TimeSeriesKMeans

class TimeSeriesKMeans(n_clusters: int = 8, init: str | ndarray = 'random', distance: str | Callable = 'msm', n_init: int = 10, max_iter: int = 300, tol: float = 1e-06, verbose: bool = False, random_state: int | RandomState | None = None, averaging_method: str | Callable[[ndarray], ndarray] = 'ba', distance_params: dict | None = None, average_params: dict | None = None, n_jobs: int | None = 1)

Bases: BaseClusterer

Time series K-means clustering implementation.

K-means [5]_ is a popular clustering algorithm that aims to partition n time series into k clusters in which each observation belongs to the cluster with the nearest centre. The centre is represented using an average which is generated during the training phase.

K-means using euclidean distance for time series generally performs poorly. However, when combined with an elastic distance it performs significantly better (in particular MSM/TWE [1]). K-means for time series can further be improved by using an elastic averaging method. The most common one is dynamic barycenter averaging [3] however, in recent years alternates using other elastic distances such as ShapeDBA [4] (Shape DTW DBA) and MBA (Msm DBA) [5]_ have shown signicant performance benefits.

Parameters:

n_clustersint, default=8

The number of clusters to form as well as the number of centroids to generate.

initstr or np.ndarray, default=’random’

Random is the default and simply chooses k time series at random as centroids. It is fast but sometimes yields sub-optimal clustering. Kmeans++ [2] and is slower but often more accurate than random. It works by choosing centroids that are distant from one another. First is the fastest method and simply chooses the first k time series as centroids. If a np.ndarray provided it must be of shape (n_clusters, n_channels, n_timepoints) and contains the time series to use as centroids.

distancestr or Callable, default=’msm’

Distance method to compute similarity between time series. A list of valid strings for measures can be found in the documentation for aeon.distances.get_distance_function. If a callable is passed it must be a function that takes two 2d numpy arrays as input and returns a float.

n_initint, default=10

Number of times the k-means algorithm will be run with different centroid seeds. The final result will be the best output of n_init consecutive runs in terms of inertia.

max_iterint, default=300

Maximum number of iterations of the k-means algorithm for a single run.

tolfloat, default=1e-6

Relative tolerance with regards to Frobenius norm of the difference in the cluster centers of two consecutive iterations to declare convergence.

verbosebool, default=False

Verbosity mode.

random_stateint, np.random.RandomState instance or None, default=None

Determines random number generation for centroid initialization. If int, random_state is the seed used by the random number generator; If np.random.RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.

averaging_methodstr or Callable, default=’ba’

Averaging method to compute the average of a cluster. Any of the following strings are valid: [‘mean’, ‘ba’]. If a Callable is provided must take the form Callable[[np.ndarray], np.ndarray]. If you specify ‘ba’ then by default the distance method used will be the same as the distance method used for clustering. If you wish to use a different distance method you can specify it by passing {“distance”: “dtw”} as averaging_params. BA yields ‘better’ clustering results but is very computationally expensive so you may want to consider setting a bounding window or using a different averaging method if time complexity is a concern.

distance_paramsdict, default=None

Dictionary containing kwargs for the distance being used. For example if you wanted to specify a window for DTW you would pass distance_params={“window”: 0.2}. See documentation of aeon.distances for more details.

average_paramsdict, default=None

Dictionary containing kwargs for averaging_method. See documentation of aeon.clustering.averaging and aeon.distances for more details. NOTE: if you want to use custom distance params during averaging here you must specify them in this dict in addition to custom averaging params. For example to specify a window as a distance param and verbosity for the averaging you would pass average_params={“window”: 0.2, “verbose”: True}.

n_jobsint, default=1

The number of jobs to run in parallel. If -1, then the number of jobs is set to the number of CPU cores. If 1, then the function is executed in a single thread. If greater than 1, then the function is executed in parallel.

Attributes:

cluster_centers_3d np.ndarray

Array of shape (n_clusters, n_channels, n_timepoints)) Time series that represent each of the cluster centers.

labels_1d np.ndarray

1d array of shape (n_case,) Labels that is the index each time series belongs to.

inertia_float

Sum of distances of samples to their closest cluster center, weighted by the sample weights if provided.

n_iter_int

Number of iterations run.

Notes

Capabilities

Missing Values	No
Multithreading	Yes
Univariate	Yes
Multivariate	Yes
Unequal Length	No

References

[1]

Holder, Christopher & Middlehurst, Matthew & Bagnall, Anthony. (2022).

A Review and Evaluation of Elastic Distance Functions for Time Series Clustering. 10.48550/arXiv.2205.15181.

[2]

Arthur, David & Vassilvitskii, Sergei. (2007). K-Means++: The Advantages of

Careful Seeding. Proc. of the Annu. ACM-SIAM Symp. on Discrete Algorithms. 8. 1027-1035. 10.1145/1283383.1283494.

[3]

Holder, Christopher & Guijo-Rubio, David & Bagnall, Anthony. (2023).

Clustering time series with k-medoids based algorithms. In proceedings of the 8th Workshop on Advanced Analytics and Learning on Temporal Data (AALTD 2023).

[4]

Ali Ismail-Fawaz & Hassan Ismail Fawaz & Francois Petitjean &

Maxime Devanne & Jonathan Weber & Stefano Berretti & Geoffrey I. Webb & Germain Forestier ShapeDBA: Generating Effective Time Series Prototypes using ShapeDTW Barycenter Averaging. In proceedings of the 8th Workshop on Advanced Analytics and Learning on Temporal Data (AALTD 2023).

..[5] Lloyd, S. P. (1982). Least squares quantization in pcm. IEEE Trans. Inf. Theory, 28:129–136.

Examples

>>> import numpy as np
>>> from aeon.clustering import TimeSeriesKMeans
>>> X = np.random.random(size=(10,2,20))
>>> clst = TimeSeriesKMeans(distance="dtw", n_clusters=2)
>>> clst.fit(X)
TimeSeriesKMeans(distance='dtw', n_clusters=2)
>>> preds = clst.predict(X)

Methods

clone([random_state])	Obtain a clone of the object with the same hyperparameters.
fit(X[, y])	Fit time series clusterer to training data.
fit_predict(X[, y])	Compute cluster centers and predict cluster index for each time series.
get_class_tag(tag_name[, raise_error, ...])	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_params([deep])	Get parameters for this estimator.
get_tag(tag_name[, raise_error, ...])	Get tag value from estimator class.
get_tags()	Get tags from estimator.
predict(X)	Predict the closest cluster each sample in X belongs to.
predict_proba(X)	Predicts labels probabilities for sequences in X.
reset([keep])	Reset the object to a clean post-init state.
set_params(**params)	Set the parameters of this estimator.
set_tags(**tag_dict)	Set dynamic tags to given values.

clone(random_state=None)

Obtain a clone of the object with the same hyperparameters.

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)).

Parameters:

random_stateint, RandomState instance, or None, default=None

Sets the random state of the clone. If None, the random state is not set. If int, random_state is the seed used by the random number generator. If RandomState instance, random_state is the random number generator.

Returns:

estimatorobject

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

fit(X, y=None) → BaseCollectionEstimator

Fit time series clusterer to training data.

Parameters:

X3D np.ndarray (any number of channels, equal length series)

of shape (n_cases, n_channels, n_timepoints)

or 2D np.array (univariate, equal length series)

of shape (n_cases, n_timepoints)

or list of numpy arrays (any number of channels, unequal length series)

of shape [n_cases], 2D np.array (n_channels, n_timepoints_i), where n_timepoints_i is length of series i

other types are allowed and converted into one of the above.

y: ignored, exists for API consistency reasons.

Returns:

self:

Fitted estimator.

fit_predict(X, y=None) → ndarray

Compute cluster centers and predict cluster index for each time series.

Convenience method; equivalent of calling fit(X) followed by predict(X)

Parameters:

Xnp.ndarray (2d or 3d array of shape (n_cases, n_timepoints) or shape

(n_cases, n_channels, n_timepoints)). Time series instances to train clusterer and then have indexes each belong to return.

y: ignored, exists for API consistency reasons.

Returns:

np.ndarray (1d array of shape (n_cases,))

Index of the cluster each time series in X belongs to.

classmethod get_class_tag(tag_name, raise_error=True, tag_value_default=None)

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

Parameters:

tag_namestr

Name of tag value.

raise_errorbool, default=True

Whether a ValueError is raised when the tag is not found.

tag_value_defaultany type, default=None

Default/fallback value if tag is not found and error is not raised.

Returns:

tag_value

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

Raises:

ValueError

if raise_error is True and tag_name is not in self.get_tags().keys()

Examples

>>> from aeon.classification import DummyClassifier
>>> DummyClassifier.get_class_tag("capability:multivariate")
True

classmethod get_class_tags()

Get class tags from estimator class and all its parent classes.

Returns:

collected_tagsdict

Dictionary of tag name and tag value pairs. Collected from _tags class attribute via nested inheritance. These are not overridden by dynamic tags set by set_tags or class __init__ calls.

get_fitted_params(deep=True)

Get fitted parameters.

State required:

Requires state to be “fitted”.

Parameters:

deepbool, default=True

If True, will return the fitted parameters for this estimator and contained subobjects that are estimators.

Returns:

fitted_paramsdict

Fitted parameter names mapped to their values.

get_params(deep=True)

Get parameters for this estimator.

Parameters:

deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns:

paramsdict

Parameter names mapped to their values.

get_tag(tag_name, raise_error=True, tag_value_default=None)

Get tag value from estimator class.

Includes dynamic and overridden tags.

Parameters:

tag_namestr

Name of tag to be retrieved.

raise_errorbool, default=True

Whether a ValueError is raised when the tag is not found.

tag_value_defaultany type, default=None

Default/fallback value if tag is not found and error is not raised.

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 and tag_name is not in self.get_tags().keys()

Examples

>>> from aeon.classification import DummyClassifier
>>> d = DummyClassifier()
>>> d.get_tag("capability:multivariate")
True

get_tags()

Get tags from estimator.

Includes dynamic and overridden tags.

Returns:

collected_tagsdict

Dictionary of tag name and tag value pairs. Collected from _tags class attribute via nested inheritance and then any overridden and new tags from __init__ or set_tags.

predict(X) → ndarray

Predict the closest cluster each sample in X belongs to.

Parameters:

X3D np.ndarray

Input data, any number of channels, equal length series of shape ( n_cases, n_channels, n_timepoints) or 2D np.array (univariate, equal length series) of shape (n_cases, n_timepoints) or list of numpy arrays (any number of channels, unequal length series) of shape [n_cases], 2D np.array (n_channels, n_timepoints_i), where n_timepoints_i is length of series i. Other types are allowed and converted into one of the above.

Returns:

np.array

shape ``(n_cases)`, index of the cluster each time series in X. belongs to.

predict_proba(X) → ndarray

Predicts labels probabilities for sequences in X.

Default behaviour is to call _predict and set the predicted class probability to 1, other class probabilities to 0. Override if better estimates are obtainable.

Parameters:

X3D np.ndarray

Input data, any number of channels, equal length series of shape ( n_cases, n_channels, n_timepoints) or 2D np.array (univariate, equal length series) of shape (n_cases, n_timepoints) or list of numpy arrays (any number of channels, unequal length series) of shape [n_cases], 2D np.array (n_channels, n_timepoints_i), where n_timepoints_i is length of series i. Other types are allowed and converted into one of the above.

Returns:

y2D array of shape [n_cases, n_classes] - predicted class probabilities

1st dimension indices correspond to instance indices in X 2nd dimension indices correspond to possible labels (integers) (i, j)-th entry is predictive probability that i-th instance is of class j

reset(keep=None)

Reset the object to a clean post-init state.

After a self.reset() call, self is equal or similar in value to type(self)(**self.get_params(deep=False)), assuming no other attributes were kept using keep.

Detailed 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 hyperparameters (result of get_params)

Not affected by the reset are:

object attributes containing double-underscores class and object methods, class attributes any attributes specified in the keep argument

Parameters:

keepNone, str, or list of str, default=None

If None, all attributes are removed except hyperparameters. If str, only the attribute with this name is kept. If list of str, only the attributes with these names are kept.

Returns:

selfobject

Reference to self.

Raises:

TypeError

If ‘keep’ is not a string or a list of strings.

set_params(**params)

Set the parameters of this estimator.

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

Parameters:

**paramsdict

Estimator parameters.

Returns:

selfestimator instance

Estimator instance.

set_tags(**tag_dict)

Set dynamic tags to given values.

Parameters:

**tag_dictdict

Dictionary of tag name and tag value pairs.

Returns:

selfobject

Reference to self.