silhouette_measure module¶

The silhouette coefficient to assess a clustering.

The silhouette coefficient \(s_i\) is a measure of how similar a point \(x_i\) is to its own cluster \(C_{k_i}\) (cohesion) compared to other clusters (separation):

\[s_i = \frac{b_i-a_i}{\max(a_i,b_i)}\]

with \(a_i=\frac{1}{|C_{k_i}|-1} \sum_{j\in C_{k_i}\setminus\{i\} } \|x_i-x_j\|\) and \(b_i = \underset{\ell=1,\cdots,K\atop{\ell\neq k_i}}{\min} \frac{1}{|C_\ell|} \sum_{j\in C_\ell} \|x_i-x_j\|\)

where

\(K\) is the number of clusters,
\(C_k\) are the indices of the points belonging to the cluster \(k\),
\(|C_k|\) is the size of \(C_k\).

class gemseo.mlearning.quality_measures.silhouette_measure.SilhouetteMeasure(algo, fit_transformers=True)[source]¶

Bases: MLPredictiveClusteringMeasure

The silhouette coefficient to assess a clustering.

Parameters:

algo (MLPredictiveClusteringAlgo) – A clustering algorithm.
fit_transformers (bool) –
Whether to re-fit the transformers when using resampling techniques. If False, use the transformers of the algorithm fitted from the whole learning dataset.

By default it is set to True.

class EvaluationFunctionName(value)¶

Bases: StrEnum

The name of the function associated with an evaluation method.

BOOTSTRAP = 'evaluate_bootstrap'¶

KFOLDS = 'evaluate_kfolds'¶

LEARN = 'evaluate_learn'¶

LOO = 'evaluate_loo'¶

TEST = 'evaluate_test'¶

class EvaluationMethod(value)¶

Bases: StrEnum

The evaluation method.

BOOTSTRAP = 'BOOTSTRAP'¶: The name of the method to evaluate the measure by bootstrap.

KFOLDS = 'KFOLDS'¶: The name of the method to evaluate the measure by cross-validation.

LEARN = 'LEARN'¶: The name of the method to evaluate the measure on the learning dataset.

LOO = 'LOO'¶: The name of the method to evaluate the measure by leave-one-out.

TEST = 'TEST'¶: The name of the method to evaluate the measure on a test dataset.

compute_bootstrap_measure(n_replicates=100, samples=None, multioutput=True, seed=None)[source]¶

Evaluate the quality measure using the bootstrap technique.

Parameters:

n_replicates (int) –
The number of bootstrap replicates.

By default it is set to 100.
samples (Sequence[int] | None) – The indices of the learning samples. If None, use the whole learning dataset.
multioutput (bool) –
Whether the quality measure is returned for each component of the outputs. Otherwise, the average quality measure.

By default it is set to True.
seed (int | None) – The seed of the pseudo-random number generator. If None, an unpredictable generator will be used.

Returns:

The value of the quality measure.

Return type:

MeasureType

compute_cross_validation_measure(n_folds=5, samples=None, multioutput=True, randomize=True, seed=None)[source]¶

Evaluate the quality measure using the k-folds technique.

Parameters:

n_folds (int) –
The number of folds.

By default it is set to 5.
samples (Sequence[int] | None) – The indices of the learning samples. If None, use the whole learning dataset.
multioutput (bool) –
Whether the quality measure is returned for each component of the outputs. Otherwise, the average quality measure.

By default it is set to True.
randomize (bool) –
Whether to shuffle the samples before dividing them in folds.

By default it is set to True.
seed (int | None) – The seed of the pseudo-random number generator. If None, an unpredictable generator is used.

Returns:

The value of the quality measure.

Return type:

MeasureType

compute_learning_measure(samples=None, multioutput=True)¶

Evaluate the quality measure from the learning dataset.

Parameters:

samples (Sequence[int] | None) – The indices of the learning samples. If None, use the whole learning dataset.
multioutput (bool) –
Whether the quality measure is returned for each component of the outputs. Otherwise, the average quality measure.

By default it is set to True.

Returns:

The value of the quality measure.

Return type:

MeasureType

compute_leave_one_out_measure(samples=None, multioutput=True, store_resampling_result=True)¶

Evaluate the quality measure using the leave-one-out technique.

Parameters:

samples (Sequence[int] | None) – The indices of the learning samples. If None, use the whole learning dataset.
multioutput (bool) –
Whether the quality measure is returned for each component of the outputs. Otherwise, the average quality measure.

By default it is set to True.
store_resampling_result (bool) –
Whether to store the \(n\) machine learning algorithms and associated predictions generated by the resampling stage where \(n\) is the number of learning samples.

By default it is set to True.

Returns:

The value of the quality measure.

Return type:

MeasureType

compute_test_measure(test_data, samples=None, multioutput=True)[source]¶

Evaluate the quality measure using a test dataset.

Parameters:

test_data (Dataset) – The test dataset.
samples (Sequence[int] | None) – The indices of the learning samples. If None, use the whole learning dataset.
multioutput (bool) –
Whether the quality measure is returned for each component of the outputs. Otherwise, the average quality measure.

By default it is set to True.

Returns:

The value of the quality measure.

Return type:

MeasureType

evaluate_bootstrap(n_replicates=100, samples=None, multioutput=True, seed=None, store_resampling_result=False)¶

Evaluate the quality measure using the bootstrap technique.

Parameters:

n_replicates (int) –
The number of bootstrap replicates.

By default it is set to 100.
samples (Sequence[int] | None) – The indices of the learning samples. If None, use the whole learning dataset.
multioutput (bool) –
Whether the quality measure is returned for each component of the outputs. Otherwise, the average quality measure.

By default it is set to True.
seed (int | None) – The seed of the pseudo-random number generator. If None, an unpredictable generator will be used.
store_resampling_result (bool) –
Whether to store the \(n\) machine learning algorithms and associated predictions generated by the resampling stage where \(n\) is the number of bootstrap replicates.

By default it is set to False.

Returns:

The value of the quality measure.

Return type:

MeasureType

evaluate_kfolds(n_folds=5, samples=None, multioutput=True, randomize=True, seed=None, store_resampling_result=False)¶

Evaluate the quality measure using the k-folds technique.

Parameters:

n_folds (int) –
The number of folds.

By default it is set to 5.
samples (Sequence[int] | None) – The indices of the learning samples. If None, use the whole learning dataset.
multioutput (bool) –
Whether the quality measure is returned for each component of the outputs. Otherwise, the average quality measure.

By default it is set to True.
randomize (bool) –
Whether to shuffle the samples before dividing them in folds.

By default it is set to True.
seed (int | None) – The seed of the pseudo-random number generator. If None, an unpredictable generator is used.
store_resampling_result (bool) –
Whether to store the \(n\) machine learning algorithms and associated predictions generated by the resampling stage where \(n\) is the number of folds.

By default it is set to False.

Returns:

The value of the quality measure.

Return type:

MeasureType

evaluate_learn(samples=None, multioutput=True)¶

Evaluate the quality measure from the learning dataset.

Parameters:

samples (Sequence[int] | None) – The indices of the learning samples. If None, use the whole learning dataset.
multioutput (bool) –
Whether the quality measure is returned for each component of the outputs. Otherwise, the average quality measure.

By default it is set to True.

Returns:

The value of the quality measure.

Return type:

MeasureType

evaluate_loo(samples=None, multioutput=True, store_resampling_result=True)¶

Evaluate the quality measure using the leave-one-out technique.

Parameters:

samples (Sequence[int] | None) – The indices of the learning samples. If None, use the whole learning dataset.
multioutput (bool) –
Whether the quality measure is returned for each component of the outputs. Otherwise, the average quality measure.

By default it is set to True.
store_resampling_result (bool) –
Whether to store the \(n\) machine learning algorithms and associated predictions generated by the resampling stage where \(n\) is the number of learning samples.

By default it is set to True.

Returns:

The value of the quality measure.

Return type:

MeasureType

evaluate_test(test_data, samples=None, multioutput=True)¶

Evaluate the quality measure using a test dataset.

Parameters:

test_data (Dataset) – The test dataset.
samples (Sequence[int] | None) – The indices of the learning samples. If None, use the whole learning dataset.
multioutput (bool) –
Whether the quality measure is returned for each component of the outputs. Otherwise, the average quality measure.

By default it is set to True.

Returns:

The value of the quality measure.

Return type:

MeasureType

classmethod is_better(val1, val2)¶

Compare the quality between two values.

This method returns True if the first one is better than the second one.

For most measures, a smaller value is “better” than a larger one (MSE etc.). But for some, like an R2-measure, higher values are better than smaller ones. This comparison method correctly handles this, regardless of the type of measure.

Parameters:

val1 (float) – The value of the first quality measure.
val2 (float) – The value of the second quality measure.

Returns:

Whether val1 is of better quality than val2.

Return type:

bool

SMALLER_IS_BETTER: ClassVar[bool] = False¶: Whether to minimize or maximize the measure.

algo: MLPredictiveClusteringAlgo¶: The machine learning algorithm whose quality we want to measure.

Examples using SilhouetteMeasure¶

Advanced mixture of experts