Directed Graph Research Articles

H3GNN: Hybrid Hierarchical HyperGraph Neural Network for Personalized Session-based Recommendation

Personalized Session-based recommendation (PSBR) is a general and challenging task in the real world, aiming to recommend a session’s next clicked item based on the session’s item transition information and the corresponding user’s historical sessions. A session is defined as a sequence of interacted items during a short period. The PSBR problem has a natural hierarchical architecture in which each session consists of a series of items, and each user owns a series of sessions. However, the existing PSBR methods can merely capture the pairwise relation information within items and users. To effectively capture the hierarchical information, we propose a novel hierarchical hypergraph neural network to model the hierarchical architecture. Moreover, considering that the items in sessions are sequentially ordered, while the hypergraph can only model the set relation, we propose a directed graph aggregator (DGA) to aggregate the sequential information from the directed global item graph. By attentively combining the embeddings of the above two modules, we propose a framework dubbed H3GNN (Hybrid Hierarchical HyperGraph Neural Network). Extensive experiments on three benchmark datasets demonstrate the superiority of our proposed model compared to the state-of-the-art methods, and ablation experiment results validate the effectiveness of all the proposed components.

Scaling up machine learning-based chemical plant simulation: A method for fine-tuning a model to induce stable fixed points

Idealized first-principles models of chemical plants can be inaccurate. An alternative is to fit a Machine Learning (ML) model directly to plant sensor data. We use a structured approach: Each unit within the plant gets represented by one ML model. After fitting the models to the data, the models are connected into a flowsheet-like directed graph. We find that for smaller plants, this approach works well, but for larger plants, the complex dynamics arising from large and nested cycles in the flowsheet lead to instabilities in the solver during model initialization. We show that a high accuracy of the single-unit models is not enough: The gradient can point in unexpected directions, which prevents the solver from converging to the correct stationary state. To address this problem, we present a way to fine-tune ML models such that initialization, even with very simple solvers, becomes robust.

OPTIMAL MODEL FOR EVALUATING THE TOTAL DURATION OF A BUSINESS PROCESS

When assessing the performance of business processes, it should be noted that one of the most important operational indicators and evaluation criteria of any company should be the indicator of the duration of the process completion cycle. Cycle duration is the amount of time that passes from the start of a task to the moment it is completed. Time is a critical metric for completing any task as it relates to customer satisfaction and the cost of completing that service. Based on this, the main goal of this work is to find the critical path of a business process and build a mathematical model to determine the objective function. To achieve the set goals, the problem of finding the maximum path in a directed graph constructed according to the list of works of the information system implementation project is considered. In accordance with the list of works, the relationships between them were determined, a network schedule for project planning was constructed, and the main relationships and patterns were identified. Studies of the constructed mathematical model were carried out using the MS Excel software application. The critical path of the business process of implementing an information system was found and conclusions were drawn on the total duration of the project. Thus, operations lying on the critical path require additional slack planning.

Spatio-Temporal-Attention-Based Vehicle Trajectory Prediction Considering Multi-Vehicle Interaction in Mixed Traffic Flow

As a link connecting the environmental perception system and the decision-making system, accurate obstacle trajectory prediction provides a reliable guarantee of correct decision-making by autonomous vehicles. Oriented toward a mixed human-driven and machine-driven traffic environment, a vehicle trajectory prediction algorithm based on an encoding–decoding framework composed of a multiple-attention mechanism is proposed. Firstly, a directed graph is used to describe vehicle–vehicle motion dependencies. Then, by calculating the repulsive force between vehicles using a priori edge information based on the artificial potential field theory, vehicle–vehicle interaction coefficients are extracted via a graph attention mechanism (GAT). Subsequently, after concatenating the vehicle–vehicle interaction feature with the encoded vehicle trajectory vectors, a spatio-temporal attention mechanism is applied to determine the coupling relationship of hidden vectors. Finally, the predicted trajectory is generated by a gated recurrent unit (GRU) decoder. The training and evaluation of the proposed model were conducted on the NGSIM public dataset. The test results demonstrated that compared with existing baseline models, our approach has fewer prediction errors and better robustness. In addition, introducing artificial potential fields into the attention mechanism causes the model to have better interpretability.

Spatio-temporal data prediction of multiple air pollutants in multi-cities based on 4D digraph convolutional neural network.

In response to the problem that current multi-city multi-pollutant prediction methods based on one-dimensional undirected graph neural network models cannot accurately reflect the two-dimensional spatial correlations and directedness, this study proposes a four-dimensional directed graph model that can capture the two-dimensional spatial directed information and node correlation information related to multiple factors, as well as extract temporal correlation information at different times. Firstly, A four-dimensional directed GCN model with directed information graph in two-dimensional space was established based on the geographical location of the city. Secondly, Spectral decomposition and tensor operations were then applied to the two-dimensional directed information graph to obtain the graph Fourier coefficients and graph Fourier basis. Thirdly, the graph filter of the four-dimensional directed GCN model was further improved and optimized. Finally, an LSTM network architecture was introduced to construct the four-dimensional directed GCN-LSTM model for synchronous extraction of spatio-temporal information and prediction of atmospheric pollutant concentrations. The study uses the 2020 atmospheric six-parameter data of the Taihu Lake city cluster and applies canonical correlation analysis to confirm the data's temporal, spatial, and multi-factor correlations. Through experimentation, it is verified that the proposed 4D-DGCN-LSTM model achieves a MAE reduction of 1.12%, 4.91%, 5.62%, and 11.67% compared with the 4D-DGCN, GCN-LSTM, GCN, and LSTM models, respectively, indicating the good performance of the 4D-DGCN-LSTM model in predicting multiple types of atmospheric pollutants in various cities.

Confidence in causal inference under structure uncertainty in linear causal models with equal variances

Abstract Inferring the effect of interventions within complex systems is a fundamental problem of statistics. A widely studied approach uses structural causal models that postulate noisy functional relations among a set of interacting variables. The underlying causal structure is then naturally represented by a directed graph whose edges indicate direct causal dependencies. In a recent line of work, additional assumptions on the causal models have been shown to render this causal graph identifiable from observational data alone. One example is the assumption of linear causal relations with equal error variances that we will take up in this work. When the graph structure is known, classical methods may be used for calculating estimates and confidence intervals for causal-effects. However, in many applications, expert knowledge that provides an a priori valid causal structure is not available. Lacking alternatives, a commonly used two-step approach first learns a graph and then treats the graph as known in inference. This, however, yields confidence intervals that are overly optimistic and fail to account for the data-driven model choice. We argue that to draw reliable conclusions, it is necessary to incorporate the remaining uncertainty about the underlying causal structure in confidence statements about causal-effects. To address this issue, we present a framework based on test inversion that allows us to give confidence regions for total causal-effects that capture both sources of uncertainty: causal structure and numerical size of non-zero effects.

CONSTRUCTION OF BICYCLIC GRAPH AND ITS APPLICATION IN TRANS JOGJA ROUTES

A bicyclic graph is a type of graph that consists of exactly two cycles. A cycle is a graph that is a closed path where no vertices are repeated except the first and last vertices which are the same. The cycles in bicyclic graph can be of different lengths and shapes, but they must have at least one common vertex. Bicyclic graphs can be divided into two categories based on the types of induced subgraphs they contain. One category consists of graphs that include an -graph as an induced subgraph, while the other category comprises graphs that contain a -graph as an induced subgraph. There are 3 types of bicyclic graph without pendant vertex. A directed graph, also referred to as a digraph, is a graph in which each edge is assigned a specific direction. A directed bicyclic graph is a special kind of directed graph that contains precisely two distinct directed cycles. This graph can be applied in transportation problem. In this article, we give some examples of directed bicyclic graph in Trans Jogja routes.

An algorithmic characterization and spectral analysis of canonical splitting signed graph ξ(Σ)

An ordered pair Σ=(Σu,σ) is called the signed graph, where Σu=(V,E) is an underlying graph and σ is a signed mapping, called signature, from E to the sign set {+,−}. A marking of Σ is a function μ:V(Σ)→{+,−}. The canonical marking of a signed graph Σ, denoted μσ, is given asμσ(v)=Πvu∈E(Σ)σ(vu).The canonical splitting signed graphξ(Σ) of a signed graph Σ is defined as a signed graph ξ(Σ)=(V(ξ),E(ξ)) , with V(ξ)=V(Σ)∪V′, where V′is copy of a vertex set in V(Σ) s.t. for each vertex u∈V(Σ), take a new vertex u′ and E(ξ) is defined as, join u′ to all the vertices of Σ adjacent to u by negative edge if μσ(u)=μσ(v)=−, where v∈N(u) and by positive edge otherwise. The objective of this paper is to propose an algorithm for the generation of a canonical splitting signed graph, a splitting root signed graph from a given signed graph, provided it exists and to give the characterization of balanced canonical splitting signed graph. Additionally, we conduct a spectral analysis of the resulting graph. Spectral analysis is performed on the adjacency and Laplacian matrices of the canonical splitting signed graph to study its eigenvalues and eigenvectors. A relationship between the energy of the original signed graph Σ and the energy of the canonical splitting signed graph ξ(Σ) is established.•Algorithm to generate canonical splitting signed graph ξ(Σ).•Spectral Analysis is performed for both adjacency and Laplacian matrices of canonical splitting signed graph ξ(Σ).

Parallel path detection for fraudulent accounts in banks based on graph analysis.

This article presents a novel parallel path detection algorithm for identifying suspicious fraudulent accounts in large-scale banking transaction graphs. The proposed algorithm is based on a three-step approach that involves constructing a directed graph, shrinking strongly connected components, and using a parallel depth-first search algorithm to mark potentially fraudulent accounts. The algorithm is designed to fully exploit CPU resources and handle large-scale graphs with exponential growth. The performance of the algorithm is evaluated on various datasets and compared with serial time baselines. The results demonstrate that our approach achieves high performance and scalability on multi-core processors, making it a promising solution for detecting suspicious accounts and preventing money laundering schemes in the banking industry. Overall, our work contributes to the ongoing efforts to combat financial fraud and promote financial stability in the banking sector.

Stable fixed points of combinatorial threshold-linear networks

Combinatorial threshold-linear networks (CTLNs) are a special class of recurrent neural networks whose dynamics are tightly controlled by an underlying directed graph. Recurrent networks have long been used as models for associative memory and pattern completion, with stable fixed points playing the role of stored memory patterns in the network. In prior work, we showed that target-free cliques of the graph correspond to stable fixed points of the dynamics, and we conjectured that these are the only stable fixed points possible [19,8]. In this paper, we prove that the conjecture holds in a variety of special cases, including for networks with very strong inhibition and graphs of size n≤4. We also provide further evidence for the conjecture by showing that sparse graphs and graphs that are nearly cliques can never support stable fixed points. Finally, we translate some results from extremal combinatorics to obtain an upper bound on the number of stable fixed points of CTLNs in cases where the conjecture holds.

The Complexity Landscape of Fixed-Parameter Directed Steiner Network Problems

Given a directed graph G and a list ( s 1 , t 1 ), …, ( s d , t d ) of terminal pairs, the Directed Steiner Network problem asks for a minimum-cost subgraph of G that contains a directed s i → t i path for every 1≤ i ≤ d . The special case Directed Steiner Tree (when we ask for paths from a root r to terminals t 1 , …, t d ) is known to be fixed-parameter tractable parameterized by the number of terminals, while the special case Strongly Connected Steiner Subgraph (when we ask for a path from every t i to every other t j ) is known to be W[1]-hard parameterized by the number of terminals. We systematically explore the complexity landscape of directed Steiner problems to fully understand which other special cases are FPT or W[1]-hard. Formally, if ℋ is a class of directed graphs, then we look at the special case of Directed Steiner Network where the list ( s 1 , t 1 ), …, ( s d , t d ) of demands form a directed graph that is a member of ℋ. Our main result is a complete characterization of the classes ℋ resulting in fixed-parameter tractable special cases: we show that if every pattern in ℋ has the combinatorial property of being “transitively equivalent to a bounded-length caterpillar with a bounded number of extra edges,” then the problem is FPT, and it is W[1]-hard for every recursively enumerable ℋ not having this property. This complete dichotomy unifies and generalizes the known results showing that Directed Steiner Tree is FPT [Dreyfus and Wagner, Networks 1971], q -Root Steiner Tree is FPT for constant q [Suchý, WG 2016], Strongly Connected Steiner Subgraph is W[1]-hard [Guo et al., SIAM J. Discrete Math. 2011], and Directed Steiner Network is solvable in polynomial-time for constant number of terminals [Feldman and Ruhl, SIAM J. Comput. 2006], and moreover reveals a large continent of tractable cases that were not known before.

Decentralized Asynchronous Nonconvex Stochastic Optimization on Directed Graphs

We consider a decentralized stochastic optimization problem over a network of agents, modeled as a directed graph: Agents aim to asynchronously minimize the average of their individual losses (possibly non-convex), each one having access only to a noisy estimate of the gradient of its own function. We propose an asynchronous distributed algorithm for such a class of problems. The algorithm combines stochastic gradients with tracking in an asynchronous push-sum framework and obtains a sublinear convergence rate, matching the rate of the centralized stochastic gradient descent applied to the nonconvex minimization. Our experiments on a non-convex image classification task using convolutional neural network validate the convergence of our proposed algorithm across different number of nodes and graph connectivity percentages.

Optimal Synchronization for Multiagent Systems Under Directed Graphs by Scalable Distributed Event-Triggered Control

Optimal Synchronization for Multiagent Systems Under Directed Graphs by Scalable Distributed Event-Triggered Control

An Incremental Gradient Method for Optimization Problems With Variational Inequality Constraints

We consider minimizing a sum of agent-specific nondifferentiable merely convex functions over the solution set of a variational inequality (VI) problem in that each agent is associated with a local monotone mapping. This problem finds an application in computation of the best equilibrium in nonlinear complementarity problems arising in transportation networks. We develop an iteratively regularized incremental gradient method where at each iteration, agents communicate over a directed cycle graph to update their solution iterates using their local information about the objective and the mapping. The proposed method is single-timescale in the sense that it does not involve any excessive hard-to-project computation per iteration. We derive non-asymptotic agent-wise convergence rates for the suboptimality of the global objective function and infeasibility of the VI constraints measured by a suitably defined dual gap function. The proposed method appears to be the first fully iterative scheme equipped with iteration complexity that can address distributed optimization problems with VI constraints over cycle graphs.

Nash Equilibrium Seeking for Multicluster Games of Multiple Nonidentical Euler–Lagrange Systems

The problem of seeking Nash equilibrium in multicluster games is studied. Different from the existing multi-cluster game studies, the participants considered in this paper have Euler-Lagrange (EL) dynamics and cannot directly obtain the information of non-neighbor participants. Agents can only communicate through directed communication graphs. In addition, there are coupling constraints between agent decisions in the same cluster. Under the widely used assumptions, two distributed algorithms are proposed to solve the Nash equilibrium (NE) of the multi-cluster game based on gradient descent, state feedback, and consensus protocol. The convergence of the two algorithms is analyzed by singular perturbation analysis and variational analysis. The theoretical results show that the first algorithm achieves exponential convergence when the parameters are certain, while the other algorithm also achieves global asymptotic convergence when the parameters are uncertain. Finally, the effectiveness of the search strategy is verified by numerical examples.

Push–Pull With Device Sampling

We consider decentralized optimization problems in which a number of agents collaborate to minimize the average of their local functions by exchanging over an underlying communication graph. Specifically, we place ourselves in an asynchronous model where only a random portion of nodes perform computation at each iteration, while the information exchange can be conducted between all the nodes and in an asymmetric fashion. For this setting, we propose an algorithm that combines gradient tracking with a network-level variance reduction (in contrast to variance reduction within each node). This enables the nodes to track the average of the gradients of the objective functions. Our theoretical analysis shows that the algorithm converges linearly, when the local objective functions are strongly convex, under mild connectivity conditions on the expected mixing matrices. In particular, our result does not require the mixing matrices to be doubly stochastic. In the experiments, we investigate a broadcast mechanism that transmits information from computing nodes to their neighbors, and confirm the linear convergence of our method on both synthetic and real-world datasets.

A Stochastic Binary Vertex-Triggering Resetting Algorithm for Global Synchronization of Pulse-Coupled Oscillators

In this paper, we propose a novel stochastic binary resetting algorithm for networks of pulse-coupled oscillators (or, simply, agents) to reach global synchronization. The algorithm is simple to state: Every agent in a network oscillates at a common frequency. Upon completing an oscillation, an agent generates a Bernoulli random variable to decide whether it sends pulses to all of its out-neighbours or it stays quiet. Upon receiving a pulse, an agent resets its state by following a binary phase update rule. We show that such an algorithm can guarantee <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">global</i> synchronization of the agents almost surely as long as the underlying information flow topology is a rooted directed graph. The proof of the result relies on the use of a stochastic hybrid dynamical system approach. Toward the end of the paper, we present numerical demonstrations for the validity of the result and, also, numerical studies about the units of time needed to reach synchronization for networks with various information flow topologies.

SOZIL: Self-Optimal Zero-Shot Imitation Learning

Zero-shot imitation learning has demonstrated its superiority to learn complex robotic tasks with less human participation. Recent studies show convincing performance under the condition that the robot follows the demonstration strictly by the learned inverse model. However, these methods are difficult to achieve satisfactory performance in imitation when the demonstration is suboptimal, and the learning of the learned inverse models is vulnerable to label ambiguity issues. In this paper, we propose Self-Optimal Zero-shot Imitation Learning (SOZIL) to tackle these problems. The contribution of SOZIL is twofold. First, Goal Consistency Loss (GCL) is designed to learn the multi-step goal-conditioned policy from exploration data. By directly using the goal state as supervision, GCL solves the label ambiguity problem caused by trajectory and action diversity. Second, Estimation-based Keyframe Extraction (EKE) is developed to optimize demonstrations. We formulate the keyframe extraction process as a path optimization problem under suboptimal control. By predicting the performance of the learned policy in executing transitions of any two states, EKE creates a directed graph containing all candidate paths and extracts keyframes by solving the graph’s shortest path problem. Furthermore, the proposed method is evaluated with various simulated and real-world robotic manipulating experiments such as cable harness assembly, rope manipulation, and block moving. Experimental results show that SOZIL achieves a superior success rate and manipulation efficiency than baselines.

DEVELOPMENT OF A FUZZY COGNITIVE MAP MODEL FOR CREATING STEM PROJECTS IN PROFESSIONAL TRAINING OF FUTURE SPECIALISTS IN ENGINEERING AND PEDAGOGICAL SPECIALTIES

The article examines the issues of STEM education development in the context of the strategy for the development of higher education in Ukraine for 2022-2032. In particular, the emphasis is on the importance of reorienting the educational process to the training of specialists in engineering and pedagogical specialties with practical skills and up-to-date knowledge. It is necessary to strategically rethink educational approaches, giving priority to the training of specialists in engineering and pedagogical specialties who possess not only theoretical knowledge, but also specific practical skills that meet the requirements of the labor market. Special attention is paid to STEM education, which is defined as a key tool in the formation of competencies for future specialists in the field of engineering and pedagogy. This approach involves not only the transfer of theoretical knowledge, but also emphasizes practical aspects, contributing to the development of specific skills and abilities that are necessary in practice. Dedication to STEM education in the context of engineering and pedagogical fields allows future specialists to be ready for the challenges and tasks presented to them by modern labor markets, and to meet the current requirements and standards in these fields. The technical orientation of STEM projects contributes to the implementation of practical tasks and the formation of skills in demand on the labor market. The purpose of the article is to present the algorithm for building a lighting control system prototype using the example of the STEM project “Lighting control system in the library”. For building a logical model, to justify the structure of the system, the NCC is used. The development of the STEM project “Lighting control system in the library” is presented, which involves the creation of a fuzzy cognitive map in the Mental Modeler environment. An algorithm for building a logical model for a STEM project under conditions of uncertainty has been developed and described. The basis of the built model is a cognitive map. A cognitive map is a symbolic directed graph, at the vertices of which the key factors of the object of modeling (concepts) connected by cause-and-effect relationships are placed. A cognitive map is a type of mathematical modeling used to formalize a complex system in the form of a set of concepts that reflect system factors and causal relationships between them, taking into account the nature of their interaction. Based on the analysis of the logical model of the system, it was determined that for each concept it is necessary to set the level of communication on the visual form of the Mental Modeler map, which allows you to set the level of assessment of its dependence. The paper presents a logical model on the example of a prototype of a computer lighting control system in a library using fuzzy logical derivation. Fuzzy cognitive maps were used to justify the structure of the management system. The sequence of building a prototype of the lighting control system in the library and the analysis of the parameters of such a system can be used by students of engineering and pedagogical specialties for the educational purpose of building various STEM projects. Cognitive modeling methodology is used for analysis and decision-making in conditions of uncertainty. It is developing in the direction of improving the situation analysis and modeling apparatus. Therefore, to implement a STEM project in ill-defined situations, it is advisable to build a logical model. It defines the structure of the modeled system. The basis for building this model is a fuzzy cognitive map.

Fault diagnosis-based SDG transfer for zero-sample fault symptom

The traditional fault diagnosis models cannot achieve good fault diagnosis accuracy when a new unseen fault class appears in the test set, but there is no training sample of this fault in the training set. Therefore, studying the unseen cause-effect problem of fault symptoms is extremely challenging. As various faults often occur in a chemical plant, it is necessary to perform fault causal-effect diagnosis to find the root cause of the fault. However, only some fault causal-effect data are always available to construct a reliable causal-effect diagnosis model. Another worst thing is that measurement noise often contaminates the collected data. The above problems are very common in industrial operations. However, past-developed data-driven approaches rarely include causal-effect relationships between variables, particularly in the zero-shot of causal-effect relationships. This would cause incorrect inference of seen faults and make it impossible to predict unseen faults. This study effectively combines zero-shot learning, conditional variational autoencoders (CVAE), and the signed directed graph (SDG) to solve the above problems. Specifically, the learning approach that determines the cause-effect of all the faults using SDG with physics knowledge to obtain the fault description. SDG is used to determine the attributes of the seen and unseen faults. Instead of the seen fault label space, attributes can easily create an unseen fault space from a seen fault space. After having the corresponding attribute spaces of the failure cause, some failure causes are learned in advance by a CVAE model from the available fault data. The advantage of the CVAE is that process variables are mapped into the latent space for dimension reduction and measurement noise deduction; the latent data can more accurately represent the actual behavior of the process. Then, with the extended space spanned by unseen attributes, the migration capabilities can predict the unseen causes of failure and infer the causes of the unseen failures. Finally, the feasibility of the proposed method is verified by the data collected from chemical reaction processes.