Clustering evaluation

Purity, Efficiency (other terms used are Precision and Recall or Specificity and Sensitivity, respectively) and Jaccard scores are all external indices used for clustering and classification assessment. These scores are calculated subsequently to the clustering and their generalized version is defined as follows:

Where:

· n₁₁ is the number of pairs that are classified together, both in the ‘expert’ classification and in the classification obtained by the algorithm.

· n₁₀ is the number of pairs that are classified together in the ‘expert’ classification, but not in the algorithm’s classification.

· n₀₁ is the number of pairs that are classified together in the algorithm’s classification, but not in the ‘expert’ classification.

The Jaccard score reflects the ‘intersection over union' between the algorithm's clustering assignments and the expected classification. Its values range from 0 (no match) to 1 (perfect match), and it is a lower bound of both the Purity and Efficiency. An important attribute of the Jaccard score is its normalization. Since the formula excludes n₀₀ (the number of pairs that aren't classified together in the algorithm and in the expected classification), it reflects a value that does not depended on the size of the cluster.