202511171448 Status: idea Tags: Datascience, Machine Learning

Silhouette Score

The Silhouette Score ($s(i)$) measures how well each data point fits within its cluster. The value of the silhouette score ranges from -1 to +1.

1. Calculation for a Single Data Point ($i$)

For a single data point $i$, the silhouette score $s(i)$ is calculated as:

$s(i)=\frac{b(i)-a(i)}{\max (a(i),b(i))}$

Where:

• $a(i)$ = Average distance from $i$ to other points in the same cluster (Cohesion). This measures how close the data point is to the other points in its own cluster. A smaller $a(i)$ is desirable.
• $b(i)$ = Average distance from $i$ to points in the nearest different cluster (Separation). This measures how far the data point is from the points in the nearest neighboring cluster. A larger $b(i)$ is desirable.

2. Interpretation of $s(i)$

• $s(i)\approx +1$: The data point $i$ is well-clustered and far from the neighboring clusters. This indicates strong cohesion and separation.
• $s(i)\approx 0$: The data point $i$ is on or very close to the decision boundary between two neighboring clusters.
• $s(i)\approx -1$: The data point $i$ is misclassified and is likely assigned to the wrong cluster. Its nearest neighbors are in a different cluster.

3. The Mean Silhouette Score ($S$)

The overall Mean Silhouette Score ($S$) for the entire clustering result is the average of the silhouette scores for all data points ($n$) in the dataset:

$S=\frac{1}{n}{\sum }_{i=1}^{n}s(i)$

The mean silhouette score is used to evaluate the overall quality of the clustering solution. A higher mean score indicates a better, more dense, and well-separated clustering structure.

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References

Dit is iets wat we leren voor Datascience. dit was informatie vanuit avans 2-2 datascience 2025-11-10. en daarbij horen deze slides