Hierarchy Graph Research Articles

Research on Entity Label Value Assignment Method in Knowledge Graph

The lack of entity label values is one of the problems faced by the application of Knowledge Graph. The method of automatically assigning entity label values still has shortcomings, such as costing more resources during training, leading to inaccurate label value assignment because of lacking entity semantics. In this paper, oriented to domain-specific Knowledge Graph, based on the situation that the initial entity label values of all triples are completely unknown, an Entity Label Value Assignment Method (ELVAM) based on external resources and entropy is proposed. ELVAM first constructs a Relationship Triples Cluster according to the relationship type, and randomly extracts the triples data from each cluster to form a Relationship Triples Subset; then collects the extended semantic text of the entities in the subset from the external resources to obtain nouns. Information Entropy and Conditional Entropy of the nouns are calculated through Ontology Category Hierarchy Graph, so as to obtain the entity label value with moderate granularity. Finally, the Label Triples Pattern of each Relationship Triples Cluster is summarized, and the corresponding entity is assigned the label value according to the pattern. The experimental results verify the effectiveness of ELVAM in assigning entity label values in Knowledge Graph.

The concept of hierarchy of algebras and graphs

This paper deals with the concept of hierarchy of algebras and graphs. In the case of algebras, the work constitutes a generalization to any algebra of the concept of hierarchy that Tian gave for a particular type of them, evolution algebras, via concepts of occurrence and persistence. This new hierarchy proves to be invariant under isomorphism of algebras, which leads to a necessary condition for two generic algebras to be isomorphic. Furthermore, the task of how to effectively obtain the hierarchy of an algebra is also discussed, arriving to the association of a certain type of graphs to generic algebras, which leads us to introduce new concepts, based in hierarchy, in graph theory.

Reversibility and Composition of Rewriting in Hierarchies

In this paper, we study how graph transformations based on sesqui-pushout rewriting can be reversed and how the composition of rewrites can be constructed. We illustrate how such reversibility and composition can be used to design an audit trail system for individual graphs and graph hierarchies. This provides us with a compact way to maintain the history of updates of an object, including its multiple versions. The main application of the designed framework is an audit trail of updates to knowledge represented by hierarchies of graphs. Therefore, we introduce the notion of rule hierarchy that represents a transformation of the entire hierarchy, study how rule hierarchies can be applied to hierarchies and analyse the conditions under which this application is reversible. We then present a theory for constructing the composition of consecutive hierarchy rewrites. The prototype audit trail system for transformations in hierarchies of simple graphs with attributes is implemented as part of the ReGraph Python library.

The Maximum Colorful Arborescence problem: How (computationally) hard can it be?

Given a vertex-colored arc-weighted directed acyclic graph G, the Maximum Colorful Subtree problem (or MCS) aims at finding an arborescence of maximum weight in G, in which no color appears more than once. The problem was originally introduced in [1] in the context of de novo identification of metabolites by tandem mass spectrometry. However, a thorough analysis of the initial motivation shows that the formal definition of MCS should be amended, since the input graph G actually possesses extra properties, which have been unexploited so far. This leads us to describe in this paper a more precise model that we call Maximum Colorful Arborescence (MCA), which we extensively study in terms of algorithmic complexity. In particular, we show that exploiting the implied Color Hierarchy Graph of the input graph G can lead to exact polynomial algorithms and approximation algorithms. We also develop Fixed-Parameter Tractable (FPT) algorithms for the problem parameterized by the “dual parameter” ℓC, defined as the minimum number of vertices of G which are not kept in the solution.

Hierarchy Graph Convolution Network and Tree Classification for Epileptic Detection on Electroencephalography Signals

The epileptic detection with electroencephalography (EEG) has been deeply studied and developed. However, previous research gave little attention to the physical appearance and early onset warnings of seizure. When a seizure occurs, electrodes near the epileptic foci will exhibit significantly fluctuating and inconsistent voltages. In this article, a novel approach to epileptic detection based on the hierarchy graph convolution network (HGCN) structure is proposed. Multiple features of time or frequency domains extracted from the raw EEG signals are taken as the input of HGCN. The topological relationship between every single electrode is utilized by HGCN. The tree classification (TC) and preictal fuzzification (PF) are proposed to adapt both multiclassification tasks and refine-classification tasks. Experiments are performed on the CHB-MIT and TUH data sets. Compared with the state of the art, our proposed model achieves a 5.77% improvement of accuracy on the CHB-MIT data set, and an improvement of 2.43% and 19.7% for sensitivity and specificity on the TUH data set, respectively.

Knowledge representation and update in hierarchies of graphs

A mathematical theory is presented for the representation of knowledge in the form of a directed acyclic hierarchy of objects in a category where all paths between any given pair of objects are required to be equal. The conditions under which knowledge update, in the form of the sesqui-pushout rewriting of an object in a hierarchy, can be propagated to the rest of the hierarchy, in order to maintain all required path equalities, are analysed: some rewrites must be propagated forwards, in the direction of the arrows, while others must be propagated backwards, against the direction of the arrows, and, depending on the precise form of the hierarchy, certain composability conditions may also be necessary. The implementation of this theory, in the ReGraph Python library for (simple) directed graphs with attributes on nodes and edges, is then discussed in the context of two significant use cases.

Identifying multiple line-structured lights from images via a local-to-global graph representation.

Identifying multiple line-structured lights from an image is a fundamental yet challenging issue in the active 3D visual reconstruction. The existing approaches using complex coding schemes are typically time-consuming and inapplicable to real-time sparse 3D reconstruction. In this paper, we solve the multi-line ambiguity from a new viewpoint-distribution pattern of the light segments in the image. We construct a local-to-global graph framework to fully describe the hierarchical distribution of multiple line-structured lights in a 2D image. The lights are firstly grouped as several local graphs according to a light overlapping metric. Then, the hierarchies of the local graphs are unified via the depth of the node, leading to a global graph. The lights in the same level of the global graph come from the same laser plane. The experimental results show the applicability of the proposed algorithm to identify scattered light segments and the robustness to varying sensor poses. We further apply the proposed algorithm to a 3D reconstruction case, achieving a reconstruction precision of 0.025mm. The proposed approach avoids complex auxiliary laser coding and thus is more convenient to conduct.

Simplifying TugGraph using zipping algorithms

Graphs are an invaluable modelling tool in many domains, but visualising large graphs in their entirety can be difficult. Hierarchical graph visualisation – recursively clustering a graph’s nodes to view it at a higher level of abstraction – has thus become popular. However, this can hide important information that a user needs to understand a graph’s topology, e.g. nodes’ neighbourhoods. TugGraph addressed this by ‘separating out’ a given node’s neighbours from their hierarchy ancestors to visualise them independently. Its original implementation was straightforward, but copied parts of the hierarchy, making it slow and memory-hungry. An optimised later version, which we refer to as FastTug, avoided this, but at a cost in clarity. Optimising TugGraph without sacrificing clarity is difficult because of the need to keep every hierarchy node connected, a common challenge for graph hierarchy editing algorithms. Recently, this problem has been addressed by ‘zipping’ algorithms, multi-level split/merge algorithms that preserve hierarchy node connectedness and can be built upon for higher-level editing. In this paper, we generalise the original unzipping algorithms to implement SimpleTug, a simple, modular version of TugGraph that is easy to understand and implement, and even faster and more memory-efficient than FastTug. We formally prove its equivalence to FastTug, and show how both can be parallelised. Using our millipede hierarchical image segmentation system, we show experimentally that both the serial and parallel versions of SimpleTug are around 25% faster than their FastTug counterparts, whilst using considerably less memory. Finally, we discuss the interesting theoretical connections between TugGraph and zipping, and suggest ideas for further work.

Pragmatic Aspects of Discourse Production for the Automatic Identification of Alzheimer's Disease

Clinical literature provides convincing evidence that language deficits in Alzheimer's disease (AD) allow for distinguishing patients with dementia from healthy subjects. Currently, computational approaches have widely investigated lexicosemantic aspects of discourse production, while pragmatic aspects like cohesion and coherence, are still mostly unexplored. In this article, we aim at providing a more comprehensive characterization of language abilities for the automatic identification of AD in narrative description tasks by also incorporating pragmatic aspects of speech production. To this end, we investigate the relevance of a recently proposed set of pragmatic features extracted from an automatically generated topic hierarchy graph in combination with a complementary set of state-of-the-art features encoding lexical, syntactic and semantic cues. Experimental results on the DementiaBank corpus show an accuracy improvement from 82.6% to 85.5% in identifying AD patients when pragmatic features are incorporated to the set of lexicosemantic features. Nevertheless, these results are obtained relying on manual transcriptions, which strongly limits the applicability of computational analysis to clinical settings. Thus, in this work we additionally carry out an analysis of the errors introduced by a speech recognition system and the way in which they impact the performance of the proposed method. In spite of the high word error rates obtained on these data (∼40%), automatic AD identification accuracy decreased only to 79.7%, which is considered a remarkable result when compared with solutions based on manual transcriptions.

A Novel Approach for Business Process Similarity Measure Based on Role Relation Network Mining

Existing business process similarity measure methods mainly focus on the control-flow (e.g., the activity and process model). However, the active factors of business processes, i.e., the roles that execute activities and organizations to which activities belong, have yet received enough attention. Roles are the subject of activities, many changes of process can be summarized as the management of roles and their relationship. In many cases, measuring process similarity from role perspective help find similarities and differences between processes and measure business process similarity more in a comprehensive way. This paper starts from activities and roles, and measures process similarity by constructing two role relation models. One is the Role Relation Network (RRN) that is defined based on the work delivery relation among roles, and the other is the Role Hierarchy Relation Network (RHRN) that is based on the role relation network and the role hierarchy graph. Then, we propose the corresponding business process similarity measure method. The proposed methods extend the applicability of existing process similarity measure methods to a larger application domain. Finally, experiments are designed to demonstrate the effectiveness of the proposed methods.

DEPTH FIRST SEARCH (DFS) UNTUK MENENTUKAN DIAMETER GRAF HIRARKI

Let G = (V, E) be a graph. The distance d (u, v) between two vertices u and v is the length of the shortest path between them. The diameter of the graph is the length of the longest path of the shortest paths between any two graph vertices (u ,v) of a graph, . In this paper we propose algorithms for finding diameter of a hierarchy graph using DFS. Diameter of the hierarchy graph using DFS algoritm is four.

Hierarchical stochastic graphlet embedding for graph-based pattern recognition

Despite being very successful within the pattern recognition and machine learning community, graph-based methods are often unusable because of the lack of mathematical operations defined in graph domain. Graph embedding, which maps graphs to a vectorial space, has been proposed as a way to tackle these difficulties enabling the use of standard machine learning techniques. However, it is well known that graph embedding functions usually suffer from the loss of structural information. In this paper, we consider the hierarchical structure of a graph as a way to mitigate this loss of information. The hierarchical structure is constructed by topologically clustering the graph nodes and considering each cluster as a node in the upper hierarchical level. Once this hierarchical structure is constructed, we consider several configurations to define the mapping into a vector space given a classical graph embedding, in particular, we propose to make use of the stochastic graphlet embedding (SGE). Broadly speaking, SGE produces a distribution of uniformly sampled low-to-high-order graphlets as a way to embed graphs into the vector space. In what follows, the coarse-to-fine structure of a graph hierarchy and the statistics fetched by the SGE complements each other and includes important structural information with varied contexts. Altogether, these two techniques substantially cope with the usual information loss involved in graph embedding techniques, obtaining a more robust graph representation. This fact has been corroborated through a detailed experimental evaluation on various benchmark graph datasets, where we outperform the state-of-the-art methods.

Globally Optimal State-Feedback LQG Control for Large-Scale Systems With Communication Delays and Correlated Subsystem Process Noises

This paper studies the optimal decentralized state-feedback control of large-scale systems. The large-scale system is composed of subsystems and defined over a connected digraph. One step time is required for information to travel across an edge in the graph. Under the above-mentioned setup, when subsystem process noises are uncorrelated, the explicit optimal state-feedback controller can be designed by independence decomposition based on information hierarchy graph. However, this decomposition method fails when the subsystem process noises are correlated. In this paper, we propose a new decomposition method for system state and control input, and split the optimal state-feedback control problem with correlated process noises into two subproblems that can be solved separately. The solution to the first subproblem can be obtained by solving a linear matrix equation. The second subproblem is solved by algebraic Ricatti equation.

Fracking and metaphor: Analysing newspaper discourse in the USA, Australia and the United Kingdom

We apply a mixed-method design centred on the deployment of metaphors to explore the role that language plays in the structuring of the public discourses of unconventional hydrocarbon development (UHD) across three major developed economies. We analyse UHD-related metaphorical devices deployed in broadsheet newspapers in Australia, the UK and the USA between January 2006 and May 2018. We develop an innovative Type Hierarchy Approach to metaphors by mapping through directed graph hierarchies. These allow concept-mapping analysis in terms of supertypes and subtypes, i.e. concepts ordered in terms of generality and inclusion as in “rapid expansion” → “explosion”. We find two broad discourses, each containing metaphorical constructions: economic gain across temporal horizons (incorporating boom, bonanza, revolution and death metaphors); and risk tolerance and decision-making (incorporating gamble and insanity metaphors). At the level of individual metaphors, deployment trends and patterns can be mapped along country borders rather than for example political alignment. Boom and bonanza appear most widespread in the USA, whereas UHD as a revolution is more closely associated with UK newspapers. Over time, UHD-related metaphor use decreases in all three countries, potentially reflecting an increasing public acceptance of UHD and moving shale gas from unconventional to conventional hydrocarbon development.

ATP: Directed Graph Embedding with Asymmetric Transitivity Preservation

Directed graphs have been widely used in Community Question Answering services (CQAs) to model asymmetric relationships among different types of nodes in CQA graphs, e.g., question, answer, user. Asymmetric transitivity is an essential property of directed graphs, since it can play an important role in downstream graph inference and analysis. Question difficulty and user expertise follow the characteristic of asymmetric transitivity. Maintaining such properties, while reducing the graph to a lower dimensional vector embedding space, has been the focus of much recent research. In this paper, we tackle the challenge of directed graph embedding with asymmetric transitivity preservation and then leverage the proposed embedding method to solve a fundamental task in CQAs: how to appropriately route and assign newly posted questions to users with the suitable expertise and interest in CQAs. The technique incorporates graph hierarchy and reachability information naturally by relying on a nonlinear transformation that operates on the core reachability and implicit hierarchy within such graphs. Subsequently, the methodology levers a factorization-based approach to generate two embedding vectors for each node within the graph, to capture the asymmetric transitivity. Extensive experiments show that our framework consistently and significantly outperforms the state-of-the-art baselines on three diverse realworld tasks: link prediction, and question difficulty estimation and expert finding in online forums like Stack Exchange. Particularly, our framework can support inductive embedding learning for newly posted questions (unseen nodes during training), and therefore can properly route and assign these kinds of questions to experts in CQAs.

Geometry of Matrix Polynomial Spaces

We study how small perturbations of general matrix polynomials may change their elementary divisors and minimal indices by constructing the closure hierarchy (stratification) graphs of matrix polynomials’ orbits and bundles. To solve this problem, we construct the stratification graphs for the first companion Fiedler linearization of matrix polynomials. Recall that the first companion Fiedler linearization as well as all the Fiedler linearizations is matrix pencils with particular block structures. Moreover, we show that the stratification graphs do not depend on the choice of Fiedler linearization which means that all the spaces of the matrix polynomial Fiedler linearizations have the same geometry (topology). This geometry coincides with the geometry of the space of matrix polynomials. The novel results are illustrated by examples using the software tool StratiGraph extended with associated new functionality.

Hierarchy Graph Based Barrier Coverage Strategy with a Minimum Number of Sensors for Underwater Sensor Networks.

Underwater sensor networks based barrier coverage is increasingly important for intrusion detection due to the scarcity of underwater sensor resource. To improve UWSNs’ detection performance and prolong their lifetime, an efficient barrier coverage strategy is very important. In this paper, a novel concept: hierarchy graph is proposed. Hierarchy graph can make the network’s topology more clarity. In accordance with the hierarchy graph, 1-barrier coverage algorithm and k-barrier coverage algorithm are presented to construct the barrier with less sensors for higher energy efficiency. Both analytical and simulation studies demonstrate that the proposed algorithms can provide high detection probability and long lifetime for UWSNs.

Hierarchy Visualization for Group Recommender Systems

Most recommender systems (RSs), especially group RSs, focus on methods and accuracy but lack explanations, hence users find them difficult to trust. We present a hierarchy visualization method for group recommender (HVGR) systems to provide visual presentation and intuitive explanation. We first use a hierarchy graph to organize all the entities using nodes (e.g., neighbor nodes and recommendation nodes) and illustrate the overall recommender process using edges. Second, a pie chart is attached to every entity node in which each slice represents a single member, which makes it easy to track the influence of each member on a specific entity. HVGR can be extended to adapt different pseudouser modeling methods by resizing group member nodes and pseudouser nodes. It can also be easily extended to individual RSs through the use of a single member group. An implementation has been developed and feasibility is tested using a real data set.

Multi-scale detection of hierarchical community architecture in structural and functional brain networks.

Community detection algorithms have been widely used to study the organization of complex networks like the brain. These techniques provide a partition of brain regions (or nodes) into clusters (or communities), where nodes within a community are densely interconnected with one another. In their simplest application, community detection algorithms are agnostic to the presence of community hierarchies: clusters embedded within clusters of other clusters. To address this limitation, we exercise a multi-scale extension of a common community detection technique, and we apply the tool to synthetic graphs and to graphs derived from human neuroimaging data, including structural and functional imaging data. Our multi-scale community detection algorithm links a graph to copies of itself across neighboring topological scales, thereby becoming sensitive to conserved community organization across levels of the hierarchy. We demonstrate that this method is sensitive to topological inhomogeneities of the graph’s hierarchy by providing a local measure of community stability and inter-scale reliability across topological scales. We compare the brain’s structural and functional network architectures, and we demonstrate that structural graphs display a more prominent hierarchical community organization than functional graphs. Finally, we build an explicitly multimodal multiplex graph that combines both structural and functional connectivity in a single model, and we identify the topological scales where resting state functional connectivity and underlying structural connectivity show similar versus unique hierarchical community architecture. Together, our results demonstrate the advantages of the multi-scale community detection algorithm in studying hierarchical community structure in brain graphs, and they illustrate its utility in modeling multimodal neuroimaging data.

$D$-Stratification and Hierarchy Graphs of the Space of Order 2 and 3 Matrix Pencils

Small changes in the entries of a matrix pencil may lead to important changes in its Kronecker normal form. Studies about the effect of small perturbations have been made when considering the stratification associated with the strict equivalence between matrix pencils. In this work, we consider a partition in the space of pairs of matrices associated to regular matrix pencils, which will be proved to be a finite stratification of the space of such matrix pencils, called D-stratification. Matrix pencils in the same strata are those having some prescribed Segre indices. We study the effect of perturbations which lead to changes in the Kronecker canonical form, preserving the order of the nilpotent part. Our goal is to determine which $D$-strata can be reached. In the cases where the order of the matrix pencils is 2 or 3, we obtain the corresponding hierarchy graphs, illustrating the $D$-strata that can be reached when applying some small perturbations.