silhouette 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):
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.qual_measure.silhouette.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.
- evaluate(method='learn', samples=None, **options)¶
Evaluate the quality measure.
- Parameters:
method (str) –
The name of the method to evaluate the quality measure.
By default it is set to “learn”.
samples (Sequence[int] | None) – The indices of the learning samples. If
None
, use the whole learning dataset.**options (OptionType | None) – The options of the estimation method (e.g.
test_data
for the test method,n_replicates
for the bootstrap one, …).
- Returns:
The value of the quality measure.
- Raises:
ValueError – When the name of the method is unknown.
- Return type:
float | ndarray
- evaluate_bootstrap(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) –
If
True
, return the quality measure for each output component. Otherwise, average these measures.By default it is set to True.
seed (int | None) – The seed of the pseudo-random number generator. If
None
, then an unpredictable generator will be used.
- Returns:
The value of the quality measure.
- Return type:
float | ndarray
- evaluate_kfolds(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) –
If
True
, return the quality measure for each output component. Otherwise, average these measures.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
, then an unpredictable generator will be used.
- Returns:
The value of the quality measure.
- Return type:
float | ndarray
- evaluate_learn(samples=None, multioutput=True)¶
Evaluate the quality measure from the learning dataset.
- Parameters:
- Returns:
The value of the quality measure.
- Return type:
float | ndarray
- evaluate_loo(samples=None, multioutput=True)¶
Evaluate the quality measure using the leave-one-out technique.
- Parameters:
- Returns:
The value of the quality measure.
- Return type:
float | ndarray
- evaluate_test(test_data, samples=None, multioutput=True)[source]¶
Evaluate the quality measure using a test dataset.
- Parameters:
- Returns:
The value of the quality measure.
- Return type:
float | ndarray
- 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.
- BOOTSTRAP: ClassVar[str] = 'bootstrap'¶
The name of the method to evaluate the measure by bootstrap.
- KFOLDS: ClassVar[str] = 'kfolds'¶
The name of the method to evaluate the measure by cross-validation.