sklearn.metrics.dcg_score(y_true, y_score, *, k=None, log_base=2, sample_weight=None, ignore_ties=False)[source]#

Compute Discounted Cumulative Gain.

Sum the true scores ranked in the order induced by the predicted scores, after applying a logarithmic discount.

This ranking metric yields a high value if true labels are ranked high by y_score.

Usually the Normalized Discounted Cumulative Gain (NDCG, computed by ndcg_score) is preferred.

y_truearray-like of shape (n_samples, n_labels)

True targets of multilabel classification, or true scores of entities to be ranked.

y_scorearray-like of shape (n_samples, n_labels)

Target scores, can either be probability estimates, confidence values, or non-thresholded measure of decisions (as returned by “decision_function” on some classifiers).

kint, default=None

Only consider the highest k scores in the ranking. If None, use all outputs.

log_basefloat, default=2

Base of the logarithm used for the discount. A low value means a sharper discount (top results are more important).

sample_weightarray-like of shape (n_samples,), default=None

Sample weights. If None, all samples are given the same weight.

ignore_tiesbool, default=False

Assume that there are no ties in y_score (which is likely to be the case if y_score is continuous) for efficiency gains.


The averaged sample DCG scores.

See also


The Discounted Cumulative Gain divided by the Ideal Discounted Cumulative Gain (the DCG obtained for a perfect ranking), in order to have a score between 0 and 1.


Wikipedia entry for Discounted Cumulative Gain.

Jarvelin, K., & Kekalainen, J. (2002). Cumulated gain-based evaluation of IR techniques. ACM Transactions on Information Systems (TOIS), 20(4), 422-446.

Wang, Y., Wang, L., Li, Y., He, D., Chen, W., & Liu, T. Y. (2013, May). A theoretical analysis of NDCG ranking measures. In Proceedings of the 26th Annual Conference on Learning Theory (COLT 2013).

McSherry, F., & Najork, M. (2008, March). Computing information retrieval performance measures efficiently in the presence of tied scores. In European conference on information retrieval (pp. 414-421). Springer, Berlin, Heidelberg.


>>> import numpy as np
>>> from sklearn.metrics import dcg_score
>>> # we have ground-truth relevance of some answers to a query:
>>> true_relevance = np.asarray([[10, 0, 0, 1, 5]])
>>> # we predict scores for the answers
>>> scores = np.asarray([[.1, .2, .3, 4, 70]])
>>> dcg_score(true_relevance, scores)
>>> # we can set k to truncate the sum; only top k answers contribute
>>> dcg_score(true_relevance, scores, k=2)
>>> # now we have some ties in our prediction
>>> scores = np.asarray([[1, 0, 0, 0, 1]])
>>> # by default ties are averaged, so here we get the average true
>>> # relevance of our top predictions: (10 + 5) / 2 = 7.5
>>> dcg_score(true_relevance, scores, k=1)
>>> # we can choose to ignore ties for faster results, but only
>>> # if we know there aren't ties in our scores, otherwise we get
>>> # wrong results:
>>> dcg_score(true_relevance,
...           scores, k=1, ignore_ties=True)