DWT_MLEAD¶

class DWT_MLEAD(start_level: int = 3, quantile_boundary_type: str = 'percentile', quantile_epsilon: float = 0.01)[source]¶

DWT-MLEAD anomaly detector.

DWT-MLEAD is an anomaly detection algorithm that uses the Discrete Wavelet Transform (DWT) and Maximum Likelihood Estimation (MLE) to detect anomalies in univariate time series. The algorithm performs mutli-level DWT using the Haar wavelet, slides windows over the DWT coefficients, and estimates the likelihood of each window using a Gaussian distribution. Anomalies are detected by comparing the likelihoods to a quantile boundary in each level and passing down the anomaly counts to the individual time points, which we use as anomaly scores. The original paper [1] subsequently clusters the anomalies to determine the anomaly centers. This step is not implemented in this version.

Capabilities¶
Input data format	univariate
Output data format	anomaly scores
Learning Type	unsupervised

Parameters:

start_levelint, default=3: The level at which to start the anomaly detection. Must be >= 0 and less than log_2(n_timepoints).
quantile_boundary_typestr, default=’percentile’: The type of boundary to use for the quantile. Must be ‘percentile’, ‘monte-carlo’ is not implemented yet.
quantile_epsilonfloat, default=0.01: The epsilon value for the quantile boundary. Must be in [0, 1].

Attributes:

is_fitted: Whether fit has been called.

Notes

This implementation does not exactly match the original paper [1]. We make the following changes:

We use window sizes for the DWT coefficients that decrease with the level number because otherwise we would have too few items to slide the window over.
We exclude the highest level coefficients because they contain only a single entry and are, thus, not suitable for sliding a window of length 2 over it.
We have not implemented the Monte Carlo quantile boundary type yet.
We do not perform the anomaly clustering step to determine the anomaly centers. Instead, we return the anomaly scores for each timestep in the original time series.

References

[1] (1,2)

Thill, Markus, Wolfgang Konen, and Thomas Bäck. “Time Series Anomaly Detection with Discrete Wavelet Transforms and Maximum Likelihood Estimation.” In Proceedings of the International Conference on Time Series (ITISE). Granada, Spain, 2017.

Examples

>>> import numpy as np
>>> from aeon.anomaly_detection import DWT_MLEAD
>>> X = np.array([1, 2, 3, 4, 1, 2, 3, 3, 2, 8, 9, 8, 1, 2, 3, 4], dtype=np.float_)
>>> detector = DWT_MLEAD(
...    start_level=1, quantile_boundary_type='percentile', quantile_epsilon=0.01
... )
>>> detector.fit_predict(X)
array([0., 0., 0., 0., 0., 0., 0., 0., 2., 2., 2., 2., 0., 0., 0., 0.])

Methods

`check_is_fitted`()	Check if the estimator has been fitted.
`clone`()	Obtain a clone of the object with same hyper-parameters.
`clone_tags`(estimator[, tag_names])	Clone/mirror tags from another estimator as dynamic override.
`create_test_instance`([parameter_set, ...])	Construct Estimator instance if possible.
`create_test_instances_and_names`([parameter_set])	Create list of all test instances and a list of names for them.
`fit`(X[, y, axis])	Fit time series anomaly detector to X.
`fit_predict`(X[, y, axis])	Fit time series anomaly detector and find anomalies for X.
`get_class_tag`(tag_name[, tag_value_default, ...])	Get tag value from estimator class (only class tags).
`get_class_tags`()	Get class tags from estimator class and all its parent classes.
`get_fitted_params`([deep])	Get fitted parameters.
`get_metadata_routing`()	Get metadata routing of this object.
`get_param_defaults`()	Get parameter defaults for the object.
`get_param_names`()	Get parameter names for the object.
`get_params`([deep])	Get parameters for this estimator.
`get_tag`(tag_name[, tag_value_default, ...])	Get tag value from estimator class.
`get_tags`()	Get tags from estimator class.
`get_test_params`([parameter_set])	Return testing parameter settings for the estimator.
`is_composite`()	Check if the object is composite.
`load_from_path`(serial)	Load object from file location.
`load_from_serial`(serial)	Load object from serialized memory container.
`predict`(X[, axis])	Find anomalies in X.
`reset`()	Reset the object to a clean post-init state.
`save`([path])	Save serialized self to bytes-like object or to (.zip) file.
`set_fit_request`(*[, axis])	Request metadata passed to the `fit` method.
`set_params`(**params)	Set the parameters of this object.
`set_predict_request`(*[, axis])	Request metadata passed to the `predict` method.
`set_tags`(**tag_dict)	Set dynamic tags to given values.

classmethod get_test_params(parameter_set='default')[source]¶

Return testing parameter settings for the estimator.

Only supports ‘default’-parameter set.

Parameters:

parameter_setstr, default=”default”: Name of the set of test parameters to return, for use in tests. If no special parameters are defined for a value, will return “default” set.

Returns:

paramsdict or list of dict, default={}: Parameters to create testing instances of the class. Each dict are parameters to construct an “interesting” test instance, i.e., MyClass(**params) or MyClass(**params[i]) creates a valid test instance. create_test_instance uses the first (or only) dictionary in params.

check_is_fitted()[source]¶

Check if the estimator has been fitted.

Raises:

NotFittedError: If the estimator has not been fitted yet.

clone()[source]¶

Obtain a clone of the object with same hyper-parameters.

A clone is a different object without shared references, in post-init state. This function is equivalent to returning sklearn.clone of self. Equal in value to type(self)(**self.get_params(deep=False)).

Returns:

instance of type(self), clone of self (see above)

clone_tags(estimator, tag_names=None)[source]¶

Clone/mirror tags from another estimator as dynamic override.

Parameters:

estimatorobject: Estimator inheriting from :class:BaseEstimator.
tag_namesstr or list of str, default = None: Names of tags to clone. If None then all tags in estimator are used as tag_names.

Returns:

Self: Reference to self.

Notes

Changes object state by setting tag values in tag_set from estimator as dynamic tags in self.

classmethod create_test_instance(parameter_set='default', return_first=True)[source]¶

Construct Estimator instance if possible.

Calls the get_test_params method and returns an instance or list of instances using the returned dict or list of dict.

Parameters:

parameter_setstr, default=”default”: Name of the set of test parameters to return, for use in tests. If no special parameters are defined for a value, will return “default” set.
return_firstbool, default=True: If True, return the first instance of the list of instances. If False, return the list of instances.

Returns:

instanceBaseEstimator or list of BaseEstimator: Instance of the class with default parameters. If return_first is False, returns list of instances.

classmethod create_test_instances_and_names(parameter_set='default')[source]¶

Create list of all test instances and a list of names for them.

Parameters:

parameter_setstr, default=”default”: Name of the set of test parameters to return, for use in tests. If no special parameters are defined for a value, will return “default” set.

Returns:

objslist of instances of cls: i-th instance is cls(**cls.get_test_params()[i]).
nameslist of str, same length as objs: i-th element is name of i-th instance of obj in tests convention is {cls.__name__}-{i} if more than one instance otherwise {cls.__name__}.
parameter_setstr, default=”default”: Name of the set of test parameters to return, for use in tests. If no special parameters are defined for a value, will return “default” set.

fit(X, y=None, axis=1)[source]¶

Fit time series anomaly detector to X.

If the tag fit_is_empty is true, this just sets the is_fitted tag to true. Otherwise, it checks self can handle X, formats X into the structure required by self then passes X (and possibly y) to _fit.

Parameters:

Xone of aeon.base._base_series.VALID_INPUT_TYPES: The time series to fit the model to. A valid aeon time series data structure. See aeon.base._base_series.VALID_INPUT_TYPES for aeon supported types.
yone of aeon.base._base_series.VALID_INPUT_TYPES, default=None: The target values for the time series. A valid aeon time series data structure. See aeon.base._base_series.VALID_INPUT_TYPES for aeon supported types.
axisint: The time point axis of the input series if it is 2D. If axis==0, it is assumed each column is a time series and each row is a time point. i.e. the shape of the data is (n_timepoints, n_channels). axis==1 indicates the time series are in rows, i.e. the shape of the data is (n_channels, n_timepoints).

Returns:

BaseAnomalyDetector: The fitted estimator, reference to self.

fit_predict(X, y=None, axis=1) → ndarray[source]¶

Fit time series anomaly detector and find anomalies for X.

Parameters:

Xone of aeon.base._base_series.VALID_INPUT_TYPES: The time series to fit the model to. A valid aeon time series data structure. See aeon.base._base_series.VALID_INPUT_TYPES for aeon supported types.
yone of aeon.base._base_series.VALID_INPUT_TYPES, default=None: The target values for the time series. A valid aeon time series data structure. See aeon.base._base_series.VALID_INPUT_TYPES for aeon supported types.
axisint, default=1: The time point axis of the input series if it is 2D. If axis==0, it is assumed each column is a time series and each row is a time point. i.e. the shape of the data is (n_timepoints, n_channels). axis==1 indicates the time series are in rows, i.e. the shape of the data is (n_channels, n_timepoints).

Returns:

np.ndarray: A boolean, int or float array of length len(X), where each element indicates whether the corresponding subsequence is anomalous or its anomaly score.

classmethod get_class_tag(tag_name, tag_value_default=None, raise_error=False)[source]¶

Get tag value from estimator class (only class tags).

Parameters:

tag_namestr: Name of tag value.
tag_value_defaultany type: Default/fallback value if tag is not found.
raise_errorbool: Whether a ValueError is raised when the tag is not found.

Returns:

tag_value: Value of the tag_name tag in self. If not found, returns an error if raise_error is True, otherwise it returns tag_value_default.

Raises:

ValueError if raise_error is True i.e. if tag_name is not in self.get_tags(
).keys()

See also

get_tag: Get a single tag from an object.
get_class_tags: Get all tags from a class.
get_class_tag: Get a single tag from a class.

Examples

>>> from aeon.classification import DummyClassifier
>>> d = DummyClassifier()
>>> tags = d.get_tags()

is_composite()[source]¶

Check if the object is composite.

A composite object is an object which contains objects, as parameters. Called on an instance, since this may differ by instance.

Returns:

composite: bool: Whether self contains a parameter which is BaseObject.

property is_fitted[source]¶: Whether fit has been called.

classmethod load_from_path(serial)[source]¶

Load object from file location.

Parameters:

serialobject: Result of ZipFile(path).open(“object).

Returns:

deserialized self resulting in output at path, of cls.save(path)

classmethod load_from_serial(serial)[source]¶

Load object from serialized memory container.

Parameters:

serialobject: First element of output of cls.save(None).

Returns:

deserialized self resulting in output serial, of cls.save(None).

predict(X, axis=1) → ndarray[source]¶

Find anomalies in X.

Parameters:

Xone of aeon.base._base_series.VALID_INPUT_TYPES: The time series to fit the model to. A valid aeon time series data structure. See aeon.base._base_series.VALID_INPUT_TYPES for aeon supported types.
axisint, default=1: The time point axis of the input series if it is 2D. If axis==0, it is assumed each column is a time series and each row is a time point. i.e. the shape of the data is (n_timepoints, n_channels). axis==1 indicates the time series are in rows, i.e. the shape of the data is (n_channels, n_timepoints).

Returns:

np.ndarray: A boolean, int or float array of length len(X), where each element indicates whether the corresponding subsequence is anomalous or its anomaly score.

reset()[source]¶

Reset the object to a clean post-init state.

Equivalent to sklearn.clone but overwrites self. After self.reset() call, self is equal in value to type(self)(**self.get_params(deep=False))

Detail behaviour: removes any object attributes, except:

hyper-parameters = arguments of __init__ object attributes containing double-underscores, i.e., the string “__”

runs __init__ with current values of hyper-parameters (result of get_params)

Not affected by the reset are: object attributes containing double-underscores class and object methods, class attributes

save(path=None)[source]¶

Save serialized self to bytes-like object or to (.zip) file.

Behaviour: if path is None, returns an in-memory serialized self if path is a file location, stores self at that location as a zip file

saved files are zip files with following contents: _metadata - contains class of self, i.e., type(self) _obj - serialized self. This class uses the default serialization (pickle).

Parameters:

pathNone or file location (str or Path).: if None, self is saved to an in-memory object if file location, self is saved to that file location. If:

path=”estimator” then a zip file estimator.zip will be made at cwd. path=”/home/stored/estimator” then a zip file estimator.zip will be stored in /home/stored/.

Returns:

if path is None - in-memory serialized self
if path is file location - ZipFile with reference to the file.

set_fit_request(*, axis: bool | None | str = '$UNCHANGED$') → DWT_MLEAD[source]¶

Request metadata passed to the fit method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

True: metadata is requested, and passed to fit if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to fit.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:

axisstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for axis parameter in fit.

Returns:

selfobject: The updated object.

set_params(**params)[source]¶

Set the parameters of this object.

The method works on simple estimators as well as on nested objects. The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters:

**paramsdict: BaseObject parameters

Returns:

selfreference to self (after parameters have been set)

set_predict_request(*, axis: bool | None | str = '$UNCHANGED$') → DWT_MLEAD[source]¶

Request metadata passed to the predict method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

True: metadata is requested, and passed to predict if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to predict.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:

axisstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for axis parameter in predict.

Returns:

selfobject: The updated object.

set_tags(**tag_dict)[source]¶

Set dynamic tags to given values.

Parameters:

**tag_dictdict: Dictionary of tag name : tag value pairs.

Returns:

Self: Reference to self.

Notes

Changes object state by setting tag values in tag_dict as dynamic tags in self.