Hierarchical graph contrastive learning with diffusion-enhanced for multi-behavior recommendation

Convex drawings of hierarchical planar graphs and clustered planar graphs

Algebraic hierarchical graph transformation

Hierarchical random graph representation of handwritten characters and its application to Hangul recognition

The fault diagnosis of the tail-drive of helicopter is a crucial task for helicopter system operation and maintenance. Recently, graph convolution network (GCN) has been the focus in fault diagnosis for its powerful representational ability in relationship mining. However, with the difficulty of obtaining node and edge information in the high-order domain, the stable performance of the long-range message-passing process of the deep GCN is unknown limits the application of GCN in fault diagnosis. To address these issues, a multi-grained hierarchical message graph convolutional network (MHGCN) is proposed to diagnose faults of helicopter tail-drive system. First, time-frequency characteristics of the original vibration signals are extracted to construct the graph nodes. The original graph nodes are aggregated by Louvain community detection, which can effectively learn the multi-grained features. Then, the hierarchical graph is introduced to learn the features of high-order neighbourhoods. Finally, a particular message-passing method is used to encode long-range information spanning the graph structure and realise accurate classification. Experiments on a test rig of helicopter tail-drive system are performed to verify the efficacy of the proposed method.

Existing object re-identification methods usually utilize backbone networks developed based on classification tasks to obtain the final object features. However, these backbone networks lack a unique mechanism to explore discriminative feature representation and handle rich scale changes. For that, a novel hierarchical similarity graph module (HSGM) is proposed to relieve the conflict of backbone networks and mine the discriminative features. Specifically, the proposed HSGM constructs a rich hierarchical graph to explore the pairwise relationships among global-local and local-local. Then, in each hierarchical graph, the HSGM regards local features extracted from different locations as nodes and utilizes the similarity scores between nodes to construct a similarity graph. During the HSGM's propagation, a learnable parameter is reweighted at each spatial position to optimize the correlation between adjacent nodes. Besides, the HSGM can be readily inserted into backbone networks at any depth to improve object discrimination. Extensive experiments on two large-scale object datasets (i.e., VeRi776 and Market-1501) demonstrate that the proposed HSGM is superior to state-of-the-art object re-identification approaches.

In this paper, we investigate the problem of facial kinship verification by learning hierarchical reasoning graph networks. Conventional methods usually focus on learning discriminative features for each facial image of a paired sample and neglect how to fuse the obtained two facial image features and reason about the relations between them. To address this, we propose a Star-shaped Reasoning Graph Network (S-RGN). Our S-RGN first constructs a star-shaped graph where each surrounding node encodes the information of comparisons in a feature dimension and the central node is employed as the bridge for the interaction of surrounding nodes. Then we perform relational reasoning on this star graph with iterative message passing. The proposed S-RGN uses only one central node to analyze and process information from all surrounding nodes, which limits its reasoning capacity. We further develop a Hierarchical Reasoning Graph Network (H-RGN) to exploit more powerful and flexible capacity. More specifically, our H-RGN introduces a set of latent reasoning nodes and constructs a hierarchical graph with them. Then bottom-up comparative information abstraction and top-down comprehensive signal propagation are iteratively performed on the hierarchical graph to update the node features. Extensive experimental results on four widely used kinship databases show that the proposed methods achieve very competitive results.

We study the algebraic decay of the survival probability in open hierarchical graphs. We present a model of a persistent random walk on a hierarchical graph and study the spectral properties of the Frobenius–Perron operator. Using a perturbative scheme, we derive the exponent of the classical algebraic decay in terms of two parameters of the model. One parameter defines the geometrical relation between the length scales on the graph, and the other relates to the probabilities for the random walker to go from one level of the hierarchy to another. The scattering resonances of the corresponding hierarchical quantum graphs are also studied. The width distribution shows the scaling behavior P(Γ)∼1/Γ.

Accurate prediction of molecular properties is crucial for selecting compounds with ideal properties and reducing the costs and risks of trials. Traditional methods based on manually crafted features and graph-based methods have shown promising results in molecular property prediction. However, traditional methods rely on expert knowledge and often fail to capture the complex structures and interactions within molecules. Similarly, graph-based methods typically overlook the chemical structure and function hidden in molecular motifs and struggle to effectively integrate global and local molecular information. To address these limitations, we propose a novel fingerprint-enhanced hierarchical graph neural network (FH-GNN) for molecular property prediction that simultaneously learns information from hierarchical molecular graphs and fingerprints. The FH-GNN captures diverse hierarchical chemical information by applying directed message-passing neural networks (D-MPNN) on a hierarchical molecular graph that integrates atomic-level, motif-level, and graph-level information along with their relationships. Additionally, we used an adaptive attention mechanism to balance the importance of hierarchical graphs and fingerprint features, creating a comprehensive molecular embedding that integrated hierarchical molecular structures with domain knowledge. Experiments on eight benchmark datasets from MoleculeNet showed that FH-GNN outperformed the baseline models in both classification and regression tasks for molecular property prediction, validating its capability to comprehensively capture molecular information. By integrating molecular structure and chemical knowledge, FH-GNN provides a powerful tool for the accurate prediction of molecular properties and aids in the discovery of potential drug candidates.

Hierarchical graphs are used in order to describe systems with a sequential composition of sub-systems. A hierarchical graph consists of a vector of subgraphs. Vertices in a subgraph may “call” other subgraphs. The reuse of subgraphs, possibly in a nested way, causes hierarchical graphs to be exponentially more succinct than equivalent flat graphs. Early research on hierarchical graphs and the computational price of their succinctness suggests that there is no strong correlation between the complexity of problems when applied to flat graphs and their complexity in the hierarchical setting. That is, the complexity in the hierarchical setting is higher, but all “jumps” in complexity up to an exponential one are exhibited, including no jumps in some problems. We continue the study of the complexity of algorithms for hierarchical graphs, with the following contributions: (1) In many applications, the subgraphs have a small, often a constant, number of exit vertices, namely vertices from which control returns to the calling subgraph. We offer a parameterized analysis of the complexity and point to problems where the complexity becomes lower when the number of exit vertices is bounded by a constant. (2) We describe a general methodology for algorithms on hierarchical graphs. The methodology is based on an iterative compression of subgraphs in a way that maintains the solution to the problems and results in subgraphs whose size depends only on the number of exit vertices, and (3) we handle labeled hierarchical graphs, where edges are labeled by letters from some alphabet, and the problems refer to the languages of the graphs.

Hierarchical graphs were invented to formalize heuristic Migdal–Kadanoff renormalization arguments. In such graphs, certain characteristic patterns (motifs) appear as construction elements. Real-world complex networks may also contain such patterns. Itzkovitz and Alon in 2005 Phys. Rev. E 71, selected five most typical motifs, which include the triangle. In 2011 Condens. Matter. Phys. 14, Kotorowicz and Kozitsky introduced and described hierarchical random graphs in which these five motifs appear at each hierarchy level. In the present work, we study the equilibrium states of the Ising spin model living on the graph of this kind based on the triangle. The main result is the description of annealed phase transitions in this model. In particular, we show that—depending on the parameters—the model may be in an unordered or ordered states at all temperatures, as well as to have a critical point. The key aspect of our theory is detecting the appearance of an ordered state by the non-ergodicity of a certain nonhomogeneous Markov chain.

In this article, we present a novel hierarchical bidirected graph convolution network (HiBi-GCN) for large-scale 3-D point cloud place recognition. Unlike place recognition methods based on 2-D images, those based on 3-D point cloud data are typically robust to substantial changes in real-world environments. However, these methods have difficulty in defining convolution for point cloud data to extract informative features. To solve this problem, we propose a new hierarchical kernel defined as a hierarchical graph structure through unsupervised clustering from the data. In particular, we pool hierarchical graphs from the fine to coarse direction using pooling edges and fuse the pooled graphs from the coarse to fine direction using fusing edges. The proposed method can, thus, learn representative features hierarchically and probabilistically; moreover, it can extract discriminative and informative global descriptors for place recognition. Experimental results demonstrate that the proposed hierarchical graph structure is more suitable for point clouds to represent real-world 3-D scenes.

Fashion outfit recommendation has attracted increasing attentions from online shopping services and fashion communities.Distinct from other scenarios (e.g., social networking or content sharing) which recommend a single item (e.g., a friend or picture) to a user, outfit recommendation predicts user preference on a set of well-matched fashion items.Hence, performing high-quality personalized outfit recommendation should satisfy two requirements -- 1) the nice compatibility of fashion items and 2) the consistence with user preference. However, present works focus mainly on one of the requirements and only consider either user-outfit or outfit-item relationships, thereby easily leading to suboptimal representations and limiting the performance. In this work, we unify two tasks, fashion compatibility modeling and personalized outfit recommendation. Towards this end, we develop a new framework, Hierarchical Fashion Graph Network(HFGN), to model relationships among users, items, and outfits simultaneously. In particular, we construct a hierarchical structure upon user-outfit interactions and outfit-item mappings. We then get inspirations from recent graph neural networks, and employ the embedding propagation on such hierarchical graph, so as to aggregate item information into an outfit representation, and then refine a user's representation via his/her historical outfits. Furthermore, we jointly train these two tasks to optimize these representations. To demonstrate the effectiveness of HFGN, we conduct extensive experiments on a benchmark dataset, and HFGN achieves significant improvements over the state-of-the-art compatibility matching models like NGNN and outfit recommenders like FHN.

Protein-protein interactions regulate the dynamic operation of intracellular molecular networks, serving as the molecular basis for revealing protein functions and disease mechanisms. Recently, several computational methods for predicting protein-protein interaction sites (PPIs) have been presented as alternatives to costly and labor-intensive traditional experiments. However, existing methods generally ignore the inherent hierarchical structure of protein chains. Furthermore, the equivariance of graph structure during spatial transformations is often neglected when applying graph neural networks to modeling. Therefore, accurately identifying PPIs remains a challenging task. In this work, we propose an end-to-end GNN-based computational method, EGCPPIS, for efficiently identifying protein-protein interaction sites. First, we construct a hierarchical graph representation of the protein chain, including residue-level graph and atom-level graph. Next, EGCPPIS designs an E(n) Equivariant Graph Neural Network (EGNN) module to learn residue-level embeddings with equivariant features. After further extracting atom-level embeddings using the GraphSAGE module, we introduce the contrastive learning strategy to integrate hierarchical graph features. This strategy enables us to learn consistent embeddings between residue-level and atom-level representations. Finally, the fused embeddings are weighted using an improved gated multi-head attention mechanism. Comprehensive evaluation results on multiple datasets demonstrate that EGCPPIS significantly outperforms state-of-the-art methods. Extensive comparative experiments and case studies further confirm that EGCPPIS can reveal the decision-making patterns in PPIs prediction, facilitating the discovery of potential PPIs. The original datasets and code of EGCPPIS are available at https://github.com/GuicongSun/EGCPPIS.

Node classification and graph classification are two graph learning problems that predict the class label of a node and the class label of a graph respectively. A node of a graph usually represents a real-world entity, e.g., a user in a social network, or a document in a document citation network. In this work, we consider a more challenging but practically useful setting, in which a node itself is a graph instance. This leads to a hierarchical graph perspective which arises in many domains such as social network, biological network and document collection. We study the node classification problem in the hierarchical graph where a "node" is a graph instance. As labels are usually limited, we design a novel semi-supervised solution named SEAL-CI. SEAL-CI adopts an iterative framework that takes turns to update two modules, one working at the graph instance level and the other at the hierarchical graph level. To enforce a consistency among different levels of hierarchical graph, we propose the Hierarchical Graph Mutual Information (HGMI) and further present a way to compute HGMI with theoretical guarantee. We demonstrate the effectiveness of this hierarchical graph modeling and the proposed SEAL-CI method on text and social network data.

In the formal approach to reactive controller synthesis, a symbolic controller for a possibly hybrid system is obtained by algorithmically computing a winning strategy in a two-player game. Such game-solving algorithms scale poorly as the size of the game graph increases. However, in many applications, the game graph has a natural hierarchical structure. In this paper, we propose a modeling formalism and a synthesis algorithm that exploits this hierarchical structure for more scalable synthesis. We define local games on hierarchical graphs as a modeling formalism that decomposes a large-scale reactive synthesis problem in two dimensions. First, the construction of a hierarchical game graph introduces abstraction layers, where each layer is again a two-player game graph. Second, every such layer is decomposed into multiple local game graphs, each corresponding to a node in the higher level game graph. While local games have the potential to reduce the state space for controller synthesis, they lead to more complex synthesis problems where strategies computed for one local game can impose additional requirements on lower-level local games. Our second contribution is a procedure to construct a dynamic controller for local game graphs over hierarchies. The controller computes assume-admissible winning strategies that satisfy local specifications in the presence of environment assumptions, and dynamically updates specifications and strategies due to interactions between games at different abstraction layers at each step of the play. We show that our synthesis procedure is sound: the controller constructs a play that satisfies all local specifications. We illustrate our results through an example controlling an autonomous robot in a building with known floor plan and provide simulation results using an implementation of our algorithm on top of LTLMoP.