Social collaborative filtering recommender systems extend the traditional user-to-item interaction with explicit user-to-user relationships, thereby allowing for a wider exploration of correlations among users and items, that potentially lead to better recommendations. A number of methods have been proposed in the direction of exploring the social network, either locally (i.e. the vicinity of each user) or globally. In this paper, we propose a novel methodology for collaborative filtering social recommendation that tries to combine the merits of both the aforementioned approaches, based on the soft-clustering of the Friend-of-a-Friend (FoaF) network of each user. This task is accomplished by the non-negative factorization of the adjacency matrix of the FoaF graph, while the edge-centric logic of the factorization algorithm is ameliorated by incorporating more general structural properties of the graph, such as the number of edges and stars, through the introduction of the exponential random graph models. The preliminary results obtained reveal the potential of this idea.

The popularity of recommendation systems has made them a substantial component of many applications and projects. This work proposes a framework for package recommendations that try to meet users' preferences as much as possible through the satisfaction of several criteria. This is achieved by modeling the relation between the items and the categories these items belong to aiming to recommend to each user the top-k packages which cover their preferred categories and the restriction of a maximum package cost. Our contribution includes an optimal and a greedy solution. The novelty of the optimal solution is that it combines the collaborative filtering predictions with a graph based model to produce recommendations. The problem is expressed through a minimum cost flow network and is solved by integer linear programming. The greedy solution performs with a low computational complexity and provides recommendations which are close to the optimal solution. We have evaluated and compared our framework with a baseline method by using two popular recommendation datasets and we have obtained promising results on a set of widely accepted evaluation metrics.