – Estimated number of components.

singular_values_

array-like of shape (n_components,) – Singular values corresponding to each of the selected components.

components_

explained_variance_

explained_variance_ratio_

mean_

n_components_

noise_variance_

score(X, y=None)

Compute the mean log-likelihood of the given data.

Parameters:

• X (array-like of shape (n_samples, n_features)) – Data.
• y (ignored) –

Returns:

score – Mean log-likelihood of the given data.

Return type:

float

singular_values_

kenchi.outlier_detection.statistical module

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)

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.

threshold_

float – Threshold.

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.

converged_

covariances_

lower_bound_

means_

n_iter_

precisions_

precisions_cholesky_

score(X, y=None)

Compute the mean log-likelihood of the given data.

Parameters:

• X (array-like of shape (n_samples, n_features)) – Data.
• y (ignored.) –

Returns:

score – Mean log-likelihood of the given data.

Return type:

float

weights_

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

Bases: kenchi.outlier_detection.base.BaseOutlierDetector

Histogram-based outlier detector.

Parameters:

• bins (int, str or array-like, 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.

threshold_

float – Threshold.

bin_edges_

array-like – Bin edges.

bin_widths_

array-like – Bin widths.

data_min_

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

data_max_

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

hist_

array-like of shape (n_features, bins) – Values of the histogram.

X_

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

References

[1]	Goldstein, M., and Dengel, A., “Histogram-based outlier score (HBOS): A fast unsupervised anomaly detection algorithm,” KI‘12: Poster and Demo Track, pp. 59-63, 2012.

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)

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.

threshold_

float – Threshold.

X_

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

X_

score(X, y=None)

Compute the mean log-likelihood of the given data.

Parameters:

• X (array-like of shape (n_samples, n_features)) – Data.
• y (ignored) –

Returns:

score – Mean log-likelihood of the given data.

Return type:

float

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)

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.

threshold_

float – Threshold.

covariance_

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

graphical_model_

networkx Graph – GGM.

isolates_

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

labels_

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

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.

precision_

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

References

[2]	Ide, T., Lozano, C., Abe N., and Liu, Y., “Proximity-based anomaly detection using sparse structure learning,” In Proceedings of SDM‘09, pp. 97-108, 2009.

covariance_

featurewise_anomaly_score(X)

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_

isolates_

labels_

location_

n_iter_

partial_corrcoef_

plot_graphical_model(**kwargs)

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)

Plot the partial correlation coefficient matrix.

Parameters:

• ax (matplotlib Axes, default None) – Target axes instance.
• cbar (bool, default True.) – Whether 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_

score(X, y=None)

Compute the mean log-likelihood of the given data.

Parameters:

• X (array-like of shape (n_samples, n_features)) – Data.
• y (ignored) –

Returns:

score – Mean log-likelihood of the given data.

Return type:

float

Module contents

Submodules

kenchi.pipeline module

kenchi.pipeline.make_pipeline(*steps)

Construct a Pipeline from the given estimators. This is a shorthand for the Pipeline constructor; it does not require, and does not permit, naming the estimators. Instead, their names will be set to the lowercase of their types automatically.

Parameters:*steps (list) – List of estimators. Returns:p Return type:Pipeline

class kenchi.pipeline.Pipeline(steps, memory=None)

Bases: sklearn.pipeline.Pipeline

Pipeline of transforms with a final estimator.

Parameters:

• steps (list) – List of (name, transform) tuples (implementing fit/transform) that are chained, in the order in which they are chained, with the last object an estimator.
• memory (instance of joblib.Memory or string, default None) – Used to cache the fitted transformers of the pipeline. By default, no caching is performed. If a string is given, it is the path to the caching directory. Enabling caching triggers a clone of the transformers before fitting. Therefore, the transformer instance given to the pipeline cannot be inspected directly. Use the attribute named_steps or steps to inspect estimators within the pipeline. Caching the transformers is advantageous when fitting is time consuming.

named_steps

dict – Read-only attribute to access any step parameter by user given name. Keys are step names and values are steps parameters.

anomaly_score(X, normalize=False)

Apply transforms, and compute the anomaly score for each sample with the final estimator.

Parameters:

• X (array-like of shape (n_samples, n_features)) – Data.
• normalize (bool, default False) – If True, return the normalized anomaly score.

Returns:

anomaly_score – Anomaly score for each sample.

Return type:

array-like of shape (n_samples,)

featurewise_anomaly_score(X)

Apply transforms, and compute the feature-wise anomaly scores for each sample with the final estimator.

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) Raises:ValueError

plot_anomaly_score(X, **kwargs)

Apply transoforms, and plot the anomaly score for each sample with the final estimator.

Parameters:

• X (array-like of shape (n_samples, n_features)) – Data.
• ax (matplotlib Axes, default None) – Target axes instance.
• bins (int, str or array-like, default 'auto') – Number of hist bins.
• figsize (tuple, default None) – Tuple denoting figure size of the plot.
• filename (str, default None) – If provided, save the current figure.
• hist (bool, default True) – If True, plot a histogram of anomaly scores.
• kde (bool, default True) – If True, plot a gaussian kernel density estimate.
• title (string, default None) – Axes title. To disable, pass None.
• xlabel (string, default 'Samples') – X axis title label. To disable, pass None.
• xlim (tuple, default None) – Tuple passed to ax.xlim.
• ylabel (string, default 'Anomaly score') – Y axis title label. To disable, pass None.
• ylim (tuple, default None) – Tuple passed to ax.ylim.
• **kwargs (dict) – Other keywords passed to ax.plot.

Returns:

ax – Axes on which the plot was drawn.

Return type:

matplotlib Axes

plot_graphical_model

Apply transforms, and plot the Gaussian Graphical Model (GGM) with the final estimator.

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

Apply transforms, and plot the partial correlation coefficient matrix with the final estimator.

Parameters:

• ax (matplotlib Axes, default None) – Target axes instance.
• cbar (bool, default True.) – Whether 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

plot_roc_curve(X, y, **kwargs)

Apply transoforms, and plot the Receiver Operating Characteristic (ROC) curve with the final estimator.

Parameters:

• X (array-like of shape (n_samples, n_features)) – Data.
• y (array-like of shape (n_samples,)) – Labels.
• 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.
• title (string, default 'ROC curve') – Axes title. To disable, pass None.
• xlabel (string, default 'FPR') – X axis title label. To disable, pass None.
• ylabel (string, default 'TPR') – Y axis title label. To disable, pass None.
• **kwargs (dict) – Other keywords passed to ax.plot.

Returns:

ax – Axes on which the plot was drawn.

Return type:

matplotlib Axes

kenchi.visualization module

kenchi.visualization.plot_anomaly_score(anomaly_score, ax=None, bins='auto', figsize=None, filename=None, hist=True, kde=True, threshold=None, title=None, xlabel='Samples', xlim=None, ylabel='Anomaly score', ylim=None, **kwargs)

Plot the anomaly score for each sample.

Parameters:

• anomaly_score (array-like of shape (n_samples,)) – Anomaly score for each sample.
• ax (matplotlib Axes, default None) – Target axes instance.
• bins (int, str or array-like, default 'auto') – Number of hist bins.
• figsize (tuple, default None) – Tuple denoting figure size of the plot.
• filename (str, default None) – If provided, save the current figure.
• hist (bool, default True) – If True, plot a histogram of anomaly scores.
• kde (bool, default True) – If True, plot a gaussian kernel density estimate.
• threshold (float, default None) – Threshold.
• title (string, default None) – Axes title. To disable, pass None.
• xlabel (string, default 'Samples') – X axis title label. To disable, pass None.
• xlim (tuple, default None) – Tuple passed to ax.xlim.
• ylabel (string, default 'Anomaly score') – Y axis title label. To disable, pass None.
• ylim (tuple, default None) – Tuple passed to ax.ylim.
• **kwargs (dict) – Other keywords passed to ax.plot.

Returns:

ax – Axes on which the plot was drawn.

Return type:

matplotlib Axes

Examples

kenchi.visualization.plot_roc_curve(y_true, y_score, ax=None, figsize=None, filename=None, title='ROC curve', xlabel='FPR', ylabel='TPR', **kwargs)

Plot the Receiver Operating Characteristic (ROC) curve.

Parameters:

• y_true (array-like of shape (n_samples,)) – True Labels.
• y_score (array-like of shape (n_samples,)) – Target scores.
• 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.
• title (string, default 'ROC curve') – Axes title. To disable, pass None.
• xlabel (string, default 'FPR') – X axis title label. To disable, pass None.
• ylabel (string, default 'TPR') – Y axis title label. To disable, pass None.
• **kwargs (dict) – Other keywords passed to ax.plot.

Returns:

ax – Axes on which the plot was drawn.

Return type:

matplotlib Axes

Examples

kenchi.visualization.plot_graphical_model(G, ax=None, figsize=None, filename=None, random_state=None, title='GGM', **kwargs)

Plot the Gaussian Graphical Model (GGM).

Parameters:

• G (networkx Graph) – GGM.
• 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') – 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

Examples

kenchi.visualization.plot_partial_corrcoef(partial_corrcoef, ax=None, cbar=True, figsize=None, filename=None, title='Partial correlation', **kwargs)

Plot the partial correlation coefficient matrix.

Parameters:

• partial_corrcoef (array-like of shape (n_features, n_features)) – Partial correlation coefficient matrix.
• ax (matplotlib Axes, default None) – Target axes instance.
• cbar (bool, default True.) – Whether 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

Examples

Module contents

Indices and tables

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