def calc_conditional_entropy(joint_prob: np.ndarray, p_marginal_truth: np.ndarray, p_marginal_alg: np.ndarray,
idx_truth: np.ndarray, idx_alg: np.ndarray, evaluation: Evaluation, is_subgraph: bool = False) -> Evaluation:
"""Calculates the conditional entropy metrics between the algorithmic and truth partitions. The following metrics
are calculated:
entropy of the truth partition given the algorithm partition
entropy of the algorithm partition given the truth partition
the mutual information between the algorithm and truth partitions
Parameters
---------
Returns
------
evaluation : Evaluation
the evaluation object, updated with the entropy-based goodness of partition metrics
is_subgraph : bool
True if evaluation is for a subgraph. Default = False
"""
conditional_prob_b2_b1 = np.zeros(joint_prob.shape)
conditional_prob_b1_b2 = np.zeros(joint_prob.shape)
conditional_prob_b2_b1[idx_truth, :] = joint_prob[idx_truth, :] / p_marginal_truth[idx_truth, None]
conditional_prob_b1_b2[:, idx_alg] = joint_prob[:, idx_alg] / p_marginal_alg[None, idx_alg]
# compute the conditional entropies
idx = np.nonzero(joint_prob)
H_b2_b1 = -np.sum(np.sum(joint_prob[idx] * np.log(conditional_prob_b2_b1[idx])))
H_b1_b2 = -np.sum(np.sum(joint_prob[idx] * np.log(conditional_prob_b1_b2[idx])))
# compute the mutual information (symmetric)
marginal_prod = np.dot(p_marginal_truth[:, None], np.transpose(p_marginal_alg[:, None]))
MI_b1_b2 = np.sum(np.sum(joint_prob[idx] * np.log(joint_prob[idx] / marginal_prod[idx])))
if is_subgraph:
evaluation.subgraph_entropy_truth_given_algorithm = H_b1_b2
evaluation.subgraph_entropy_algorithm_given_truth = H_b2_b1
evaluation.subgraph_mutual_info = MI_b1_b2
else:
evaluation.entropy_truth_given_algorithm = H_b1_b2
evaluation.entropy_algorithm_given_truth = H_b2_b1
evaluation.mutual_info = MI_b1_b2
print('Conditional entropy of truth partition given alg. partition: {}'.format(abs(H_b1_b2)))
print('Conditional entropy of alg. partition given truth partition: {}'.format(abs(H_b2_b1)))
print('Mutual informationion between truth partition and alg. partition: {}'.format(abs(MI_b1_b2)))
return evaluation
