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Completeness Score

The completeness score is a mesure of how all memebers of a given class are assigned to the same cluster.

It measures how many similar samples are put together by the clustering algorithm, it if formally defined by this formula:

h=1−H(K∣C)H(K)h = 1 - \frac{H(K|C)}{H(K)}
Where,H(K∣C)=−∑k,cnkcNlognkcncWhere, H(K|C) = -\sum_{k,c} \frac {n_kc}{N} log \frac {n_kc}{n_c}

When all data points are assigned to one cluster, the completeness score is 1.(highest)

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And when all data point are assigned their own cluster, the completeness score is 0.(lowest)

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Here we can notice how homogeneity score is inversely proportional to the completeness score.

Higher the completeness score, lower the homogeneity score and vice versa.