"""
This is the implementation of the Expected Free Discovery metric.
It proceeds from a user-wise computation, and average the values over the users.
"""
__version__ = '0.3.1'
__author__ = 'Vito Walter Anelli, Claudio Pomo'
__email__ = 'vitowalter.anelli@poliba.it, claudio.pomo@poliba.it'
import math
import numpy as np
from elliot.evaluation.metrics.base_metric import BaseMetric
[docs]class EFD(BaseMetric):
r"""
Expected Free Discovery (EFD)
This class represents the implementation of the Expected Free Discovery recommendation metric.
For further details, please refer to the `paper <https://dl.acm.org/doi/pdf/10.1145/2043932.2043955>`_
Note:
EFD can be read as the expected ICF of seen recommended items
.. math::
\mathrm {EFD}=C \sum_{i_{k} \in R} {disc}(k) p({rel} \mid i_{k}, u)( -\log _{2} p(i \mid {seen}, \theta))
To compute the metric, add it to the config file adopting the following pattern:
.. code:: yaml
simple_metrics: [EFD]
"""
def __init__(self, recommendations, config, params, eval_objects):
"""
Constructor
:param recommendations: list of recommendations in the form {user: [(item1,value1),...]}
:param config: SimpleNameSpace that represents the configuration of the experiment
:param params: Parameters of the model
:param eval_objects: list of objects that may be useful for the computation of the different metrics
"""
super().__init__(recommendations, config, params, eval_objects)
self._cutoff = self._evaluation_objects.cutoff
self._relevance = self._evaluation_objects.relevance.binary_relevance
[docs] @staticmethod
def name():
"""
Metric Name Getter
:return: returns the public name of the metric
"""
return "EFD"
def __user_EFD(self, user_recommendations, user, cutoff):
"""
Per User Expected Free Discovery
:param user_recommendations: list of user recommendation in the form [(item1,value1),...]
:param cutoff: numerical threshold to limit the recommendation list
:param user_relevant_items: list of user relevant items in the form [item1,...]
:return: the value of the Precision metric for the specific user
"""
nov = 0
norm = 0
for r, (i, _) in enumerate(user_recommendations[:cutoff]):
nov += self._relevance.get_rel(user, i) * self._relevance.logarithmic_ranking_discount(r) * self._item_novelty_dict.get(i, self._max_nov)
norm += self._relevance.logarithmic_ranking_discount(r)
if norm > 0:
nov /= norm
return nov
# @staticmethod
# def __discount_k(k):
# return (1 / math.log(k + 2)) * math.log(2)
# def eval(self):
# """
# Evaluation function
# :return: the overall averaged value of Expected Free Discovery
# """
#
# self._item_count = {}
# for u_h in self._evaluation_objects.data.train_dict.values():
# for i in u_h.keys():
# self._item_count[i] = self._item_count.get(i, 0) + 1
#
# novelty_profile = self._item_count.values()
# norm = sum(novelty_profile)
# self._max_nov = -math.log(min(novelty_profile) / norm) / math.log(2)
# self._item_novelty_dict = {i: -math.log(v / norm) / math.log(2) for i, v in self._item_count.items()}
#
# return np.average([self.__user_EFD(u_r, self._cutoff, self._relevant_items[u])
# for u, u_r in self._recommendations.items() if len(self._relevant_items[u])])
[docs] def eval_user_metric(self):
"""
Evaluation function
:return: the overall averaged value of Expected Free Discovery per user
"""
self._item_count = {}
for u_h in self._evaluation_objects.data.train_dict.values():
for i in u_h.keys():
self._item_count[i] = self._item_count.get(i, 0) + 1
novelty_profile = self._item_count.values()
norm = sum(novelty_profile)
self._max_nov = -math.log(min(novelty_profile) / norm) / math.log(2)
self._item_novelty_dict = {i: -math.log(v / norm) / math.log(2) for i, v in self._item_count.items()}
return {u: self.__user_EFD(u_r, u, self._cutoff)
for u, u_r in self._recommendations.items() if len(self._relevance.get_user_rel(u))}