Hierarchy Graph Research Articles

SUBGROUPS: a computer tool at the Bilbao Crystallographic Server for the study of pseudo-symmetric or distorted structures.

SUBGROUPS is a free online program at the Bilbao Crystallographic Server (https://www.cryst.ehu.es/). It permits the exploration of all possible symmetries resulting from the distortion of a higher-symmetry parent structure, provided that the relation between the lattices of the distorted and parent structures is known. The program calculates all the subgroups of the parent space group which comply with this relation. The required minimal input is the space-group information of the parent structure and the relation of the unit cell of the distorted or pseudo-symmetric structure with that of the parent structure. Alternatively, the wavevector(s) observed in the diffraction data characterizing the distortion can be introduced. Additional conditions can be added, including filters related to space-group representations. The program provides very detailed information on all the subgroups, including group-subgroup hierarchy graphs. If a Crystallographic Information Framework (CIF) file of the parent high-symmetry structure is uploaded, the program generates CIF files of the parent structure described under each of the chosen lower symmetries. These CIF files may then be used as starting points for the refinement of the distorted structure under these possible symmetries. They can also be used for density functional theory calculations or for any other type of analysis. The power and efficiency of the program are illustrated with a few examples.

Hierarchical Graph Neural Network: A Lightweight Image Matching Model with Enhanced Message Passing of Local and Global Information in Hierarchical Graph Neural Networks

Graph Neural Networks (GNNs) have gained popularity in image matching methods, proving useful for various computer vision tasks like Structure from Motion (SfM) and 3D reconstruction. A well-known example is SuperGlue. Lightweight variants, such as LightGlue, have been developed with a focus on stacking fewer GNN layers compared to SuperGlue. This paper proposes the h-GNN, a lightweight image matching model, with improvements in the two processing modules, the GNN and matching modules. After image features are detected and described as keypoint nodes of a base graph, the GNN module, which primarily aims at increasing the h-GNN’s depth, creates successive hierarchies of compressed-size graphs from the base graph through a clustering technique termed SC+PCA. SC+PCA combines Principal Component Analysis (PCA) with Spectral Clustering (SC) to enrich nodes with local and global information during graph clustering. A dual non-contrastive clustering loss is used to optimize graph clustering. Additionally, four message-passing mechanisms have been proposed to only update node representations within a graph cluster at the same hierarchical level or to update node representations across graph clusters at different hierarchical levels. The matching module performs iterative pairwise matching on the enriched node representations to obtain a scoring matrix. This matrix comprises scores indicating potential correct matches between the image keypoint nodes. The score matrix is refined with a ‘dustbin’ to further suppress unmatched features. There is a reprojection loss used to optimize keypoint match positions. The Sinkhorn algorithm generates a final partial assignment from the refined score matrix. Experimental results demonstrate the performance of the proposed h-GNN against competing state-of-the-art (SOTA) GNN-based methods on several image matching tasks under homography, estimation, indoor and outdoor camera pose estimation, and 3D reconstruction on multiple datasets. Experiments also demonstrate improved computational memory and runtime, approximately 38.1% and 26.14% lower than SuperGlue, and an average of about 6.8% and 7.1% lower than LightGlue. Future research will explore the effects of integrating more recent simplicial message-passing mechanisms, which concurrently update both node and edge representations, into our proposed model.

Unsupervised mapping and semantic user localisation from first-person monocular video

We propose an unsupervised probabilistic framework for learning a human-centred representation of a person’s environment from first-person video. Specifically, non-geometric maps modelled as hierarchies of probabilistic place graphs and view graphs are learned. Place graphs model a user’s patterns of transition between physical locations whereas view graphs capture an aspect of user behaviour within those locations. Furthermore, we describe an implementation in which the notion of place is divided into stations and the routes that interconnect them. Stations typically correspond to rooms or areas where a user spends time. Visits to stations are temporally segmented based on qualitative visual motion. We describe how to learn maps online in an unsupervised manner, and how to localise the user within these maps. We report experiments on two datasets, including comparison of performance with and without view graphs, and demonstrate better online mapping than when using offline clustering.

MPASL: multi-perspective learning knowledge graph attention network for synthetic lethality prediction in human cancer.

Synthetic lethality (SL) is widely used to discover the anti-cancer drug targets. However, the identification of SL interactions through wet experiments is costly and inefficient. Hence, the development of efficient and high-accuracy computational methods for SL interactions prediction is of great significance. In this study, we propose MPASL, a multi-perspective learning knowledge graph attention network to enhance synthetic lethality prediction. MPASL utilizes knowledge graph hierarchy propagation to explore multi-source neighbor nodes related to genes. The knowledge graph ripple propagation expands gene representations through existing gene SL preference sets. MPASL can learn the gene representations from both gene-entity perspective and entity-entity perspective. Specifically, based on the aggregation method, we learn to obtain gene-oriented entity embeddings. Then, the gene representations are refined by comparing the various layer-wise neighborhood features of entities using the discrepancy contrastive technique. Finally, the learned gene representation is applied in SL prediction. Experimental results demonstrated that MPASL outperforms several state-of-the-art methods. Additionally, case studies have validated the effectiveness of MPASL in identifying SL interactions between genes.

Identifiability of Hierarchical Latent Attribute Models

Hierarchical Latent Attribute Models (HLAMs) are a family of discrete latent variable models that are attracting increasing attention in educational, psychological, and behavioral sciences. The key ingredients of an HLAM include a binary structural matrix and a directed acyclic graph specifying hierarchical constraints on the configurations of latent attributes. These components encode practitioners' design information and carry important scientific meanings. Despite the popularity of HLAMs, the fundamental identifiability issue remains unaddressed. The existence of the attribute hierarchy graph leads to degenerate parameter space, and the potentially unknown structural matrix further complicates the identifiability problem. This paper addresses this issue of identifying the latent structure and model parameters underlying an HLAM. We develop sufficient and necessary identifiability conditions. These results directly and sharply characterize the different impacts on identifiability cast by different attribute types in the graph. The proposed conditions not only provide insights into diagnostic test designs under the attribute hierarchy, but also serve as tools to assess the validity of an estimated HLAM.

Identification of vortex in unstructured mesh with graph neural networks

Deep learning has been employed to identify flow characteristics from Computational Fluid Dynamics (CFD) databases to assist the researcher to better understand the flow field, to optimize the geometry design and to select the correct CFD configuration for corresponding flow characteristics. Convolutional Neural Network (CNN) is one of the most popular algorithms used to extract and identify flow features. However its use, without any additional flow field interpolation, is limited to the simple domain geometry and regular meshes which limits its application to real industrial cases where complex geometry and irregular meshes are usually used. Aiming at the aforementioned problems, we present a Graph Neural Network (GNN) based model with U-Net architecture to identify the vortex in CFD results on unstructured meshes. The graph generation and graph hierarchy construction using algebraic multigrid method from CFD meshes are introduced. A vortex auto-labeling method is proposed to label vortex regions in 2D CFD meshes. We precise our approach by firstly optimizing the input set on CNNs, then benchmarking current GNN kernels against CNN model and evaluating the performances of GNN kernels in terms of classification accuracy, training efficiency and identified vortex morphology. Finally, we demonstrate the adaptability of our approach to unstructured meshes and generality to unseen cases with different turbulence models at different Reynolds numbers.

Task-driven cleaning and pruning of noisy knowledge graph

Many knowledge graphs, especially those that are collaboratively or automatically generated, are prone to noise and cross-domain entries, which can impede domain-specific applications. Existing methods for pruning inaccurate or out-of-domain information from knowledge graphs often rely on topological graph-pruning strategies. However, these approaches have two major drawbacks: they may discard logical structure and semantic information, and they allow multiple inheritance. To address these limitations, this study introduces KGPruning, which is a novel approach that can effectively clean and prune noisy knowledge graphs by guiding tasks with a given set of concepts and automatically generating a domain-specific taxonomy. Specifically, KGPruning employs a graph hierarchy inference method that is based on the Agony model to precisely identify and eliminate noisy entries while striving to preserve the underlying hierarchy of semantic relations as much as possible. Furthermore, to establish a tree-structured taxonomy, KGPruning integrates semantic relations and structural characteristics to effectively eliminate out-of-domain information and multiple inheritance. Through extensive experimental evaluations conducted on open benchmark datasets as well as large-scale real-world problems, the superior performance of KGPruning over state-of-the-art methods is demonstrated on the task of pruning noisy knowledge graphs.

A graph neural network-based framework to identify flow phenomena on unstructured meshes

Driven by the abundant data generated from computational fluid dynamics (CFD) simulations, machine learning (ML) methods surpass the deterministic criteria on flow phenomena identification in the way that they are independent of a case-by-case threshold by combining the flow field properties and the topological distribution of the phenomena. The current most popular and successful ML models based on convolutional neural networks are limited to structured meshes and unable to directly digest the data generated from unstructured meshes, which are more widely used in real industrial CFD simulations. We proposed a framework based on graph neural networks with the proposed fast Gaussian mixture model as the convolution kernel and U-Net architecture to detect flow phenomena based on a graph hierarchy generated by the algebraic multigrid method embedded in the open-source CFD solver, code_saturne. We demonstrate the superiority of the proposed kernel and U-Net architecture, along with the generality of the framework to unstructured mesh and unseen case, on detecting the vortices once trained on a single backward-facing step case. Our proposed framework can be trivially extended to detect more flow phenomena in three dimensional cases, which is ongoing work.

TANGO: A GO-Term Embedding Based Method for Protein Semantic Similarity Prediction.

We aim to quantitatively predict protein semantic similarities (PSS), which is vital to making biological discoveries. Previously, researchers commonly exploited Gene Ontology (GO) graphs (containing standardized hierarchically-organized GO terms for annotating distinct protein attributes) to learn GO term embeddings (vector representations) for quantifying protein attribute similarities and aggregate these embeddings to form protein embeddings for similarity measurement. However, two key properties of GO terms and annotated proteins are not yet well-explored by these learning-based methods: (1) taxonomy relations between GO terms; (2) GO terms' different contributions in describing protein semantics. In this paper, we propose TANGO, a new framework composed of a TAxoNomy-aware embedding module and an aggreGatiOn module. Our Embedding Module encodes taxonomic information into GO term embeddings by incorporating GO term topological distances in the GO graph hierarchy. Hence, distances between GO term embeddings can be used to more accurately measure shared meanings between correlated protein attributes. Our Aggregation Module automatically determines the contributions of GO terms when merging into the target protein embeddings, by mining GO term concept dependency relations in the GO graph and correlations in protein annotations. We conduct extensive experiments on several public datasets. On two PSS metrics, our new method significantly outperforms known methods by a large margin.

NI-UDA: Graph Contrastive Domain Adaptation for Nonshared-and-Imbalanced Unsupervised Domain Adaptation

With the technology development, information networks continuously generate a large amount of integrated labeled Big Data. Some types of labeled data in real scenes are scarce and difficult to obtain, such as some aerospace data. It is important to address the problem of nonshared and imbalanced unsupervised domain adaptation (NI-UDA) from the labeled Big Data with nonshared and long-tail distribution to unlabeled specified small and imbalanced space applications, where nonshared classes mean the label space out of the target domain. Previous methods proposed to integrate the semantic knowledge of Big Data to help the unsupervised domain adaptation for sparse data. However, they have the challenges of limited effect of knowledge sharing for long-tail Big Data and the imbalanced domain adaptation. To solve them, our goal is to leverage priori hierarchy knowledge to enhance domain contrastive aligned feature representation with graph reasoning. Our method consists of hierarchy graph reasoning (HGR) layer and K-positive contrastive domain adaptation (K-CDA). Our HGR contributes to learn direct semantic patterns for sparse classes by hierarchy attention in self-attention, nonlinear mapping, and graph normalization. For alleviating imbalanced domain adaptation, we proposed K-CDA, which explores k-positive instances for each class to every mini-batch with contrastive learning to align imbalanced feature representations. Compared with the previous contrastive UDA, our K-CDA alleviates the problems of large memory consumption and high computational cost. Experiments on three benchmark datasets shows our methods consistently improve the state-of-the-art contrastive UDA algorithms.

On the Hamiltonian Property Hierarchy of 3-Connected Planar Graphs

The prism over a graph $G$ is the Cartesian product of $G$ with the complete graph $K_2$. The graph $G$ is prism-hamiltonian if the prism over $G$ has a Hamilton cycle. A good even cactus is a connected graph in which every block is either an edge or an even cycle and every vertex is contained in at most two blocks. It is known that good even cacti are prism-hamiltonian. Indeed, showing the existence of a spanning good even cactus has become the most common technique in proving prism-hamiltonicity. Špacapan [S. Špacapan. A counterexample to prism-hamiltonicity of 3-connected planar graphs. J. Combin. Theory Ser. B, 146:364--371, 2021] asked whether having a spanning good even cactus is equivalent to having a hamiltonian prism for 3-connected planar graphs. In this article we answer his question in the negative, by showing that there are infinitely many 3-connected planar prism-hamiltonian graphs that have no spanning good even cactus. In addition, we prove the existence of an infinite class of 3-connected planar graphs that have a spanning good even cactus but no spanning good even cactus with maximum degree three.

Video as Conditional Graph Hierarchy for Multi-Granular Question Answering

Video question answering requires the models to understand and reason about both the complex video and language data to correctly derive the answers. Existing efforts have been focused on designing sophisticated cross-modal interactions to fuse the information from two modalities, while encoding the video and question holistically as frame and word sequences. Despite their success, these methods are essentially revolving around the sequential nature of video- and question-contents, providing little insight to the problem of question-answering and lacking interpretability as well. In this work, we argue that while video is presented in frame sequence, the visual elements (e.g., objects, actions, activities and events) are not sequential but rather hierarchical in semantic space. To align with the multi-granular essence of linguistic concepts in language queries, we propose to model video as a conditional graph hierarchy which weaves together visual facts of different granularity in a level-wise manner, with the guidance of corresponding textual cues. Despite the simplicity, our extensive experiments demonstrate the superiority of such conditional hierarchical graph architecture, with clear performance improvements over prior methods and also better generalization across different type of questions. Further analyses also demonstrate the model's reliability as it shows meaningful visual-textual evidences for the predicted answers.

A Noise History Decomposition Approach for Decentralized Optimal Control of Large-Scale Systems Defined Over a Weakly Connected Graph

This article investigates the decentralized optimal linear quadratic regulation (LQR) control for large-scale systems. The large-scale system is defined over a weakly connected graph. Assume that the information is transmitted along the edges in the graph, and one sampling period is required for the information to travel across an edge. Under the above setup, the LQR control problem for the strongly connected graph case has been fully solved. However, for the weakly connected graph case, the existing results fail. In this article, a new decomposition approach for noise history is proposed. Then, the LQR control problem of large-scale systems defined over a weakly connected graph can be well solved. In addition, the decentralized realization of the control input is derived based on the decentralized information hierarchy graph (DIHG). The DIHG construction algorithm is also provided. Finally, the effectiveness of the developed design scheme is illustrated by a numerical example.

Post-hoc recommendation explanations through an efficient exploitation of the DBpedia category hierarchy

Leveraging knowledge graphs for post-hoc recommendation explanations has been investigated in recent years. Existing approaches rely mainly on the overlap properties (encoded by knowledge graphs) that characterize both user liked items and the recommended ones. These approaches, however, do not fully leverage the property hierarchy of knowledge graphs which may lead to flawed explanations. In this paper we introduce an approach that takes the whole property hierarchy into account. This is done with a limited computation time overhead thanks to efficient algorithmic optimizations relying on sub-ontology extraction. The hierarchical relationships among properties are also considered to avoid redundant properties for explanation. We carried out a user study of 155 participants in the movie recommendation domain and used both offline and online metrics to assess the proposed approach. Significant improvements, in terms of informativeness (by 39%), persuasiveness (by 22%), engagement (by 29%) and user trust (by 26%), are suggested by the obtained results, as compared to the state-of-the-art property-based explanation model. Our findings indicate the superiority of accounting for the whole property hierarchy when dealing with post-hoc recommendation explanations.

Knowledge embedding via hyperbolic skipped graph convolutional networks

With the aim of constructing a low-dimensional representation space, Hyperbolic Knowledge Embeddings have gradually become a hot spot in various information retrieval and machine learning tasks. However, most of the existing Hyperbolic knowledge embedding methods focus on the shallow embedding, and often ignore the network structure characteristics (e.g., hierarchy) of Knowledge Graphs. Therefore, this paper designs a novel Hyperbolic Skipped Knowledge Graph Convolutional Network, HSKGCN, to improve link prediction accuracy with low embedding dimension requirements. Firstly, the model is designed based on the hyperbolic geometric operations on the Poincaré ball, which can effectively utilize the characteristics of the hyperbolic geometry (e.g., Poincaré ball) to capture the hierarchy of Knowledge Graphs; Secondly, each single-layer convolutional layer introduces the feature aggregation weight, which ensures the reasonable distribution of node features during the aggregation process; In addition, the skip-connection mechanism is applied to HSKGCN to weaken the information loss caused by the stacked of the graph convolutional layers; Finally, we evaluate HSKGCN on benchmark datasets, WN18RR and FB15k-237. Experiments show that HSKGCN achieves substantial improvements against state-of-the-art models on the 32-dimensional embedding task, and the results of different relations on WN18RR show graphs similar with tree topology can performer better.

Multi-criteria linear optimization classifier with semantically weighted kernels for Chinese word formation pattern prediction

For many classification methods, different features in these classification models are usually organized into a flat and equal-length vector while semantically restrictive relations or nonparallel structures among them are often ignored. However, sometimes the semantic relations or structures among different attributes derived from the domain knowledge are very important, for instance, natural language processing and biological data mining, which can help to increase the performance of classification models considerably. For Chinese semantic word formation analysis with the large-scale Chinese corpus, the feature set is horizontally composed of different morpheme types, semantic types and part of speech (POS) while it vertically consists of three levels of big, medium and small classes. If a classifier model does not consider these relations or structures, then it can lead to information loss and distortion, and the degenerated classifier model can be ultimately obtained. In this paper, in view of the aforementioned limitations, by defining a new conceptual hierarchy graph, the semantic weights of different features are obtained, then semantically weighted kernels are formulated and introduced to multi-criteria linear optimization classifier (MCLOC). Thus, a new semantically weighted MCLOC (SW-MCLOC) using the linear and radius basic function (RBF) kernels is proposed and applied to Chinese word formation pattern prediction. The experimental results and comparison among MCLOC, SVM and SW-MCLOC show that our proposed model can effectively increase the separation of different word formation patterns, the predictive accuracy of target patterns and the generalization power of pattern classification on new compound words.

Extended Hierarchical Fuzzy Interpreted Petri Net.

Petri nets (PNs) have many advantages such as graphical representation, formal description, and the possibility of sequential and concurrent control. An important aspect of using PNs is hierarchical modeling, which may be provided in different ways. In this paper, a new concept and definition of the hierarchical structure for Fuzzy Interpreted Petri Net (FIPN) are proposed. The concept of macroplace with several input, output, and input-output places is introduced to the net. The functionality of the macroplace instances and the hierarchy graph are also proposed. They are implemented in a computer simulator called HFIPN-SML. In this study, FIPN is employed since it allows the use of analogue sensors directly for process control. Better visualization and more precise control are among advantages of the introduced approach.

Graph hierarchy: a novel framework to analyse hierarchical structures in complex networks

Trophic coherence, a measure of a graph’s hierarchical organisation, has been shown to be linked to a graph’s structural and dynamical aspects such as cyclicity, stability and normality. Trophic levels of vertices can reveal their functional properties, partition and rank the vertices accordingly. Trophic levels and hence trophic coherence can only be defined on graphs with basal vertices, i.e. vertices with zero in-degree. Consequently, trophic analysis of graphs had been restricted until now. In this paper we introduce a hierarchical framework which can be defined on any simple graph. Within this general framework, we develop several metrics: hierarchical levels, a generalisation of the notion of trophic levels, influence centrality, a measure of a vertex’s ability to influence dynamics, and democracy coefficient, a measure of overall feedback in the system. We discuss how our generalisation relates to previous attempts and what new insights are illuminated on the topological and dynamical aspects of graphs. Finally, we show how the hierarchical structure of a network relates to the incidence rate in a SIS epidemic model and the economic insights we can gain through it.

Distributivity relations on the binary operations over a fixed set

In recent years, the word magma has been used to designate a pair of the form where * is a binary operation on the set S. Inspired by that terminology, we use the notation and terminology (the magma of S) to denote the set of all binary operations on the set S (i.e. the set of all magmas with underlying set S.) We study distributivity relations among magmas in the context of a hierarchy graph having as vertices and edges occurring precisely when an operation distributes over another one. The graph theoretic imagery and terminology serve to motivate questions in an intuitive way and to express their solutions in a reasonable fashion. While most considerations are done in general for arbitrary sets, particular emphasis is placed frequently on the case when the archetypal set with n elements. In that case, parameters such as cardinalities of outsets and insets, fully connected subsets, and longest cycle-free paths are explored.

Hierarchical Graph Capsule Network

Graph Neural Networks (GNNs) draw their strength from explicitly modeling the topological information of structured data. However, existing GNNs suffer from limited capability in capturing the hierarchical graph representation which plays an important role in graph classification. In this paper, we innovatively propose hierarchical graph capsule network (HGCN) that can jointly learn node embeddings and extract graph hierarchies. Specifically, disentangled graph capsules are established by identifying heterogeneous factors underlying each node, such that their instantiation parameters represent different properties of the same entity. To learn the hierarchical representation, HGCN characterizes the part-whole relationship between lower-level capsules (part) and higher-level capsules (whole) by explicitly considering the structure information among the parts. Experimental studies demonstrate the effectiveness of HGCN and the contribution of each component. Code: https://github.com/uta-smile/HGCN