# Learning Heterogeneous Knowledge Base Embeddings for Explainable Recommendation
## 7 Results and Discussion
### Case Study for Explanation Generation  
To show the ability of our model to generate knowledge-enhanced explanations, we conduct case study for a test user (i.e., _A1P27 BGF8 NAI29_) from _Cell Phones_, for whom we have examined that the first recommendation (i.e., _B009 RXU59C_) provided by the system is correct. We plot the translation process of this user to other entity subspaces with _Purchase_, _Mention_, _Bought_together_, and _Belongs_to_ relations, as shown in Figure 4. We also show the translation of the first recommended item _B009 RXU59C_ (_B9C_) using the same relations. The top 5 entities retrieved by our system for each translation are listed along with their probabilities computed based on Equation (10).  
As we can see in Figure 4, there are three explanation paths between the user _A1P27 BGF8 NAI29_ and the item _B9C_. The first and second paths are constructed by _Purchase_ and _Bought_together_. According to our model, the user is linked to _B008 RD10 TU_ (_BTU_) and _B00 HNG1 YS_ (_BYS_) through _Purchase_+_Bought_together_ with probabilities as 27.80% and 5.48%. The item _B9C_ is linked to _BTU_ and _BYS_ through _Bought_together_ directly with probabilities as 26.57% and 3.41%. The third path is constructed by _Purchase_ and _Belongs_to_. The user is linked to the category _Chargers_ with probability as 2.53% and _B9C_ is linked to _Chargers_ with probability as 30.90%. Therefore, we can create three natural  
Figure 4: Example explanation paths between the user _A1P27 BGF8 NAI29_ and the item _B009 RXU59C_ (B9C) in _Cell Phones_.  
language explanations for the recommendation of _B9C_ by describing these explanation paths with simple templates. Example sentences and the corresponding confidences are listed below:  
* _B9C_ is recommended because the user often purchases items that are bought with _BTU_ together, and _B9C_ is also frequently bought with _BTU_ together (27.80% \(\times\) 26.57% \(=\) 7.39%).
* _B9C_ is recommended because the user often purchases items that are bought with _BYS_ together, and _B9C_ is also frequently bought with _BYS_ together (5.48% \(\times\) 3.41% \(=\) 0.19%).
* _B9C_ is recommended because the user often purchases items related to the category _Chargers_, and _B9C_ belongs to the category _Chargers_ (2.53% \(\times\) 30.90% \(=\) 0.78%).  
Among the explanation sentences, the best explanation should be the one with the highest confidence, which is the first sentence in this case.  
To better evaluate the quality of these recommendation explanations, we look at the details of each product shown in Figure 4. On Amazon.com, _B9C_ is a _High-speed Wall_ _Charger by New Trend_ for tablets, _BTU_ is an _iPad mini Keyboard Case_, and _BYS_ is an _iPad Air Keyboard Case_. If the generated explanations are reasonable, this means that the user has purchased some items that were frequently co-purchased with iPad accessories. Also, this indicates that there is a high probability that the user has an iPad. For validation proposes, we list the five training reviews written by the user in Table 4.  
As we can see in Table 4, the user has purchased several tablet accessories such as Bluetooth headsets and portable charger. The second review even explicitly mentions that the user has possessed an iPad and expresses concerns about the \"running-out-of-juice\" problem. Therefore, it is reasonable to believe that the user is likely to purchase stuff that are frequently co-purchased with iPad accessories such as _iPad mini Keyboard Case_ (_BTU_) or _iPad Air Keyboard Case_ (_BYS_), which are recommended as top items in our algorithm, and are also well-explained by the explanation paths in the knowledge graph.