This paper proposes a sparse factorization approach, KGFlex, that represents each item feature as an embedding. With KGFlex, the user-item interactions are a factorized combination of the item features relevant to the user. An entropy-driven module drives the training considering only the feature involved in the user's decision-making process. Extensive experiments confirm the approach's efectiveness, considering the ranking accuracy, diversity, and induced bias. The public implementation of KGFlex is available at https://split.to/kgflex.
demographic data [
KGFlex exploits the knowledge encoded in a knowledge graph as side information to characterize both items and users. One of the main assumptions is that users decide to enjoy an item based on a subset of its characteristics, implying that not all the item features are equally important. In the following, we show how KGFlex describes each user and item with a set of features. Taking a cue from information theory KGFlex exploits the notion of information gain to measure the relevance of a feature for a user in deciding to consume or not an item.
In KGFlex, items and users are characterized by sets of features extracted from a , a knowledge
base of semantically linked machine-understandable data [
A knowledge graph can be represented as pairs of entities linked to each other by binary relations. Each connection in is denoted by →− relation (predicate), and is an object entity. Hereinafter, we generalize the previous notion to multi-hop predicates (i.e., considering chains of predicates that connect two entities at a higher , where is a subject entity, is a directed depth). Let -hop predicate be defined as = ⟨ 1,..., ⟩ if →−
convenience, ℎ( ) = for : →− no confusion arises we will use →− to denote a generic chain with ℎ( ) ≥ 1. ∈ denotes the depth of the predicate chain, and when 1 1 →− 2 ... →− ∈ . For
Given a collection of items ℐ and a knowledge graph , we assume each element in ∈ ℐ has a mapping to a corresponding entity in . Under this assumption, an item can be explored, at depth , to identify the set ℱ() of the semantic features describing it:
ℱ() = {⟨, ⟩ | → − ∈ ,ℎ( ) ∈ {1,...,}}.
At this stage, feature filtering, graph pruning, and semantic feature selection techniques [
We describe each user ∈ with the set ℱ of the features representing the items ℐ ⊆ ℐ enjoyed by :
Finally, we define the overall set ℱ () of features in the system: ℱ() = ⋃︁ ℱ().
∈ℐ ℱ () = ⋃︁ℱ(). (1) (2) (3) (5) (6) (|) = ∑︁ ( = ,)(| = ,).
=1
Since the information gain defined in Eq. (5) returns a measure of the importance of a single attribute in distinguishing positive from negative examples in a dataset, we build, for each user , In the following, for convenience, the () superscript is omitted whenever it is not relevant in the context.
In information theory, entropy is used to measure the uncertainty of a random variable.
In particular, the entropy ( ) of a random variable with possible values in {1,...,} is defined as:
( ) = − ∑︁ ( = )log2 ( = ). (4)
=1 It is straightforward to check that a coin that always comes up heads has zero entropy, while a fair coin equally likely to come up heads or tails when flipped has entropy 1. Notably, if is a binary random variable that is true with probability , we have () = − log2 − (1− )log2(1− ). For instance, given a dataset of training samples in the form (x,), with x ∈ R and ∈ {0,1} is a binary variable that is true with probability , its entropy is () = (). As a consequence, a dataset with a balanced number of positive and negative samples has entropy 1.
In this context, the information gain (,) measures the expected reduction in information entropy obtained from the observation of one of the attributes in x:
(,) = ()− (|), where (|) is the expected entropy of conditioned on . If can assume distinct values ,1,..., with a categorical probability distribution,the dataset is partitioned into mutually exclusive subsets and the following conditioned entropy is determined: randomly picked up from ⋃︀ a balanced dataset with all the consumed items from ℐ and the same amount of negative items variables corresponding to the features in ℱ. Each variable indicates, for each item in , the presence ( = 1) or the absence ( = 0) of the corresponding feature in the set ℱ. According to the definition, () = 1. Therefore, the information gain for each feature ∈ ℱ can be computed using the dataset . Let be the number of positive samples in for which = 1, the number of negative samples for which the same feature is present, and = + . Analogously, ¬ = |ℐ|− is the number of positive samples with = 0, ¬ = |ℐ|− is the number of negative samples with = 0, and ¬ = ¬ +¬ . Following Eqq. (5) and (6): ∈,̸=ℐ ∖ℐ. Each sample in is provided with a set of binary (7) (8) (9) (10)
estimates the interaction ^ between user and item : KGFlex models the features in ℱ as collaboratively learned embeddings in a latent space. Since KGFlex promotes the idea of having user fine-tuned versions of the same model, we have both tures in ℱ ⊆ ℱ a global representation of the features in ℱ and a personal view, for each user , of the fea. Notably, the model is structured into two distinct parts. On the one hand, KGFlex keeps a set of global trainable embeddings and biases shared among all the users, with = {(g ∈ R , ∈ R), ∀ ∈ ℱ }. On the other hand, each user in KGFlex also has his/her personal representation of the features he/she interacted with, i.e., the features in ℱ. These embeddings are collected within the set , defined as = {p ∈ R , ∀ ∈ ℱ}. Then, the inner product between the personal representation p and the global representation g , plus a bias value , estimates the afinity of user
to feature . The sum of such afinities for all the features in ℱ = ℱ ∩ℱ, weighted according to the pre-computed entropy-based coeficients, (, ) = 1− (| = 1)− (| = 0), (| = 1) = (| = 0) = ¬ || ︂( || ︂( − log2 − log2
︂) , − ¬ ¬ log2 ¬ ¬ − ¬ ¬ log2 ¬
︂) ¬ .
We finally associate a weight = (, ) to each pair of user and feature to represent the influence of a feature —in the view of the user— in the prediction of user-item interactions. ^ = ∑︁ (pg + ).
∈ℱ Eq. (10) encodes the strategy KGFlex exploits to handle thousands of model features. In fact, it takes advantage of user profile to involve only a small subset of them in the estimate of the user-item afinity.
To learn the model parameters, KGFlex adopts Bayesian Personalized Ranking (BPR), the most common pair-wise Learning to Rank strategy, based on a maximum posterior estimator. Given a training set = {(,+,− ) | + ∈ ℐ ∧ − ∈ ℐ∖ℐ,∀ ∈ }, BPR optimizes the loss = ∑︀
(,+,− )∈ ln (^+ − ^− ), with the assumption that a user prefers a consumed item +
over a non-consumed item − . The model parameters are learnt with an optimization algorithm
like SGD, as described in Rendle et al. [
In the following, we present a discussion about datasets, preprocessing, baselines, and evaluation protocol that guided the experimentation of KGFlex.
The evaluation of the performance of KGFlex is conducted on two well-known datasets: Yahoo!
Movies and Facebook Books. The datasets have been binarized, retaining ratings of 3 or higher.
To ensure a fair comparison with the baselines, an iterative 10-core, and 5-core preprocessing
procedure is performed on the first and second datasets. The items have been described with a
set of semantic features retrieved through a KG exploration at depth 2 of the DBpedia using
a public DBpedia URI mapping. Some features (based on their 1-hop predicate) have not been
considered since they do not provide useful information [
To assess the efectiveness of KGFlex, we compare it with BPR-MF [
Yahoo! Movies dataset. KGFlex shows satisfactory accuracy results, being outperformed only by kaHFM and MF. It is noteworthy that KGFlex significantly outperforms BPR-MF, although both are learned with a pair-wise BPR optimization, thus underlining the beneficial role of the extracted knowledge. Moreover, examining the item coverage and Gini values, we note the high degree of personalization provided by KGFlex. We link this result to the personalized view of the knowledge granted by the framework. Moreover, in KGFlex the collaborative signal on explicit user interests ensures to recommend diverse items among the ones sharing characteristics of interest for the user. The aforementioned behavior is not confirmed in Facebook Books (see Table 1b). Indeed, the accuracy results seem to remain below the performance of other factorization-based approaches. However, the diversity results show how BPR-MF, MF, and NeuMF may have been flooded by popularity signal, which led them to perform poorly regarding the item coverage and Gini metrics. Instead, KGFlex does not sufer from this problem and approaches the superior performance of Item-kNN in terms of diversity.
4 Random BPR-MF 6 Most Popular MF 8
10 VSM NeuMF 8 10
What we have analytically observed is substantially confirmed in Figure 1. These graphs show the joint behavior of KGFlex on accuracy and distributional diversity by analyzing the value of Hit Ratio (HR) with respect to the Shannon Entropy (SE) statistics, which measures how diversely distributed are the recommended items. Among factorization-based approaches, KGFlex approaches the right-top margin to a greater extent, remarking its capability of providing highly personalized recommendations, probably due to the joint operation of the global and the personal views of the same features. The kaHFM model usually is the second-best model, while the other approaches seem to perform very poorly in at least one dimension or do not have a stable position when varying the dataset.
Oftentimes, unpopular items are not recommended and remain underrepresented [
We introduced KGFlex, a promising knowledge-aware approach to generate recommendations from implicit feedback. KGFlex has demonstrated its ability to take the best from content-based and factorization-based recommendation approaches. Moreover, thanks to the high degree of expressiveness provided by the personalized representation of content information, KGFlex guarantees satisfactory and diverse recommendations and resilience to algorithmic bias.