gemseo.mlearning.clustering.quality.silhouette_measure module#

The silhouette score to assess the quality of a clusterer.

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 SilhouetteMeasure(algo, fit_transformers=True)[source]#

Bases: BasePredictiveClustererQuality

The silhouette score to assess the quality of a clusterer.

Parameters:

  • algo (BasePredictiveClusterer) -- 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 training dataset.

    By default it is set to True.

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

Evaluate the quality of the ML model using the bootstrap technique.

Parameters:

  • n_replicates (int) --

    The number of bootstrap replicates.

    By default it is set to 100.

  • samples (Sequence[int]) --

    The indices of the learning samples. If empty, use the whole training dataset.

    By default it is set to ().

  • 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 quality of the ML model.

Return type:

MeasureType

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

Evaluate the quality of the ML model using the k-folds technique.

Parameters:

  • n_folds (int) --

    The number of folds.

    By default it is set to 5.

  • samples (Sequence[int]) --

    The indices of the learning samples. If empty, use the whole training dataset.

    By default it is set to ().

  • 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 quality of the ML model.

Return type:

MeasureType

compute_test_measure(test_data, samples=(), multioutput=True)[source]#

Evaluate the quality of the ML model from a test dataset.

Parameters:

  • test_data (Dataset) -- The test dataset.

  • samples (Sequence[int]) --

    The indices of the learning samples. If empty, use the whole training dataset.

    By default it is set to ().

  • 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 quality of the ML model.

Return type:

MeasureType

SMALLER_IS_BETTER: ClassVar[bool] = False#

Whether to minimize or maximize the measure.

algo: BasePredictiveClusterer#

The machine learning algorithm whose quality we want to measure.