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scikit-learn 1.3.2
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# `sklearn.metrics`.ndcg_score

sklearn.metrics.ndcg_score(y_true, y_score, *, k=None, sample_weight=None, ignore_ties=False)

  Compute Normalized Discounted Cumulative Gain.

  Sum the true scores ranked in the order induced by the predicted scores, after applying a logarithmic discount. Then divide by the best possible score (Ideal DCG, obtained for a perfect ranking) to obtain a score between 0 and 1.

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

  Parameters:
    y_true array-like of shape (n_samples, n_labels)

      True targets of multilabel classification, or true scores of entities to be ranked. Negative values in `y_true` may result in an output that is not between 0 and 1.

      Changed in version 1.2: These negative values are deprecated, and will raise an error in v1.4.

    y_score array-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).

    k int, default=None

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

    sample_weight array-like of shape (n_samples,), default=None

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

    ignore_ties bool, 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.

  Returns:
    normalized_discounted_cumulative_gain float in [0., 1.]

      The averaged NDCG scores for all samples.

  See also

  `dcg_score`

    Discounted Cumulative Gain (not normalized).

  References

  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.

  Examples

      >>> import numpy as np
      >>> from sklearn.metrics import ndcg_score
      >>> # we have groud-truth relevance of some answers to a query:
      >>> true_relevance = np.asarray([[10, 0, 0, 1, 5]])
      >>> # we predict some scores (relevance) for the answers
      >>> scores = np.asarray([[.1, .2, .3, 4, 70]])
      >>> ndcg_score(true_relevance, scores)
      0.69...
      >>> scores = np.asarray([[.05, 1.1, 1., .5, .0]])
      >>> ndcg_score(true_relevance, scores)
      0.49...
      >>> # we can set k to truncate the sum; only top k answers contribute.
      >>> ndcg_score(true_relevance, scores, k=4)
      0.35...
      >>> # the normalization takes k into account so a perfect answer
      >>> # would still get 1.0
      >>> ndcg_score(true_relevance, true_relevance, k=4)
      1.0...
      >>> # 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 (normalized)
      >>> # true relevance of our top predictions: (10 / 10 + 5 / 10) / 2 = .75
      >>> ndcg_score(true_relevance, scores, k=1)
      0.75...
      >>> # 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:
      >>> ndcg_score(true_relevance,
      ...           scores, k=1, ignore_ties=True)
      0.5...