ElasticSOM

class ElasticSOM(n_clusters: int = 8, distance: str | Callable = 'dtw', init: str | ndarray = 'random', sigma: float = 1.0, learning_rate: float = 0.5, decay_function: Callable | str = 'asymptotic_decay', neighborhood_function: Callable | str = 'gaussian', sigma_decay_function: Callable | str = 'asymptotic_decay', num_iterations: int = 500, distance_params: dict | None = None, random_state: int | RandomState | None = None, custom_alignment_path: Callable | None = None, verbose: bool | None = False)

Elastic Self-Organising Map (SOM) clustering algorithm.

Self-Organising Maps (SOM) [1] are a type of neural network which represents each time point in the input time series as a neuron. Each neuron is connected to n_cluster output neurons, where n_clusters is the number of clusters. Each output neuron represents a cluster. Every input neuron is connected to each output neuron using a weight vector. The weights of the connections between input neurons and output neurons are learned during training. The algorithm is iterative, where each iteration updates the weights of the connections between input neurons and output neurons.

SOM has been adapted to use elastic distances [2]. The adaptation is done by using an elastic distance function to compute the distance between the weights and a given time series to find the best matching unit (BMU). Secondly when updating the weights an alignment path is used to compute the best alignment between the weights and the time series that will update the weights. This means that the weights are updated accounting for the alignment path making the updating of the weights more efficient.

Parameters:

n_clustersint, default=8

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

distancestr or Callable, default=’dtw’

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.

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.

sigmafloat, default=1.0

Spread of the neighborhood function.

learning_ratefloat, default=0.5

Initial learning rate. For a given iterations the learning rate is: learning_rate = learning_rate / (1 + iterations / max_iter)

decay_functionUnion[Callable, str], default=’asymptotic_decay’

Decay function to use for the learning rate. Valid strings are: [‘asymptotic_decay’, ‘inverse_decay’, ‘linear_decay’]. If a Callable is provided must take the form Callable[[float, int, int], float], where the first argument is the learning rate, the second argument is the current iteration, and the third argument is the maximum number of iterations.

neighborhood_functionUnion[Callable, str], default=’gaussian’

Neighborhood function that weights the neighborhood of each time series. Valid strings are: [‘gaussian’, ‘mexican_hat’]. If a Callable is provided must take the form Callable[[np.ndarray, np.ndarray, float], np.ndarray], where the first argument is the output neuron positions (i.e. which cluster each output neuron maps to), the second argument is the index of the best matching unit (i.e. which is the closest output neuron), and the third argument is the sigma value.

sigma_decay_functionUnion[Callable, str], default=’asymptotic_decay’

Function that reduces sigma each iteration. Valid strings are: [‘asymptotic_decay’, ‘inverse_decay’, ‘linear_decay’]. If a Callable is provided must take the form Callable[[float, int, int], float], where the first argument is the current sigma value, the second argument is the current iteration, and the third argument is the maximum number of iterations.

num_iterationsint, default=500

Number of iterations to run the algorithm for each time series. The recommended value is 500 times the number of neurons in the network. Therefore the number of iterations is 500 * n_timepoints (as input neurons = n_timepoints).

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.

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.

custom_alignment_pathCallable, default=None

Custom alignment path function to use for the distance. If None, the default alignment path function for the distance will be used. If the distance method does not have an elastic alignment path then the default SOM einsum update will be used. See aeon.clustering.elastic_som.VALID_ELASTIC_SOM_METRICS for a list of distances that have an elastic alignment path. The alignment path function takes the form Callable[[np.ndarray, np.ndarray, dict], whee the dict is the kwargs for the distance function. See documentation of aeon.distances documentation for example alignment path functions. The alignment path function must return a a full alignment path with no gaps.

verbosebool, default=False

Verbosity mode.

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.

References

[1]

Vesanto, Juha & Alhoniemi, Esa. (2000). Clustering of the self-organizing

map. IEEE Transactions on Neural Networks, 11(3), 586-600.

https://doi.org/10.1109/72.846731.

[2]

Silva, Maria & Henriques, Roberto. (2020). Exploring time-series motifs through DTW-SOM. In Proceedings of the International Joint Conference on Neural Networks (IJCNN), 1-8. https://doi.org/10.1109/IJCNN48605.2020.9207614.

Examples

>>> import numpy as np
>>> from aeon.clustering import ElasticSOM
>>> X = np.random.random(size=(10,2,20))
>>> clst = ElasticSOM(n_clusters=3, random_state=1, num_iterations=10)
>>> clst.fit(X)
ElasticSOM(n_clusters=3, num_iterations=10, random_state=1)

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_metadata_routing()	Sklearn metadata routing.
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_metadata_routing()

Sklearn metadata routing.

Not supported by aeon estimators.

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.

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.