# A Hybrid Group-Based Food Recommender Framework for Handling Overlapping Memberships
## 3 ITGR Framework
The overall architecture of our proposed HTGF is shown in Figure 2. In the process of forming groups, users may be affiliated with multiple groups, each displaying unique preferences and interests. A user's food preferences might vary when dining with friends as compared to having a meal with family. To represent user-to-group associations, we employed FCM [27]. Initially, the mean nutrition ratings of users were calculated, followed by the application of FCM to organize users into different groups based on their membership values within each cluster. Subsequently, a Pearson similarity was employed to identify the user \(u\) who shared the highest similarity with every other user. The top-\(k\) users, exhibiting the most similarity, were selected to form a cohesive group. To address the sparsity issue in the group rating matrix, we employed DNCF [28] to predict ratings for unrated recipes. DNCF leveraged the implicit preferences of group members to make accurate rating predictions. As depicted in Figure 2, the average aggregation approach was utilized to calculate the group rating for a specific item \(i\). Based on the calculated average ratings for each recipe, the top-\(k\) recipes were recommended to the group. For clarity, Table 2 defines the symbols and their meanings used throughout the text. The process started with collecting and processing recipe data from Allrecipes.com. The system then performed various computational steps to ultimately provide the personalized top-K recipe recommendations. Dataset: The system started with the Allrecipes.com dataset, which contained various recipes along with their nutritional information. Nutrition Mean: The nutritional means for the recipes were calculated to standardize and summarize the nutritional data. PCC (Pearson Correlation Coefficient): User similarity was computed using the Pearson correlation coefficient based on the nutritional data. FCM (Fuzzy C-Means Clustering): This step grouped users into clusters based on their similarity, resulting in a membership matrix that indicated the degree of belonging of each user to each cluster. Groups: Users were then grouped into distinct clusters based on the membership matrix obtained from the FCM step. \begin{table}
\begin{tabular}{c c} \hline
**Notation** & **Meaning** \\ \hline DNCF & Deep neural collaborative filtering \\ PS & Peason similarity \\ PCC & Pearson correlation coefficient \\ FCM & Fuzzy C-means \\ U & Set of users \\ I & Set of items \\ R & Rating matrix \\ W & Set of genres \\ C & Set of clusters \\ Q & Set of groups \\ X & Mean genre ratings \\ M & Membership matrix \\ r\({}_{ui}\) & Rating of user u on item i \\ r\({}_{u}\) & Ratings of user u \\ W & User u’s mean nutrition ratings \\ G & Group of users \\ \hline \end{tabular}
\end{table} 
Table 2: Notations and their meanings. Figure 2: System architecture. NCF/MF (Neural Collaborative Filtering/Matrix Factorization): This step predicted group ratings for recipes. It used a matrix factorization approach enhanced by neural collaborative filtering techniques. Predicted Group Rating: The predicted ratings for each group were computed based on the matrix factorization model. Average Aggregation Strategy: The predicted group ratings were aggregated using an average strategy to derive the final ratings. Top-K Recommendations: Finally, based on the aggregated ratings, the system generated the top-K recommendations for recipes. Proposed Model  
The existing datasets did not contain the explicit information required to represent groups. The existing research offered a variety of clustering techniques to create groups [29]. FCM, being a well-known and widely used algorithm, yielded superior results compared to k-means due to its ability to handle overlapping clusters and assign degrees of membership to data points rather than strict membership [30]. FCM was used to cluster users into social groupings, such as families or friends. For instance, when dining with friends, a person may have distinct tastes from when eating with family.