# Diversity Balancing for Two-Stage Collaborative Filtering in Recommender Systems
## 2 Related Works
### Improving RS Diversity  
To improve the user experience in RSs, researchers have attempted to improve the novelty and diversity of suggested items and to improve the visibility of long tail items [24; 26; 27]. Attempts to improve RS accuracy have focused on finding items highly similar to the past preferences of active users while attempts to improve diversity have focused on evaluating \"dissimilarity\" among recommended items. Methods of improving accuracy are often incompatible with those for improving diversity. Therefore, the trade-off between accuracy and diversity must be optimized. A major challenge of designing an effective RS is to determine the maximum diversity that can be achieved for an acceptable loss in prediction accuracy.  
Proposed models for improving RS diversity can be categorized as two-stage models and unified models. Unified models [24; 25; 26; 27; 28] have a single stage optimization framework for solving the joint formulation of a weighted combination of diversity and accuracy. For example, the DiABIO single stage optimization solution proposed in [26] was based on latent factor models. A diversity enhancement regularization term was then used to improve recommendation diversity by constraining the matrix factor decomposition model. In [27], the authors presented a unified framework and a unified convex formulation based on available ratings and item metadata. The split Bregman technique used to solve this formulation achieved an acceptable accuracy-diversity trade-off. In [28], a heat conduction algorithm was proposed for solving the triple dilemma of simultaneously optimizing stability, accuracy, and diversity by ranking the stability of similarities and then considering only the most stable ones.  
The recommendation performance of unified models mainly depends on the performance of the optimization algorithms. In many cases, falling into local optimal solutions is more likely than falling into global optimal solutions. However, the first stage of a two-stage recommendation strategy [38; 39; 40] focuses on predicting the missing ratings and on using the collaborative filtering method to generate a candidate recommendation list. The second stage applies a certain ranking strategy to maximize diversity of the list. The ranking strategies often require a pre-defined heuristic threshold. Items rated above the threshold are added to the recommendation list. Unlike the item list in a conventional RS, recommended items appear in a descending order of predicted ratings. To improve diversity, various strategies have been proposed for ranking the predicted ratings in the second stage. The RS design described in [41] considered the popularity of items in addition to their relevancy. A multi-objective evolutionary algorithm for simultaneously optimizing accuracy and diversity was then proposed. In [42], clustering technique was used to segregate items. Items were then selected from each cluster to ensure a high diversity of the recommendation list. Ranking strategies developed in other works, e.g., [38; 39], have used greedy optimization, item popularity to promote diversity.  
The works discussed above either use trust relationship to alleviate the problem of cold start and sparsity so as to improve recommendation accuracy or propose new recommendation list ranking strategies to improve recommendation diversity. However, they neglect the impact of interest overlapping between the target users and trust users on both accuracy and diversity of recommendations. Trust relationships and common interests can connect two users who do not know each other, and they are equally important. Users with the same trust level may have different interests. We consider both multiple interests and trust relationships of users, so diversity and accuracy are reflected in the final recommendation list. The proposed method increases both personalized diversity and aggregate diversity with minimal loss of accuracy.