B-Cubed Metrics

A simple Python package to calculate B-Cubed precision, recall, and F1-score for clustering evaluation.

What are B-Cubed Metrics

The B-Cubed algorithm was first introduced by Bagga, A. and Baldwin B. (1998) in their paper on Entity-Based Cross-Document Coreferencing Using the Vector Space Model. The algorithm compares a predicted clustering with a ground truth (or gold standard) clustering through element-wise precision and recall scores. For each element, the predicted and ground truth clusters containing the element are compared, and then the mean over all elements is taken. The B-Cubed algorithm can be useful in unsupervised techniques where the cluster labels are not available, because unlike macro-averaged metrics, it focuses on element-wise operations.

From the paper, two simple equations were devised calculating precision and recall scores for the predicted clustering:

$$ Precision = \frac{1}{\sum {elements}}\sum_{i=1}^n {\frac{(count ; of ; element)^2}{count ; of ; all ; elements ; in ; cluster}} $$

$$ Recall = \frac{1}{\sum {elements}}\sum_{i=1}^n {\frac{(count ; of ; element)^2}{count ; of ; total ; elements ; from ; this ; category}} $$

$$ F-score = \frac{1}{k}\sum_{i=1}^n {\frac{2\times Precision(C)_k \times Recall(C)_k}{Precision(C)_k + Recall(C)_k}} $$

where $n$ above denotes the number of categories in the cluster and $k$ is the number of predicted clusters. $Precision(C)_k$ and $Recall(C)_k$ are the 'partial' precision and recalls for each cluster.

Installation and Use

Download the package from any terminal using:

pip install bcubed-metrics

To use the B-Cubed class you need to import it and provide 2 dictionaries - one for the predicted clustering, and one for the ground truth clustering (actual labels):

from bcubed_metrics.bcubed import Bcubed

predicted_clustering = [
            {'blue': 4, 'red': 2, 'green': 1},
            {'blue': 2, 'red': 2, 'green': 3},
            {'blue': 1, 'red': 5},
            {'blue': 1, 'red': 2, 'green': 3}
        ]

ground_truth_clustering = {'blue': 8, 'red': 11, 'green': 7}

bcubed = Bcubed(predicted_clustering=predicted_clustering, ground_truth_clustering=ground_truth_clustering)

metrics = bcubed.get_metrics() # returns all metrics as dictionary

bcubed.print_metrics() # prints all metrics