I stumbled across this example on scikit-learn (1.2.0), where the silhouette score alongside some other metrics is computed for DBSCAN cluster assignments. These assignments include some Noise assignments.
from sklearn.cluster import DBSCAN
from sklearn.datasets import make_blobs
from sklearn.metrics import silhouette_score
from sklearn.preprocessing import StandardScaler
centers = [[1, 1], [-1, -1], [1, -1]]
X, labels_true = make_blobs(n_samples=750, centers=centers, cluster_std=0.4,
random_state=0)
X = StandardScaler().fit_transform(X)
db = DBSCAN(eps=0.3, min_samples=10).fit(X)
labels = db.labels_
print(f"Silhouette Coefficient with Noise as one cluster: {silhouette_score(X, labels):.3f}")
# 0.626
I find strange that there is no special treatment for Noise assigments; the cluster algorithms effectively treat them as a one cluster (since it's all -1). Is this correct?
Because if I make them individual clusters instead, I get a very different result:
for idx, val in enumerate(labels):
if val == -1:
labels[idx] = -idx
print(f"Silhouette Coefficient with Noise as individual clusters: {silhouette_score(X, labels):.3f}")
# 0.092
Alternatively, one could ignore the Noise assignments altogether, although this may affect comparison with other metrics:
mask_ok = [x >= 0 for x in labels]
print(f"Silhouette Coefficient ignoring Noise: {silhouette_score(X[mask_ok], labels[mask_ok]):.3f}")
# 0.664
