How to calculate BCubed precision and recall
<p>According to the this published page BCubed precision and recall, thus F1-Measure calculation is the best technique for evaluating clustering performance. See <a href="https://www.researchgate.net/profile/Julio_Gonzalo/publication/225548032_Amigo_E_Gonzalo_J_Artiles_J_et_alA_comparison_of_extrinsic_clustering_evaluation_metrics_based_on_formal_constraints_Inform_Retriev_12461-486/links/0c96052138dbb99740000000/Amigo-E-Gonzalo-J-Artiles-J-et-alA-comparison-of-extrinsic-clustering-evaluation-metrics-based-on-formal-constraints-Inform-Retriev-12461-486.pdf?_sg%5B0%5D=BVp5-cu12hNz0BrB9Jstgk_d8LpdMbhdL5uOE_ftkdtRBmpwbh6KQbF01DKGca87wgEaOkfDRYEcBayX9x2IGQ.bGbIvD_Ohtd-TcUi3gNjRvHm2oLy-qhuy9sQ7SeZRyOuZSf1zpEXmmxi5VrYR-zEzwP5d_uPAEz9nw-w_4AJNw&amp;_sg%5B1%5D=F19xYSI3G3On97KihqlbmdQ64aGdnFyck-A7SJ-YGKAxjNnlJhI4bE5ltjIYEUCM438VJOrZ4EniRMTDSYPQA7_7yVQgbQoyxFZUbmYeSbj5.bGbIvD_Ohtd-TcUi3gNjRvHm2oLy-qhuy9sQ7SeZRyOuZSf1zpEXmmxi5VrYR-zEzwP5d_uPAEz9nw-w_4AJNw&amp;_iepl=" rel="nofollow noreferrer">Amigó, Enrique, et al. "A comparison of extrinsic clustering
evaluation metrics based on formal constraints." Information retrieval
12.4 (2009): 461-486.</a></p>

<p>It shows BCubed calculation as seen below image</p>

<p><a href="https://i.stack.imgur.com/k6ROP.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/k6ROP.png" alt="enter image description here"></a></p>

<p>So as far as i understood we calculate precision and recall for the each item and then take average of their sum? </p>

<p>However my understanding is not matching their given evaluation as can be seen at the image below</p>

<p><a href="https://i.stack.imgur.com/gdPja.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/gdPja.png" alt="enter image description here"></a></p>

<p>According to the image above cluster homogeneity example - left side, I calculate Precision of BCubed as below but not matching</p>

<pre><code>black : 4/4
gray: 4/7
Other three each one : 1/7

so average precision is : (4/4 + 4/6 + 1/7 + 1/7 + 1/7) / 5
</code></pre>

<p>However this is not matching with their result in image which is <code>0.59</code></p>

<blockquote>
  <p>BCubed precision of an item is the proportion of items in its cluster
  which have the item’s category (including itself). The overall BCubed
  precision is the averaged precision of all items in the distribution.
  Since the average is calculated over items, it is not necessary to
  apply any weighting according to the size of clusters or categories.
  The BCubed recall is analogous, replacing “cluster” with “category”.</p>
</blockquote>