IEEE Computational Intelligence Magazine - February 2022 - 52

2) Neighbours are filtered so that they are in the training set
of the user.
3) Only unseen interactions are filtered, and the similarity
score is used to rank items (in analogy to the confidence
score used to evaluate association rules).
4) The top-D predictions and their corresponding explanations
are drawn.
The implementation of kNN uses the scikit-learn library.6
3) Gaussian Mixture Model
Gaussian Mixture Model (GMM) is a probabilistic modelbased
clustering approach [40], which assumes that data is generated
by a mixture of underlying probability distributions. In
practice, this means that each cluster can be mathematically
represented by a parametric probability distribution. Under this
view, clustering a set of points into k clusters amounts to infer
the mixing probabilities (weights) and parameters of the
mixture distribution of k Gaussian probability distributions,
one for each cluster [40, Ch. 3].
A common problem of mixture models is that the value of
component k is not given a priori, and it needs to be estimated.
The search for an optimal k is usually addressed by taking
model selection criteria, such as the Bayesian information criterion
(BIC) or the Akaike information criteria (AIC), into
account. These criteria penalise models that have more parameters
(e.g., clusters) to learn, and reward models that fit the
data well. Models selected by the BIC tend to be simpler than
the ones selected by the AIC [40, Ch. 3].
The main idea of using GMM to generate explanations is
that trained embeddings, learned by black box algorithms,
reflect intrinsic similarities of users in terms of their past
interactions w.r.t. certain items. Thus, it is possible to generate
item-style explanations by taking into account the embeddings
belonging to the same cluster. Table II shows several
examples of item-style explanations that are generated using
GMM as clustering algorithm.
The explanation algorithm based on GMM works as follows:
1) User and item embeddings learned by a black box algorithm
are extracted.
6 https://scikit-learn.org/stable/
TABLE II Examples of item-style explanations.
Recommendations and item-style explanations for a random
user in ML-1M are generated from item embeddings trained
with MLP and clustered according to GMM.
RANK RECOMMENDATION
1
While You Were
Sleeping
2
3
The Doom
Generation
Persuasion
BECAUSE YOU LIKED:
& [Free Willy, Sleepless in
Seattle, Welcome to the
Dollhouse]
& [The Man Who Knew Too
Little, My Own Private
Idah, Another Stakeout]
& [I.Q., Everyone Says I Love
You, True Romance]
2) Embedding dimensions are reduced using a dimensionality
reduction technique.
3) Embeddings are clustered using GMM and BIC as criteria
for finding an optimal number of clusters.
4) Item-style explanations of each user recommendation are
extracted by taking the most similar item embeddings in
the cluster into account.
The dimensionality reduction step is required due to user and
item embeddings belonging to a high dimensional space and
making it, therefore, difficult to find clustered structures [41]. A
dimensionality reduction technique called Uniform Manifold
Approximation (UMAP) [42] was adopted to reduce the embedding
dimension. Another technique could have been t-SNE [43].
Whilst these approaches reduce the dimensions, they are also typically
able to preserve (part of) the original distances of the highdimensional
embedding space. The implementation of GMM and
UMAP uses the scikit-learn and umap-learn library respectively.7
D. Evaluating Explanations
In the offline evaluation of explanations, a formal definition
of interpretability is used as a proxy for quantifying the explanation
quality [44]. Our library implements three metrics
belonging to two categories of offline evaluation metrics for
explainability, the first of which evaluates whether a model
behaves as expected. The second category evaluates explainability
via the proxy. recoXplainer implements one metric
for the first category and two metrics for the second one.
It is important to notice that offline evaluation is not the
only approach according to which explanations should be
evaluated. In recommender systems, there is often the need to
assess
the perception of generated explanations by users.
However, online evaluation is out of the scope of this paper.
The explanations generated by our library are in fact archetypal
explanation styles, namely item- and user-style explanations,
for which a number of studies, measuring their
human-understandability, already exist (e.g., [24], [37]-[39]).
1) Mean Explainability Precision
This metric is particularly pertinent to the case of model-based
explanations (see Section III-B), when additional components
are added to the loss function. Mean Explainability Precision
(MEP) is implemented following the definition proposed by
Abdollahi and Nasraoui [32]. According to this metric, the
explainability of a recommendation list Lu
for a given user u is
measured as the ratio between the number of explainable items
in Lu
and ||,Lu
MEP =
as shown as follows:
||
1
U
# /
!
uU
|{ :, }|
||
ii LEui 20
Lu
! u
,
where U is the set of users, and Eui
is a formalisation of the
definition of interpretability as defined by the algorithm (see
Eq. 3). MEP varies from 0 to 1, with 1 being the highest
achievable score. This metric is very sensitive to the definition
7 https://pypi.org/project/umap-learn/
52 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | FEBRUARY 2022
https://www.scikit-learn.org/stable/ https://www.pypi.org/project/umap-learn/
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