In this paper1, we discuss a knowledge-aware recommendation framework based on neuro-symbolic graph embeddings that encodes first-order logical (FOL) rules. Our workflow starts from a knowledge graph (KG) encoding user preferences and item properties. Next, knowledge-aware recommendations are obtained through the combination of three modules: (i) a rule learner, that extracts FOL rules from the KG; (ii) a graph embedding module, that learns the embeddings of users and items based on the triples of the KG and the FOL rules previously extracted; (iii) a recommendation module, that uses the embeddings to feed a deep learning architecture. In the experimental session we evaluate the efectiveness of our strategy on two datasets. The results show that the combination of KG embeddings and FOL rules improves the predictive accuracy and the novelty of the recommendations.
Recommender Systems (RS) are getting a crucial role in decision-making processes [
The rest of the paper is organized as follows. In Section 2 we present related work in the area. Next, the diferent modules that compose our framework are introduced in Section 3. Results of the experiment are shown in Section 4. Finally, conclusions and future work are sketched in Section 5.
Graph Embeddings for Recommender Systems. The aim of graph embedding techniques
is to represent entities and relations in a KG as dense vectors by projecting them in a vector
space, preserving the original structure of the graph [11]. Similarly to the approach proposed
by Palumbo et al. [16], we applied graph embeddings over a tripartite graph encoding both
collaborative and content-based information. Other works (such as [17, 18, 19, 12]) showed that
recommendation models exploiting graph embedding techniques outperform typical baselines.
Next, previous research [
Knowledge-aware Recommender Systems (KARS). KARS foster the idea of injecting
information encoded in KGs and RSs. While early works were based on similarity and Linked Open
Data [21, 22, 23], more recent methods followed the wave of deep learning. Knowledge-aware
Hybrid Factorization Machines (KaHFM) [
In this section, we introduce the modules composing our framework; it relies on a knowledge graph (see Figure 2) encoding information about users, items and descriptive properties.
Basics of First-Order Logic. The logical rules [26] we exploit are typically referred to as Horn clauses2, since they are composed by several atoms connected by means of logical connectives (e.g., ∨, ∧, ⇒ . . .), in which at most one of them is positive. Each atom is composed of variables (entities) and predicates (relations). An example of logical rules is: ∀, , : (, )∧(, ) ⇒ (, ). A specific formula is called ground when every variable is replaced by a suitable entity in the graph. An example of ground rule based on the graph in Figure 2 is: (ℎ, ) ∧ ( , ) ⇒ (ℎ, ).
Mining First-Order Logical Rules. The first task carried out by our framework consists in mining FOL rules that hold in a KG to extract background knowledge concerning typical pattern encoded in the graph. The process of rule mining returns a set of FOL rules in Horn form, each with confidence score, expressing to what degree the rule holds; these scores can be used to rank the rules and encode in the model only the most promising ones. It is worth to point out that any FOL rules mining method can be used at this step. An example of the rules extracted at this step is provided in the previous paragraph.
Learning Graph Embeddings. Once the rules are extracted, a joint learning based on triples in the KG and FOL rules is carried out. In this work, we used KALE [14] as graph embedding technique, which is inspired by TransE [20] and extends it by encoding symbolic knowledge given by FOL rules.
The neuro-symbolic nature of KALE lies in the fact that the embeddings for each entity in the KG are learnt by exploiting: (i) explicit knowledge, expressed by triples encoded in KG; (ii) background knowledge, expressed by FOL rules. Explicit and background knowledge are represented in a unified framework that learns a comprehensive representation based on both information sources. Based on work by Rocktäschel et al. [27, 28], joint training is possible since triples from a KG can be seen as atoms in FOL (e.g., likes(Alice,Kill Bill)); given that also rules are expressed in a logical form, it is possible to exploit first-order logic as the common framework that allows to unify the representations and to carry out a joint learning. Due to space reasons, it is not possible to provide more details about KALE.
Recommendation Framework. Learnt embeddings are then used to feed a deep learning architecture that provides users with recommendations. Given a set of users and a set of items, our architecture aims at identify suitable recommendations, by predicting the interest of a user in an items and by ranking the items based on descending relevance score. As shown in Figure 3, we designed a simple yet efective architecture based on the combination of concatenation layers and dense layers which is inspired by previous work in the area [29] that obtained competitive results in the top-k recommendations task.
In particular, the recommendation process starts with the embeddings which are obtained as output of the graph embedding process. Each embedding is passed through three dense layers and is then merged through concatenation layer. After a second passage through three dense layers, a sigmoid activation function is used to return a score between 0 and 1 which estimates the probability that the item is relevant for user . Before making predictions, the architecture is trained by exploiting all the the ratings in the form (, ) available in the dataset and by using binary cross-entropy as loss function. See next section for more details on parameters. Once the model is learned, it can predict to what extent user would like unseen items ∈ . After this step, items are ranked based on predicted relevance score and top-k are returned as recommendations.
In the experimental session we evaluated the efectiveness of our methodology in the task of item recommendation to answer to the following research questions: RQ1: Which is the best strategy to select FOL rules to be included in the embedding process? Is there any diference in the accuracy, novelty and diversity when logical rules are encoded in the model? RQ2: How does our approach based on neuro-symbolic graph embeddings perform w.r.t. competitive baselines? 4.1. Experimental Design Datasets. Experiments were carried out in a movie recommendation and in a book recommendation scenario. In the former case, MovieLens 1M (ML1M)3 was exploited as dataset, while in the latter we used DBbook dataset4. As KG, we exploited DBpedia. To extract information from DBpedia and populate our KG, we exploited a mapping already available online5. Table 1 depicts some statistics about the datasets.
ML1M DBbook
Users 6,040 6,181
Items 3,883 6,733
Ratings 1,000.209 72,372 %Positive 57.51% 45.85%
Sparsity 96.42% 99.83%
Entities 26,858 17,505 Protocol. For both the datasets, we used a 80%-20% training-test split. Data were split in order to maintain the ratio between positive and negative ratings. As for MovieLens-1M we considered as positive only the ratings equal to 4 and 5 out of 5. As for DBbook, ratings were provided in a binary format (positive/negative). The predictive accuracy of the algorithms was evaluated on top-5 recommendation list, calculated by following the TestRatings strategy [30]. Source Code and Parameters. Rule mining was carried out by exploiting the latest version of AMIE6, while a recent Java implementation of KALE7 was used to learn graph embeddings. Finally, the source code of our deep recommendation framework is available on GitHub8 and is 3http://grouplens.org/datasets/movielens/ 4http://challenges.2014.eswc-conferences.org/index.php/RecSys 5https://github.com/sisinflab/LODrecsys-datasets 6https://github.com/lajus/amie 7https://github.com/iieir-km/KALE 8https://github.com/giuspillo/RepoNeSyRecSys2022 inspired by the implementation made available by the authors of [29] released on Github9. As regards the parameters of the tools, as for AMIE, we set maximum length rules to 4 atoms, while for each rule minimum confidence is set equal to to 0.001 and minimum coverage equal to 0.1. As regards KALE, we learnt embeddings having size=512, 768 and we learnt the representation with mini batches equal to 100 for both the datasets. Margin separating positive and negative examples = 0.1, entity learning rate = 0.05, relations learning rate = 0.05, iterations = 1000. All these parameters were set through a grid search. Finally, as regards our deep architecture, our models were trained for 25 epochs, by setting batch sizes to 512 for ML1M and to 1536 for DBbook, respectively. The parameter is set to 0.9 and learning rate is set to 0.001. As optimizer, we used ADAM for ML1M and RMSprop for for DBbook. All the parameters were tuned through a grid search.
Configurations. Throughout the experimental protocol, we compared five diferent variant of our framework: two basic configurations (which do not invole FOL rules) and three rule-based configurations. In particular, we compared the embeddings learnt on the simple user-item and user-item-properties graphs (i.e., graph encoding only ratings and graph encoding descriptive properties too). Next, rule-based configuration were run over the user-item-properties graph, and we defined three diferent heuristics to rank the rules returned by AMIE: (i) like rules, having a like relation in the head (e.g., (, ) ∧ (, ) ⇒ (, )); (ii) top-k like rules, having a like relation in the head based on the coverage of the rules; (iii) high confidence rules, having a confidence score higher than 0.75. Of course, other strategies to select FOL rules can be applied in this step.
Baselines and Evaluation Metrics. To ensure the complete reproducibility, we calculated
our evaluation metrics and we selected our baselines by using the Elliot10 framework [31]. As
regards the metrics, to assess the accuracy of the recommendations we used F1 score [32], Mean
Average Precision (MAP), and the normalized discounted cumulative gain (nDGC) [33, 34] scores;
we also considered diversity and novelty of the recommendations by calculating Gini Index and
Expected Popularity Complement (EPC) [35]. Finally, we also compared our methodology to
ten baselines available in Elliot: three matrix factorization techniques (SLIM [36], BPRMF [37]
and PureSVD), three methods based on deep learning models, (MultiVAE [38], CFGAN [39] and
NGCF [40]) and four algorithms implementing knowledge-aware techniques (Item-KNN and
User-KNN [41], KaHFM [
Baseline BPRMF PureSVD Slim MultiVAE CFGAN NGCF AttributeItemKnn AttributeUserKnn KaHFM LightGCN Our best
MAP nDCG Diversity
Gini
Novelty
EPC
Diversity
Gini
Novelty
EPC
best results are obtained for = 512, and the best-performing configuration is top-k likes rules.
Moreover, our best-performing configuration improves the baselines in terms of diversity and
novelty as well. As regards = 768, the behavior we noted is in line with that we observed
for ML1M. We can also notice that user-item often overcomes user-item-properites: this means
that descriptive properties are poorly informative; however, injecting background knowledge
encoded as FOL rules is able to overcome this issue and leads to the overall best results.
(RQ2) Comparison to Baselines. To answer RQ2, we compared our best-performing
conifguration with some competitive baselines. Table 3 show that our framework significantly
overcomes those baselines. For ML1M (Table 3), all metrics but diversity have been outperformed
with a significant gap ( < 0.01). It is worth to notice that KARS have been outperformed by
methods for matrix factorization, diferently by our expectations. Results on Dbbook confirm
these findings: all metrics, except for novelty, are overcame by our framework. The best baseline
in this case is KaHFM [
In this paper we discussed a knowledge-aware recommendation framework based on neurosymbolic graph embeddings encoding first-order logical rules ; it combines explicit knowledge provided by triples in the graph and background knowledge provided FOL rules. Our experiments provided us with the following findings: (i) joint learning based on FOL rules and KGs generates more precise embeddings and more accurate recommendations, in particular using rules with only like relation in the head; (ii) comparisons with several baselines confirmed the accuracy of our framework. A good impact is also noted in terms of novelty and diversity of the recommendations. Such promising results represent a first step in the direction of developing neuro-symbolic RSs exploiting neural and symbolic reasoning. However, given the novelty of the current work, we are aware that several limitations exist. As an example, more accurate methods for selecting the rules are needed, together with a more extensive analysis of the informative power of diferent FOL rules. As future work, we will also strengthen the level of the baselines we consider in our experiments and the number of datasets, and by evaluating the system in diferent domains (i.e., food recommendations [ 43]) and by modeling user preferences by exploiting diferent sets of features [44]. for item recommendation, in: European Semantic Web Conference, Springer, 2018, pp. 478–490. [9] Z. Sun, J. Yang, J. Zhang, A. Bozzon, L.-K. Huang, C. Xu, Recurrent knowledge graph embedding for efective recommendation, in: Proceedings of the 12th ACM Conference on Recommender Systems, 2018, pp. 297–305. [10] W. Song, Z. Duan, Z. Yang, H. Zhu, M. Zhang, J. Tang, Explainable knowledge graph-based recommendation via deep reinforcement learning, arXiv preprint arXiv:1906.09506 (2019). [11] H. Cai, V. W. Zheng, K. C.-C. Chang, A comprehensive survey of graph embedding: Problems, techniques, and applications, IEEE Transactions on Knowledge and Data Engineering 30 (2018) 1616–1637. [12] C. Musto, P. Lops, M. de Gemmis, G. Semeraro, Context-aware graph-based recommendations exploiting personalized pagerank, Knowledge-Based Systems 216 (2021) 106806. [13] M. K. Sarker, L. Zhou, A. Eberhart, P. Hitzler, Neuro-symbolic artificial intelligence, AI
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