Theory of preference modelling for communities in scale-free networks

Detecting a community structure on networks is a problem of interest in science and many other domains. Communities are special structures which may consist nodes with some common features. The identification of overlapping communities can clarify not so apparent features about relationships among the nodes of a network. A node in a community can have a membership in a community with a different degree. Here, we introduce a fuzzy based approach for overlapping community detection. A special type of fuzzy operator is used to define the membership strength for the nodes of community. Fuzzy systems and logic is a branch of mathematics which introduces many-valued logic to compute the truth value. The computed truth can have a value between 0 and 1. The preference modelling approach introduces some parameters for designing communities of particular strength. The strength of a community tells us to what degree each member of community is part of a community. As for relevance and applicability of the community detection method on different types of data and in various situations, this approach generates a possibility for the user to be able to control the overlap regions created while detecting the communities. We extend the existing methods which use local function optimization for community detection. The LFM method uses a local fitness function for a community to identify the community structures. We present a community fitness function in pliant logic form and provide mathematical proofs of its properties, then we apply the preference implication of continuous-valued logic. The preference implication is based on two important parameters $$\nu$$ ν and $$\alpha$$ α . The parameter $$\nu$$ ν of the preference-implication allows us to control the design of the communities according to our requirement of the strength of the community. The parameter $$\alpha$$ α defines the sharpness of preference implication. A smaller value of the threshold for community membership creates bigger communities and more overlapping regions. A higher value of community membership threshold creates stronger communities with nodes having more participation in the community. The threshold is controlled by $$\delta$$ δ which defines the degree of relationship of a node to a community. To balance the creation of overlap regions, stronger communities and reducing outliers we choose a third parameter $$\delta$$ δ in such a way that it controls the community strength by varying the membership threshold as community evolves over time. We test the theoretical model by conducting experiments on artificial and real scale-free networks. We test the behaviour of all the parameters on different data-sets and report the outliers found. In our experiments, we found a good relationship between $$\nu$$ ν and overlapping nodes in communities.

Discovering Collaborative Signals for Next POI Recommendation with Iterative Seq2Graph Augmentation

Being an indispensable component in location-based social networks, next point-of-interest (POI) recommendation recommends users unexplored POIs based on their recent visiting histories. However, existing work mainly models check-in data as isolated POI sequences, neglecting the crucial collaborative signals from cross-sequence check-in information. Furthermore, the sparse POI-POI transitions restrict the ability of a model to learn effective sequential patterns for recommendation. In this paper, we propose Sequence-to-Graph (Seq2Graph) augmentation for each POI sequence, allowing collaborative signals to be propagated from correlated POIs belonging to other sequences. We then devise a novel Sequence-to-Graph POI Recommender (SGRec), which jointly learns POI embeddings and infers a user's temporal preferences from the graph-augmented POI sequence. To overcome the sparsity of POI-level interactions, we further infuse category-awareness into SGRec with a multi-task learning scheme that captures the denser category-wise transitions. As such, SGRec makes full use of the collaborative signals for learning expressive POI representations, and also comprehensively uncovers multi-level sequential patterns for user preference modelling. Extensive experiments on two real-world datasets demonstrate the superiority of SGRec against state-of-the-art methods in next POI recommendation.