# New Hybrid Techniques for Business Recommender Systems
## 7 A New Hybrid Recommender Design  
In Section 2, we saw that hybrid recommender systems are commonly used to overcome the weaknesses of individual recommendation techniques. Of the seven hybrid recommender strategies described by [41], strategies such as _switching_, _cascade_ or _mixed_ are not ideal (and the others are not applicable), as the results show that the CBR recommender is clearly the better performer. Since we would like the graph-based recommender to contribute by adding more relevant elements where CBR is limited, we adopted the weighted combination method [41] because it allows us to \"overrule\" the decisions of the CBR by adjusting the importance (weight) given to either CBR or graph-based recommender. A representation of the weighted hybrid strategy designed by us is shown in Figure 2.  
For designing the hybrid strategy, we built upon the CBR configuration to retrieve the most relevant two cases, as this configuration achieved the optimum performance in the previous experiment. We now explore if the recall issue of CBR can be resolved by adding some component of the graph-based recommendations (GBR). We first normalised the scores of the individual recommendation techniques using min-max normalisation since the graph-based and CBR recommenders have their own (different) scoring mechanisms, as described in Section 5. We then combined the normalised scores of both recommenders and calculated the hybrid weighted score using Equation (2).  
\[hybrid\_score(item)=\alpha\cdot|CBR(item)|+(1-\alpha)\cdot|GBR(item)| \tag{2}\]  
where \(|\cdot|\) refers to min-max score normalisation.  
Because of the CBR recommender's strength in dealing with sparse, i.e., low-verbosity queries and the relative strength of the graph-based recommender in handling high-verbosity queries, we made the mixture parameter \(\alpha\) dependent on the query verbosity, i.e., the number of referred elements \(|q|\) in the query \(q\):  
\[\alpha=\left\{\begin{array}{ll}1-\frac{(1-\beta)\cdot|q|}{\varepsilon}& \text{if }|q|\leq\varepsilon\\ \beta&\text{otherwise}\end{array}\right.,0<\beta<1 \tag{3}\]  
Figure 2: Design of weighted hybrid recommendation strategy.  
Here, \(\bar{c}\) refers to half the average size of all cases in the case base in terms of their number of referred elements (KPIs) and serves as the \"verbosity threshold\", whereas \(\beta\) is a parameter that controls the contribution of the CBR recommender.  
Since CBR was the better performer of the two recommendation techniques, we designed Equation (3) such that the weight of the CBR recommender (\(\alpha\)) is never 0 in Equation (2). On the other hand, we do not set \(\beta\) to 1 as this would always give a full weight to CBR, which we already know has limitations performing as a \"pure\" recommender. Additionally, from the results of Experiment 1, we concluded that a CBR-dominated hybrid recommender would perform better for queries below the verbosity threshold and vice versa, also taken care of in Equation (3). Figure 3 shows the dependency between \(\alpha\) and query verbosity \(|q|\) graphically for different values of \(\beta\) and \(\bar{c}=14\). We can see that \(\alpha\) is always 1 when \(|q|\) is 0. We can also see how \(\beta\) acts as the \"minimum CBR contribution\" and that below the verbosity threshold, less and less weight is given to CBR as the verbosity increases.  
With this setup, we carried out the second experiment--leave-one-case-out evaluation for different query verbosity using the hybrid strategy. Our goal, now, was to find the appropriate combination of weights that could overcome the recall issue of CBR without impacting its performance. After every run, we compared the MAP values for each recommendation technique with that of the hybrid strategy, as seen in Table 3.  
Figure 3: Mixture parameter \(\alpha\) as a function of query verbosity \(q\), \(\beta\) controlling minimum CBR contribution.