Search Results (3)

In this paper, we define and characterize the embedding of edges and higher-order entities in directed graphs (digraphs) and relate these embeddings to those of nodes. Our edge-centric approach consists of the following: (a) Embedding line digraphs (or their iterated versions); (b) Exploiting the rank properties of these embeddings to show that edge/path similarity can be posed as a linear combination of node similarities; (c) Solving scalability issues through digraph sparsification; (d) Evaluating the performance of these embeddings for classification and clustering. We commence by identifying the motive behind the need for edge-centric approaches. Then we proceed to introduce all the elements of the approach, and finally, we validate it. Our edge-centric embedding entails a top-down mining of links, instead of inferring them from the similarities of node embeddings. This analysis is key to discovering inter-subgraph links that hold the whole graph connected, i.e., central edges. Using directed graphs (digraphs) allows us to cluster edge-like hubs and authorities. In addition, since directed edges inherit their labels from destination (origin) nodes, their embedding provides a proxy representation for node classification and clustering as well. This representation is obtained by embedding the line digraph of the original one. The line digraph provides nice formal properties with respect to the original graph; in particular, it produces more entropic latent spaces. With these properties at hand, we can relate edge embeddings to node embeddings. The main contribution of this paper is to set and prove the linearity theorem, which poses each element of the transition matrix for an edge embedding as a linear combination of the elements of the transition matrix for the node embedding. As a result, the rank preservation property explains why embedding the line digraph and using the labels of the destination nodes provides better classification and clustering performances than embedding the nodes of the original graph. In other words, we do not only facilitate edge mining but enforce node classification and clustering. However, computing the line digraph is challenging, and a sparsification strategy is implemented for the sake of scalability. Our experimental results show that the line digraph representation of the sparsified input graph is quite stable as we increase the sparsification level, and also that it outperforms the original (node-centric) representation. For the sake of simplicity, our theorem relies on node2vec-like (factorization) embeddings. However, we also include several experiments showing how line digraphs may improve the performance of Graph Neural Networks (GNNs), also following the principle of maximum entropy. Full article

A novel non-centralised dispatch strategy is presented for wake redirection to optimise large-scale offshore wind farms operation, creating a balanced control between power production and fatigue thrust loads evenly among the wind turbines. This approach is founded on a graph sparsification partitioning strategy that takes into account the impact of wake propagation. More specifically, the breadth-first search algorithm is employed to identify the subgraph based on the connectivity of the wake direction graph, while the PageRank centrality computation algorithm is utilised to determine and rank scores for the shared turbines’ affiliation with the subgraphs. By doing so, the wind farm is divided into smaller subsets of partitioned turbines, resulting in decoupling. The objective function is then formulated by incorporating penalty terms, specifically the standard deviation of fatigue thrust loads, into the maximum power equation. Meanwhile, the non-centralisation sequential quadratic programming optimisation algorithm is subsequently employed within each partition to determine the control actions while considering the objectives of the respective controllers. Finally, the simulation results of case studies prove to reduce computational costs and improve wind farm power production by balancing accumulated fatigue thrust loads over the operational lifetime as much as possible. Full article

Attempts to discover knowledge through data are gradually becoming diversified to understand complex aspects of social phenomena. Graph data analysis, which models and analyzes complex data as graphs, draws much attention as it combines the latest machine learning techniques. In this paper, we propose a new framework called link pruning for detecting clusters in complex networks, which leverages the cohesiveness of local structures by removing unimportant connections. Link pruning is a flexible framework that reduces the clustering problem in a highly mixed community structure to a simpler problem with a lowly mixed community structure. We analyze which similarities and curvatures defined on the pairs of nodes, which we call the link attributes, allow links inside and outside the community to have a different range of values. Using the link attributes, we design and analyze an algorithm that eliminates links with low attribute values to find a better community structure on the transformed graph with low mixing. Through extensive experiments, we have shown that clustering algorithms with link pruning achieve higher quality than existing algorithms in both synthetic and real-world social networks. Full article