AvgRecPopularity

class rectools.metrics.popularity.AvgRecPopularity(k: int, normalize: bool = False)[source]

Bases: MetricAtK

Average Recommendations Popularity metric.

Calculate the average popularity of the recommended items in each list, where “popularity” of an item is the number of previous interactions with this item.

\[ARP@k = \frac{1}{|U_{t}|}\sum_{u\in U_{t}^{}}\frac{\sum_{i\in L_{u}}\phi (i)}{|L_{u}|}\]
\[Normalized ARP@k = \frac{1}{|U_t|}\sum_{u\in U_t^{}}\frac{(\sum_{i\in L_u}\phi(i))/|interactions|}{|L_u|}\]
where

  • \(\phi (i)\) is the number of previous interactions with item i;

  • \(|U_{t}|\) is the number of users in the test set;

  • \(|interactions|\) is the total number of interactions;

  • \(L_{u}\) is the list of top k recommended items for user u.

Parameters

  • k (int) – Number of items at the top of recommendations list that will be used to calculate metric.

  • normalize (bool) – Flag, which says whether to normalize metric or not. Normalization is done on total items popularity. This gives a probabilistic interpretation of the metric that can be easily applied to any data.

Examples

>>> reco = pd.DataFrame(
...     {
...         Columns.User: [1, 1, 2, 2, 2, 3, 3],
...         Columns.Item: [1, 2, 3, 1, 2, 3, 2],
...         Columns.Rank: [1, 2, 1, 2, 3, 1, 2],
...     }
... )
>>> prev_interactions = pd.DataFrame(
...     {
...         Columns.User: [1, 1, 2, 2, 3, 3],
...         Columns.Item: [1, 2, 1, 3, 1, 2],
...     }
... )
>>> AvgRecPopularity(k=1).calc_per_user(reco, prev_interactions).values
array([3., 1., 1.])
>>> AvgRecPopularity(k=3).calc_per_user(reco, prev_interactions).values
array([2.5, 2. , 1.5])
>>> AvgRecPopularity(k=3, normalize=True).calc_per_user(reco, prev_interactions).values
array([0.41666667, 0.33333333, 0.25        ])
Inherited-members

Parameters

  • k (int) –

  • normalize (bool) –

Methods

calc(reco, prev_interactions)

Calculate metric value.

calc_per_user(reco, prev_interactions)

Calculate metric values for all users.

Attributes

normalize

calc(reco: DataFrame, prev_interactions: DataFrame) → float[source]

Calculate metric value.

Parameters

  • reco (pd.DataFrame) – Recommendations table with columns Columns.User, Columns.Item, Columns.Rank.

  • prev_interactions (pd.DataFrame) – Table with previous user-item interactions, with columns Columns.User, Columns.Item.

Returns

Value of metric (average between users).

Return type

float

calc_per_user(reco: DataFrame, prev_interactions: DataFrame) → Series[source]

Calculate metric values for all users.

Parameters

  • reco (pd.DataFrame) – Recommendations table with columns Columns.User, Columns.Item, Columns.Rank.

  • prev_interactions (pd.DataFrame) – Table with previous user-item interactions, with columns Columns.User, Columns.Item.

Returns

Values of metric (index - user id, values - metric value for every user).

Return type

pd.Series