亚洲男人的天堂2018av,欧美草比,久久久久久免费视频精选,国色天香在线看免费,久久久久亚洲av成人片仓井空

Computing a maximum independent set (MaxIS) is a fundamental NP-hard problem in graph theory, which has important applications in a wide spectrum of fields. Since graphs in many applications are changing frequently over time, the problem of maintaining a MaxIS over dynamic graphs has attracted increasing attention over the past few years. Due to the intractability of maintaining an exact MaxIS, this paper aims to develop efficient algorithms that can maintain an approximate MaxIS with an accuracy guarantee theoretically. In particular, we propose a framework that maintains a $(\frac{\Delta}{2} + 1)$-approximate MaxIS over dynamic graphs and prove that it achieves a constant approximation ratio in many real-world networks. To the best of our knowledge, this is the first non-trivial approximability result for the dynamic MaxIS problem. Following the framework, we implement an efficient linear-time dynamic algorithm and a more effective dynamic algorithm with near-linear expected time complexity. Our thorough experiments over real and synthetic graphs demonstrate the effectiveness and efficiency of the proposed algorithms, especially when the graph is highly dynamic.

Computing a dense subgraph is a fundamental problem in graph mining, with a diverse set of applications ranging from electronic commerce to community detection in social networks. In many of these applications, the underlying context is better modelled as a weighted hypergraph that keeps evolving with time. This motivates the problem of maintaining the densest subhypergraph of a weighted hypergraph in a {\em dynamic setting}, where the input keeps changing via a sequence of updates (hyperedge insertions/deletions). Previously, the only known algorithm for this problem was due to Hu et al. [HWC17]. This algorithm worked only on unweighted hypergraphs, and had an approximation ratio of $(1+\epsilon)r^2$ and an update time of $O(\text{poly} (r, \log n))$, where $r$ denotes the maximum rank of the input across all the updates. We obtain a new algorithm for this problem, which works even when the input hypergraph is weighted. Our algorithm has a significantly improved (near-optimal) approximation ratio of $(1+\epsilon)$ that is independent of $r$, and a similar update time of $O(\text{poly} (r, \log n))$. It is the first $(1+\epsilon)$-approximation algorithm even for the special case of weighted simple graphs. To complement our theoretical analysis, we perform experiments with our dynamic algorithm on large-scale, real-world data-sets. Our algorithm significantly outperforms the state of the art [HWC17] both in terms of accuracy and efficiency.

Message passing Graph Neural Networks (GNNs) provide a powerful modeling framework for relational data. However, the expressive power of existing GNNs is upper-bounded by the 1-Weisfeiler-Lehman (1-WL) graph isomorphism test, which means GNNs that are not able to predict node clustering coefficients and shortest path distances, and cannot differentiate between different d-regular graphs. Here we develop a class of message passing GNNs, named Identity-aware Graph Neural Networks (ID-GNNs), with greater expressive power than the 1-WL test. ID-GNN offers a minimal but powerful solution to limitations of existing GNNs. ID-GNN extends existing GNN architectures by inductively considering nodes' identities during message passing. To embed a given node, ID-GNN first extracts the ego network centered at the node, then conducts rounds of heterogeneous message passing, where different sets of parameters are applied to the center node than to other surrounding nodes in the ego network. We further propose a simplified but faster version of ID-GNN that injects node identity information as augmented node features. Altogether, both versions of ID-GNN represent general extensions of message passing GNNs, where experiments show that transforming existing GNNs to ID-GNNs yields on average 40% accuracy improvement on challenging node, edge, and graph property prediction tasks; 3% accuracy improvement on node and graph classification benchmarks; and 15% ROC AUC improvement on real-world link prediction tasks. Additionally, ID-GNNs demonstrate improved or comparable performance over other task-specific graph networks.

The accurate and interpretable prediction of future events in time-series data often requires the capturing of representative patterns (or referred to as states) underpinning the observed data. To this end, most existing studies focus on the representation and recognition of states, but ignore the changing transitional relations among them. In this paper, we present evolutionary state graph, a dynamic graph structure designed to systematically represent the evolving relations (edges) among states (nodes) along time. We conduct analysis on the dynamic graphs constructed from the time-series data and show that changes on the graph structures (e.g., edges connecting certain state nodes) can inform the occurrences of events (i.e., time-series fluctuation). Inspired by this, we propose a novel graph neural network model, Evolutionary State Graph Network (EvoNet), to encode the evolutionary state graph for accurate and interpretable time-series event prediction. Specifically, Evolutionary State Graph Network models both the node-level (state-to-state) and graph-level (segment-to-segment) propagation, and captures the node-graph (state-to-segment) interactions over time. Experimental results based on five real-world datasets show that our approach not only achieves clear improvements compared with 11 baselines, but also provides more insights towards explaining the results of event predictions.

Knowledge graph (KG) embeddings learn low-dimensional representations of entities and relations to predict missing facts. KGs often exhibit hierarchical and logical patterns which must be preserved in the embedding space. For hierarchical data, hyperbolic embedding methods have shown promise for high-fidelity and parsimonious representations. However, existing hyperbolic embedding methods do not account for the rich logical patterns in KGs. In this work, we introduce a class of hyperbolic KG embedding models that simultaneously capture hierarchical and logical patterns. Our approach combines hyperbolic reflections and rotations with attention to model complex relational patterns. Experimental results on standard KG benchmarks show that our method improves over previous Euclidean- and hyperbolic-based efforts by up to 6.1% in mean reciprocal rank (MRR) in low dimensions. Furthermore, we observe that different geometric transformations capture different types of relations while attention-based transformations generalize to multiple relations. In high dimensions, our approach yields new state-of-the-art MRRs of 49.6% on WN18RR and 57.7% on YAGO3-10.

Knowledge graph completion aims to predict missing relations between entities in a knowledge graph. While many different methods have been proposed, there is a lack of a unifying framework that would lead to state-of-the-art results. Here we develop PathCon, a knowledge graph completion method that harnesses four novel insights to outperform existing methods. PathCon predicts relations between a pair of entities by: (1) Considering the Relational Context of each entity by capturing the relation types adjacent to the entity and modeled through a novel edge-based message passing scheme; (2) Considering the Relational Paths capturing all paths between the two entities; And, (3) adaptively integrating the Relational Context and Relational Path through a learnable attention mechanism. Importantly, (4) in contrast to conventional node-based representations, PathCon represents context and path only using the relation types, which makes it applicable in an inductive setting. Experimental results on knowledge graph benchmarks as well as our newly proposed dataset show that PathCon outperforms state-of-the-art knowledge graph completion methods by a large margin. Finally, PathCon is able to provide interpretable explanations by identifying relations that provide the context and paths that are important for a given predicted relation.

Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to handle different types of hypergraphs and are typically not generic for various learning tasks. Indeed, models that can predict variable-sized heterogeneous hyperedges have not been available. Here we develop a new self-attention based graph neural network called Hyper-SAGNN applicable to homogeneous and heterogeneous hypergraphs with variable hyperedge sizes. We perform extensive evaluations on multiple datasets, including four benchmark network datasets and two single-cell Hi-C datasets in genomics. We demonstrate that Hyper-SAGNN significantly outperforms the state-of-the-art methods on traditional tasks while also achieving great performance on a new task called outsider identification. Hyper-SAGNN will be useful for graph representation learning to uncover complex higher-order interactions in different applications.

Graphs, which describe pairwise relations between objects, are essential representations of many real-world data such as social networks. In recent years, graph neural networks, which extend the neural network models to graph data, have attracted increasing attention. Graph neural networks have been applied to advance many different graph related tasks such as reasoning dynamics of the physical system, graph classification, and node classification. Most of the existing graph neural network models have been designed for static graphs, while many real-world graphs are inherently dynamic. For example, social networks are naturally evolving as new users joining and new relations being created. Current graph neural network models cannot utilize the dynamic information in dynamic graphs. However, the dynamic information has been proven to enhance the performance of many graph analytical tasks such as community detection and link prediction. Hence, it is necessary to design dedicated graph neural networks for dynamic graphs. In this paper, we propose DGNN, a new {\bf D}ynamic {\bf G}raph {\bf N}eural {\bf N}etwork model, which can model the dynamic information as the graph evolving. In particular, the proposed framework can keep updating node information by capturing the sequential information of edges, the time intervals between edges and information propagation coherently. Experimental results on various dynamic graphs demonstrate the effectiveness of the proposed framework.

Graph-based semi-supervised learning (SSL) is an important learning problem where the goal is to assign labels to initially unlabeled nodes in a graph. Graph Convolutional Networks (GCNs) have recently been shown to be effective for graph-based SSL problems. GCNs inherently assume existence of pairwise relationships in the graph-structured data. However, in many real-world problems, relationships go beyond pairwise connections and hence are more complex. Hypergraphs provide a natural modeling tool to capture such complex relationships. In this work, we explore the use of GCNs for hypergraph-based SSL. In particular, we propose HyperGCN, an SSL method which uses a layer-wise propagation rule for convolutional neural networks operating directly on hypergraphs. To the best of our knowledge, this is the first principled adaptation of GCNs to hypergraphs. HyperGCN is able to encode both the hypergraph structure and hypernode features in an effective manner. Through detailed experimentation, we demonstrate HyperGCN's effectiveness at hypergraph-based SSL.

State-of-the-art recommendation algorithms -- especially the collaborative filtering (CF) based approaches with shallow or deep models -- usually work with various unstructured information sources for recommendation, such as textual reviews, visual images, and various implicit or explicit feedbacks. Though structured knowledge bases were considered in content-based approaches, they have been largely neglected recently due to the availability of vast amount of data, and the learning power of many complex models. However, structured knowledge bases exhibit unique advantages in personalized recommendation systems. When the explicit knowledge about users and items is considered for recommendation, the system could provide highly customized recommendations based on users' historical behaviors. A great challenge for using knowledge bases for recommendation is how to integrated large-scale structured and unstructured data, while taking advantage of collaborative filtering for highly accurate performance. Recent achievements on knowledge base embedding sheds light on this problem, which makes it possible to learn user and item representations while preserving the structure of their relationship with external knowledge. In this work, we propose to reason over knowledge base embeddings for personalized recommendation. Specifically, we propose a knowledge base representation learning approach to embed heterogeneous entities for recommendation. Experimental results on real-world dataset verified the superior performance of our approach compared with state-of-the-art baselines.