recpack.metrics.NDCGK

class recpack.metrics.NDCGK(K)

Computes the normalized sum of gains of all items in a recommendation list.

The normalized Discounted Cumulative Gain (nDCG) is similar to DCG, but normalizes by dividing the resulting sum of cumulative gains by the best possible discounted cumulative gain for a list of recommendations of length K for a user with history length N.

Scores are always in the interval [0, 1]

\[\text{NormalizedDiscountedCumulativeGain}(u) = \frac{\text{DCG}(u)}{\text{IDCG}(u)}\]

where IDCG stands for Ideal Discounted Cumulative Gain, computed as:

\[\text{IDCG}(u) = \sum\limits_{j=1}^{\text{min}(K, |y^{true}_u|)} \frac{1}{\log_2 (j + 1)}\]

Parameters

K (int) – Size of the recommendation list consisting of the Top-K item predictions.

Methods

calculate(y_true, y_pred)

Computes metric given true labels y_true and predicted scores y_pred.

Attributes

col_names	The names of the columns in the results DataFrame.
name	Name of the metric.
num_items	Dimension of the item-space in both y_true and y_pred
num_users	Dimension of the user-space in both y_true and y_pred after elimination of users without interactions in y_true.
results	Get the detailed results for this metric.
value	Global metric value obtained by taking the average over all users.

calculate(y_true: scipy.sparse._csr.csr_matrix, y_pred: scipy.sparse._csr.csr_matrix) → None

Computes metric given true labels y_true and predicted scores y_pred. Only Top-K recommendations are considered.

Detailed metric results can be retrieved with results. Global aggregate metric value is retrieved as value.

Parameters

• y_true (csr_matrix) – True user-item interactions.

• y_pred (csr_matrix) – Predicted affinity of users for items.

property col_names

The names of the columns in the results DataFrame.

property name

Name of the metric.

property num_items: int

Dimension of the item-space in both y_true and y_pred

property num_users: int

Dimension of the user-space in both y_true and y_pred after elimination of users without interactions in y_true.

property results

Get the detailed results for this metric.

Contains an entry for every user.

Returns

The results DataFrame with columns: user_id, score

Return type

pd.DataFrame

property value

Global metric value obtained by taking the average over all users.